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<h1>阿姆斯格拉德</h1>
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<p>这是 <a href="https://pytorch.org">PyTorch</a> 对《<a href="https://arxiv.org/abs/1904.09237">亚当与超越的融合》一文的</a>实现。</p>
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<p>我们将其作为我们的 <a href="adam.html">Adam 优化器实现</a>的扩展。它自身的实现非常小，因为它与亚当非常相似。</p>
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<p>我们还实现了本文中描述的合成示例，其中亚当未能收敛。</p>
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<div class="highlight"><pre><span class="lineno">18</span><span></span><span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Dict</span>
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<span class="lineno">19</span>
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<span class="lineno">20</span><span class="kn">import</span> <span class="nn">torch</span>
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<span class="lineno">21</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">22</span>
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<span class="lineno">23</span><span class="kn">from</span> <span class="nn">labml_nn.optimizers</span> <span class="kn">import</span> <span class="n">WeightDecay</span>
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<span class="lineno">24</span><span class="kn">from</span> <span class="nn">labml_nn.optimizers.adam</span> <span class="kn">import</span> <span class="n">Adam</span></pre></div>
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</div>
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</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>amsGrad 优化器</h2>
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<p>这个类是从中定义的 Adam 优化器扩展而来的<a href="adam.html"><code class="highlight"><span></span><span class="n">adam</span><span class="o">.</span><span class="n">py</span></code>
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</a>。Adam 优化器正在扩展中<code class="highlight"><span></span><span class="n">GenericAdaptiveOptimizer</span></code>
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定义的类<a href="index.html"><code class="highlight"><span></span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span></code>
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</a>。</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">27</span><span class="k">class</span> <span class="nc">AMSGrad</span><span class="p">(</span><span class="n">Adam</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-2'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-2'>#</a>
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</div>
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<h3>初始化优化器</h3>
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<ul><li><code class="highlight"><span></span><span class="n">params</span></code>
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是参数列表</li>
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<li><code class="highlight"><span></span><span class="n">lr</span></code>
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是学习率<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 mathnormal" style="margin-right:0.0037em;">α</span></span></span></span></span></li>
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<li><code class="highlight"><span></span><span class="n">betas</span></code>
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是 (<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</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 ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;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 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>) 的元组</li>
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<li><code class="highlight"><span></span><span class="n">eps</span></code>
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是<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 accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eql" style=""><span class="mord mathnormal" style="">ϵ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord">^</span></span></span></span></span></span></span></span></span></span></span>或<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 eql" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span></span>基于<code class="highlight"><span></span><span class="n">optimized_update</span></code>
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</li>
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<li><code class="highlight"><span></span><span class="n">weight_decay</span></code>
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是在中<code class="highlight"><span></span><span class="n">WeightDecay</span></code>
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定义的类的实例 <a href="index.html"><code class="highlight"><span></span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span></code>
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</a></li>
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<li>“optimized_update” 是一个标志，在添加后是否要优化第二个时刻的偏差校正<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 eql" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span></span></li>
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<li><code class="highlight"><span></span><span class="n">amsgrad</span></code>
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是一个标志，指示是使用 AmsGrad 还是回退到普通的 Adam</li>
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<li><code class="highlight"><span></span><span class="n">defaults</span></code>
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是组值的默认字典。当你想扩展类时，这很有用<code class="highlight"><span></span><span class="n">Adam</span></code>
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。</li></ul>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">35</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">params</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span> <span class="n">betas</span><span class="o">=</span><span class="p">(</span><span class="mf">0.9</span><span class="p">,</span> <span class="mf">0.999</span><span class="p">),</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">,</span>
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<span class="lineno">36</span> <span class="n">weight_decay</span><span class="p">:</span> <span class="n">WeightDecay</span> <span class="o">=</span> <span class="n">WeightDecay</span><span class="p">(),</span>
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<span class="lineno">37</span> <span class="n">optimized_update</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
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<span class="lineno">38</span> <span class="n">amsgrad</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">defaults</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-3'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-3'>#</a>
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</div>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">53</span> <span class="n">defaults</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">defaults</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">defaults</span>
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<span class="lineno">54</span> <span class="n">defaults</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="nb">dict</span><span class="p">(</span><span class="n">amsgrad</span><span class="o">=</span><span class="n">amsgrad</span><span class="p">))</span>
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<span class="lineno">55</span>
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<span class="lineno">56</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="n">params</span><span class="p">,</span> <span class="n">lr</span><span class="p">,</span> <span class="n">betas</span><span class="p">,</span> <span class="n">eps</span><span class="p">,</span> <span class="n">weight_decay</span><span class="p">,</span> <span class="n">optimized_update</span><span class="p">,</span> <span class="n">defaults</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-4'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-4'>#</a>
