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<meta name="description" content="这是 Deep Q Networks（DQN）的 PyTorch 实现/教程，来自论文《用深度强化学习玩雅达利》。这包括决斗网络架构、优先重播缓冲区和 Double-Q-Network 训练。"/>
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<a href='#section-0'>#</a>
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<h1>深度 Q 网络 (DQN)</h1>
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<p>这是 <a href="https://pytorch.org">PyTorch</a> 实现的 PyTorch <a href="https://arxiv.org/abs/1312.5602">使用深度强化学习玩雅</a>达利以及<a href="model.html">决斗网络</a>、<a href="replay_buffer.html">优先回放</a>和 Double Q Network。</p>
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<p>这是<a href="experiment.html">实验</a>和<a href="model.html">模型</a>实现。</p>
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<p><a href="https://colab.research.google.com/github/labmlai/annotated_deep_learning_paper_implementations/blob/master/labml_nn/rl/dqn/experiment.ipynb"><img alt="Open In Colab" src="https://colab.research.google.com/assets/colab-badge.svg"></a></p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">24</span><span></span><span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Tuple</span>
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<span class="lineno">25</span>
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<span class="lineno">26</span><span class="kn">import</span> <span class="nn">torch</span>
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<span class="lineno">27</span><span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">nn</span>
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<span class="lineno">28</span>
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<span class="lineno">29</span><span class="kn">from</span> <span class="nn">labml</span> <span class="kn">import</span> <span class="n">tracker</span>
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<span class="lineno">30</span><span class="kn">from</span> <span class="nn">labml_helpers.module</span> <span class="kn">import</span> <span class="n">Module</span>
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<span class="lineno">31</span><span class="kn">from</span> <span class="nn">labml_nn.rl.dqn.replay_buffer</span> <span class="kn">import</span> <span class="n">ReplayBuffer</span></pre></div>
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<div class='section' id='section-1'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-1'>#</a>
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</div>
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<h2>训练模型</h2>
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<p>我们想找到最佳的动作值函数。</p>
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<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:4.34398em;vertical-align:-1.92199em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.42199em;"><span style="top:-4.42199em;"><span class="pstrut" style="height:3.15em;"></span><span class="mord"><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord mathnormal" style="">Q</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.738696em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">s</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="mclose">)</span></span></span><span style="top:-2.2719899999999997em;"><span class="pstrut" style="height:3.15em;"></span><span class="mord"><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord mathnormal" style="">Q</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.738696em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">s</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="mclose">)</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.92199em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.42199em;"><span style="top:-4.47199em;"><span class="pstrut" style="height:3.2em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.43056em;"><span style="top:-2.4em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">π</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">max</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.7em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathbb">E</span><span class="mord"><span class="delimsizing size2">[</span></span><span class="mord"><span class="mord coloredeq eqt" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal" style="margin-right:0.05556em;">γ</span><span class="mord"><span class="mord coloredeq eqt" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05556em;">γ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord"><span class="mord coloredeq eqt" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">...∣</span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathnormal">s</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="mord"><span class="delimsizing size2">]</span></span></span></span><span style="top:-2.3219900000000004em;"><span class="pstrut" style="height:3.2em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mop"><span class="mop mathbb" style="position:relative;top:0.094445em;">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-3.028128em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:3.2em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqq" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mrel mtight">∼</span><span class="mspace mtight" style="margin-right:0.3252777777777778em;"></span><span class="mord sizing reset-size3 size7"><span class="mord mathnormal">ε</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.17187200000000002em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing size2">[</span></span><span class="mord coloredeq eqt" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal" style="margin-right:0.05556em;">γ</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.43055999999999983em;"><span style="top:-2.35602em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">max</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.7439800000000001em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord mathnormal" style="">Q</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.738696em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord">∣</span><span class="mord mathnormal">s</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="mord"><span class="delimsizing size2">]</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.92199em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><h3>目标网络 🎯</h3>
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<p>为了提高稳定性，我们使用经验回放，从以前的经验中随机抽样<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqp" style=""><span class="mord mathnormal" style="margin-right:0.10903em">U</span><span class="mopen" style="">(</span><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="mclose" style="">)</span></span></span></span></span></span>。我们还使用具有一组单独参数的 Q 网络<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.088326em;vertical-align:-0.276864em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.811462em;"><span style="top:-2.4231360000000004em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span><span style="top:-3.1031310000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span></span></span></span></span></span>来计算目标。<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.088326em;vertical-align:-0.276864em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.811462em;"><span style="top:-2.4231360000000004em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span><span style="top:-3.1031310000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span></span></span></span></span></span>定期更新。这是根据论文《通过深度强化学习进行<a href="https://deepmind.com/research/dqn/">人体水平控制</a>》得出的。</p>
|
||
<p>所以损失函数是，<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathcal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="mop"><span class="mop mathbb" style="position:relative;top:0.094445em;">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.34480000000000005em;"><span style="top:-2.5198em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">s</span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqs" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqt" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">r</span></span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqq" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mclose mtight">)</span><span class="mrel mtight">∼</span><span class="mord mtight coloredeq eqp" style=""><span class="mord mathnormal mtight" style="margin-right:0.10903em">U</span><span class="mopen mtight" style="">(</span><span class="mord mathnormal mtight" style="margin-right:0.02778em">D</span><span class="mclose mtight" style="">)</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.3551999999999999em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing size3">[</span></span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord coloredeq eqt" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.565311em;vertical-align:-0.7439800000000001em;"></span><span class="mord mathnormal" style="margin-right:0.05556em;">γ</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.43055999999999983em;"><span style="top:-2.35602em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">max</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.7439800000000001em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqr" style=""><span class="mord mathnormal" style="">Q</span></span><span class="mopen">(</span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8213309999999999em;"><span style="top:-2.433005em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.266995em;"><span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="mord coloredeq eqm" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mopen" style="">(</span><span class="mord mathnormal" style="">s</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="">a</span></span><span class="mpunct" style="">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose" style="">)</span></span><span class="mord"><span class="mord"><span class="delimsizing size2">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.3540079999999999em;"><span style="top:-3.6029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord"><span class="delimsizing size3">]</span></span></span></span></span></span></span></p>
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||
<h3>双<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqr" style=""><span class="mord mathnormal" style="">Q</span></span></span></span></span></span>重学习</h3>
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||
<p>上述计算中的最大值运算符使用相同的网络来选择最佳动作和评估值。也就是说，<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.5458720000000001em;vertical-align:-0.7439800000000001em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.43055999999999983em;"><span style="top:-2.35602em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">max</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.7439800000000001em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqr" style=""><span class="mord mathnormal" style="">Q</span></span><span class="mopen">(</span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></span><span class="mord" style="color:cyan"><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop"><span class="mop"><span class="mord coloredeq eql" style=""><span class="mop" style=""><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord" style=""><span class="mord mathrm coloredeq eqt" style="">r</span></span><span class="mord mathrm" style="">gm</span><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord mathrm" style="">x</span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23383999999999996em;"><span style="top:-2.4558600000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:cyan"><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mopen">(</span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;color:cyan">θ</span><span class="mclose">)</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;color:cyan">θ</span><span class="mord"><span class="delimsizing size2">)</span></span></span></span></span></span></span>我们使用<a href="https://arxiv.org/abs/1509.06461">双重Q-L</a><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eql" style=""><span class="mop" style=""><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord" style=""><span class="mord mathrm coloredeq eqt" style="">r</span></span><span class="mord mathrm" style="">gm</span><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord mathrm" style="">x</span></span></span></span></span></span></span> earning<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord" style="color:cyan"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>，其中取自值，取自值<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.088326em;vertical-align:-0.276864em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.811462em;"><span style="top:-2.4231360000000004em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span><span style="top:-3.1031310000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span></span></span></span></span></span>。</p>
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<p>损失函数变成，</p>
|
||
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:6.600059999999999em;vertical-align:-3.0500299999999996em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5500299999999996em;"><span style="top:-5.55003em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mop"><span class="mop mathbb" style="position:relative;top:0.094445em;">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.34480000000000005em;"><span style="top:-2.5198em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">s</span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqs" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqt" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">r</span></span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqq" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mclose mtight">)</span><span class="mrel mtight">∼</span><span class="mord mtight coloredeq eqp" style=""><span class="mord mathnormal mtight" style="margin-right:0.10903em">U</span><span class="mopen mtight" style="">(</span><span class="mord mathnormal mtight" style="margin-right:0.02778em">D</span><span class="mclose mtight" style="">)</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.3551999999999999em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing size4">[</span></span><span class="mord"><span class="delimsizing size3">(</span></span></span></span><span style="top:-2.2500000000000004em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord">−</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:3.0500299999999996em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5500299999999996em;"><span style="top:-5.55003em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mord coloredeq eqt" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal" style="margin-right:0.05556em;">γ</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop"><span class="mop"><span class="mord coloredeq eql" style=""><span class="mop" style=""><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord" style=""><span class="mord mathrm coloredeq eqt" style="">r</span></span><span class="mord mathrm" style="">gm</span><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord mathrm" style="">x</span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23383999999999996em;"><span style="top:-2.4558600000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:cyan"><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mopen">(</span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:cyan"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8213309999999999em;"><span style="top:-2.433005em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.266995em;"><span></span></span></span></span></span></span></span><span class="mord"><span class="delimsizing size2">)</span></span></span></span><span style="top:-2.2500000000000004em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mord coloredeq eqm" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mopen" style="">(</span><span class="mord mathnormal" style="">s</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="">a</span></span><span class="mpunct" style="">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose" style="">)</span></span><span class="mord"><span class="mord"><span class="delimsizing size3">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.6540080000000001em;"><span style="top:-3.9029000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord"><span class="delimsizing size4">]</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:3.0500299999999996em;"><span></span></span></span></span></span></span></span></span></span></span></span></span>
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">34</span><span class="k">class</span> <span class="nc">QFuncLoss</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-2'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-2'>#</a>
|
||
</div>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">102</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gamma</span><span class="p">:</span> <span class="nb">float</span><span class="p">):</span>
|
||
<span class="lineno">103</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
|
||
<span class="lineno">104</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">=</span> <span class="n">gamma</span>
|
||
<span class="lineno">105</span> <span class="bp">self</span><span class="o">.</span><span class="n">huber_loss</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">SmoothL1Loss</span><span class="p">(</span><span class="n">reduction</span><span class="o">=</span><span class="s1">'none'</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-3'>
|
||
<div class='docs doc-strings'>
|
||
<div class='section-link'>
|
||
<a href='#section-3'>#</a>
|
||
</div>
|
||
<ul><li><code class="highlight"><span></span><span class="n">q</span></code>
|
||
-<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqr" style=""><span class="mord mathnormal" style="">Q</span></span><span class="mopen">(</span><span class="mord mathnormal">s</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></li>
|
||
<li><code class="highlight"><span></span><span class="n">action</span></code>
|
||
-<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span></span></span></span></span></li>
|
||
<li><code class="highlight"><span></span><span class="n">double_q</span></code>
|
||
-<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.001892em;vertical-align:-0.25em;"></span><span class="mord mathnormal coloredeq eqr" style="">Q</span><span class="mopen">(</span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:cyan"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></li>
|
||
<li><code class="highlight"><span></span><span class="n">target_q</span></code>
|
||
-<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.088326em;vertical-align:-0.276864em;"></span><span class="mord mathnormal coloredeq eqr" style="">Q</span><span class="mopen">(</span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.811462em;"><span style="top:-2.4231360000000004em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span><span style="top:-3.1031310000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></li>
|
||
<li><code class="highlight"><span></span><span class="n">done</span></code>
|
||
-游戏在采取行动后是否结束</li>
|
||
<li><code class="highlight"><span></span><span class="n">reward</span></code>
|
||
-<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqt" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span></span></span></span></span></li>
|
||
</ul><li><code class="highlight"><span></span><span class="n">weights</span></code>
|
||
-来自有经验的优先重播的样本的权重</li>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">107</span> <span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">q</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">action</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">double_q</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span>
|
||
<span class="lineno">108</span> <span class="n">target_q</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">done</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">reward</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span>
|
||
<span class="lineno">109</span> <span class="n">weights</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">)</span> <span class="o">-></span> <span class="n">Tuple</span><span class="p">[</span><span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">]:</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-4'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-4'>#</a>
|
||
</div>
|
||
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqm" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mopen" style="">(</span><span class="mord mathnormal" style="">s</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="">a</span></span><span class="mpunct" style="">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span></p>
|
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|
||
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|
||
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|
||
<div class="highlight"><pre><span class="lineno">121</span> <span class="n">q_sampled_action</span> <span class="o">=</span> <span class="n">q</span><span class="o">.</span><span class="n">gather</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">action</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">long</span><span class="p">)</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
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<span class="lineno">122</span> <span class="n">tracker</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="s1">'q_sampled_action'</span><span class="p">,</span> <span class="n">q_sampled_action</span><span class="p">)</span></pre></div>
|
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<p>渐变不应传播渐变<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></span><span class="mord"><span class="mord coloredeq eqc" style=""><span class="mord mathnormal coloredeq eqt" style="margin-right:0.02778em">r</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin coloredeq eqc" style="">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal coloredeq eqc" style="margin-right:0.05556em">γ</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mord coloredeq eqc" style=""><span class="delimsizing size2" style=""><span style="">(</span></span></span><span class="mord coloredeq eqc" style=""><span class="mord coloredeq eqq" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct coloredeq eqc" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop coloredeq eqc" style=""><span class="mop" style=""><span class="mord" style=""><span class="mop coloredeq eql" style=""><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord" style=""><span class="mord mathrm coloredeq eqt" style="">r</span></span><span class="mord mathrm" style="">gm</span><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord mathrm" style="">x</span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23383999999999996em;"><span style="top:-2.4558600000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqs" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:cyan"><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mopen coloredeq eqc" style="">(</span><span class="mord coloredeq eqc" style=""><span class="mord coloredeq eqq" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct coloredeq eqc" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mpunct coloredeq eqc" style="">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style="color:cyan"><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose coloredeq eqc" style="">)</span><span class="mpunct coloredeq eqc" style="">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style="color:orange"><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8213309999999999em;"><span style="top:-2.433005em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.266995em;"><span></span></span></span></span></span></span></span><span class="mord coloredeq eqc" style=""><span class="delimsizing size2" style=""><span style="">)</span></span></span></span></span></span></span></span></span></p>
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<div class="highlight"><pre><span class="lineno">130</span> <span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">():</span></pre></div>
|
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|
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<p>在州内采取最佳行动<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em;"></span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.051892em;vertical-align:-0.25em;"></span><span class="mop"><span class="mop"><span class="mord coloredeq eql" style=""><span class="mop" style=""><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord" style=""><span class="mord mathrm coloredeq eqt" style="">r</span></span><span class="mord mathrm" style="">gm</span><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord mathrm" style="">x</span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23383999999999996em;"><span style="top:-2.4558600000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:cyan"><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mopen">(</span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:cyan"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></span></p>
|
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|
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|
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|
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<div class="highlight"><pre><span class="lineno">134</span> <span class="n">best_next_action</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">double_q</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span></pre></div>
|
||
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|
||
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|
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|
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|
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|
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<p>从目标网络获取 q 值，以便在州内采取最佳行动<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em;"></span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop"><span class="mop"><span class="mord coloredeq eql" style=""><span class="mop" style=""><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord" style=""><span class="mord mathrm coloredeq eqt" style="">r</span></span><span class="mord mathrm" style="">gm</span><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord mathrm" style="">x</span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23383999999999996em;"><span style="top:-2.4558600000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:cyan"><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mopen">(</span><span class="mord coloredeq eqq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqs" style=""><span class="mord mathnormal" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:cyan"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8213309999999999em;"><span style="top:-2.433005em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.266995em;"><span></span></span></span></span></span></span></span><span class="mord"><span class="delimsizing size2">)</span></span></span></span></span></span></span></p>
|
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|
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|
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|
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<div class="highlight"><pre><span class="lineno">140</span> <span class="n">best_next_q_value</span> <span class="o">=</span> <span class="n">target_q</span><span class="o">.</span><span class="n">gather</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">best_next_action</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span></pre></div>
|
||
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|
||
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|
||
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|
||
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|
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<div class='section-link'>
|
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<a href='#section-8'>#</a>
|
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|
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<p>计算所需的 Q 值。如果游戏结束，我们将乘<code class="highlight"><span></span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">done</span><span class="p">)</span></code>
|
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以将下一个状态 Q 值归零。</p>
|
||
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></span><span class="mord"><span class="mord coloredeq eqc" style=""><span class="mord mathnormal coloredeq eqt" style="margin-right:0.02778em">r</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin coloredeq eqc" style="">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal coloredeq eqc" style="margin-right:0.05556em">γ</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mord coloredeq eqc" style=""><span class="delimsizing size2" style=""><span style="">(</span></span></span><span class="mord coloredeq eqc" style=""><span class="mord coloredeq eqq" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct coloredeq eqc" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop coloredeq eqc" style=""><span class="mop" style=""><span class="mord" style=""><span class="mop coloredeq eql" style=""><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord" style=""><span class="mord mathrm coloredeq eqt" style="">r</span></span><span class="mord mathrm" style="">gm</span><span class="mord" style=""><span class="mord mathrm coloredeq eqs" style="">a</span></span><span class="mord mathrm" style="">x</span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23383999999999996em;"><span style="top:-2.4558600000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqs" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:cyan"><span class="mord mathnormal coloredeq eqr" style="">Q</span></span><span class="mopen coloredeq eqc" style="">(</span><span class="mord coloredeq eqc" style=""><span class="mord coloredeq eqq" style=""><span class="mord mathnormal" style="">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span></span><span class="mpunct coloredeq eqc" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mpunct coloredeq eqc" style="">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style="color:cyan"><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose coloredeq eqc" style="">)</span><span class="mpunct coloredeq eqc" style="">;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style="color:orange"><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8213309999999999em;"><span style="top:-2.433005em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.266995em;"><span></span></span></span></span></span></span></span><span class="mord coloredeq eqc" style=""><span class="delimsizing size2" style=""><span style="">)</span></span></span></span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">151</span> <span class="n">q_update</span> <span class="o">=</span> <span class="n">reward</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">*</span> <span class="n">best_next_q_value</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">done</span><span class="p">)</span>
|
||
<span class="lineno">152</span> <span class="n">tracker</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="s1">'q_update'</span><span class="p">,</span> <span class="n">q_update</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-9'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-9'>#</a>
|
||
</div>
|
||
<p>时差误差<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span></span></span></span></span>用于称量重放缓冲区中的样本</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">155</span> <span class="n">td_error</span> <span class="o">=</span> <span class="n">q_sampled_action</span> <span class="o">-</span> <span class="n">q_update</span>
|
||
<span class="lineno">156</span> <span class="n">tracker</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="s1">'td_error'</span><span class="p">,</span> <span class="n">td_error</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-10'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-10'>#</a>
|
||
</div>
|
||
<p>我们采用 <a href="https://en.wikipedia.org/wiki/Huber_loss">Huber 损失</a>而不是均方误差损失，因为它对异常值不太敏感</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">160</span> <span class="n">losses</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">huber_loss</span><span class="p">(</span><span class="n">q_sampled_action</span><span class="p">,</span> <span class="n">q_update</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-11'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-11'>#</a>
|
||
</div>
|
||
<p>获取加权均值</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">162</span> <span class="n">loss</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">weights</span> <span class="o">*</span> <span class="n">losses</span><span class="p">)</span>
|
||
<span class="lineno">163</span> <span class="n">tracker</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="s1">'loss'</span><span class="p">,</span> <span class="n">loss</span><span class="p">)</span>
|
||
<span class="lineno">164</span>
|
||
<span class="lineno">165</span> <span class="k">return</span> <span class="n">td_error</span><span class="p">,</span> <span class="n">loss</span></pre></div>
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