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</div>
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<h3>初始化参数状态</h3>
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<ul><li><code class="highlight"><span></span><span class="n">state</span></code>
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是参数（张量）的优化器状态</li>
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<li><code class="highlight"><span></span><span class="n">group</span></code>
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存储参数组的优化程序属性</li>
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<li><code class="highlight"><span></span><span class="n">param</span></code>
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是参数张量<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.902771em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqj" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</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" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">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></span></span></span></span></li></ul>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">58</span> <span class="k">def</span> <span class="nf">init_state</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">state</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">],</span> <span class="n">group</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">],</span> <span class="n">param</span><span class="p">:</span> <span class="n">nn</span><span class="o">.</span><span class="n">Parameter</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-5'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-5'>#</a>
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</div>
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<p>我们正在扩展<code class="highlight"><span></span><span class="n">init_state</span></code>
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的 Call of Adam 优化器</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">68</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">init_state</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">group</span><span class="p">,</span> <span class="n">param</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-6'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-6'>#</a>
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</div>
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<p>如果 f<code class="highlight"><span></span><span class="n">amsgrad</span></code>
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lag<code class="highlight"><span></span><span class="kc">True</span></code>
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用于此参数组，则我们保持梯度平方指数移动平均线的最大值</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">72</span> <span class="k">if</span> <span class="n">group</span><span class="p">[</span><span class="s1">'amsgrad'</span><span class="p">]:</span>
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<span class="lineno">73</span> <span class="n">state</span><span class="p">[</span><span class="s1">'max_exp_avg_sq'</span><span class="p">]</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">preserve_format</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-7'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-7'>#</a>
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</div>
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||
<h3>计算<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqz" style=""><span class="mord" style=""><span class="mord mathnormal" style="">m</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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>和和<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqba" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</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:-0.03588em;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 mathnormal mtight coloredeq eqbc" style="">t</span></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>或<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 eqc" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;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="">1</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="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;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="">2</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="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="">...</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:0.03588em">v</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-left:-0.03588em;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 mathnormal mtight coloredeq eqbc" style="">t</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">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="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</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:-0.03588em;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 mathnormal mtight coloredeq eqbc" style="">t</span></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" style="">)</span></span></span></span></span></span></h3>
|
||
<ul><li><code class="highlight"><span></span><span class="n">state</span></code>
|
||
是参数（张量）的优化器状态</li>
|
||
<li><code class="highlight"><span></span><span class="n">group</span></code>
|
||
存储参数组的优化程序属性</li>
|
||
<li><code class="highlight"><span></span><span class="n">grad</span></code>
|
||
是参数的当前梯<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"><span class="mord mathnormal" style="margin-right:0.03588em;">g</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:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqbc" style=""><span class="mord mathnormal mtight" style="">t</span></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>度张量<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.902771em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqj" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</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" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">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></span></span></span></span></li></ul>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">75</span> <span class="k">def</span> <span class="nf">get_mv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">state</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">],</span> <span class="n">group</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">],</span> <span class="n">grad</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-8'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-8'>#</a>
|
||
</div>
|
||
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqba" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</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:-0.03588em;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 mathnormal mtight coloredeq eqbc" style="">t</span></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>从 <em>Adam</em> 那里得<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqz" style=""><span class="mord" style=""><span class="mord mathnormal" style="">m</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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>到</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">85</span> <span class="n">m</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">get_mv</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">group</span><span class="p">,</span> <span class="n">grad</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>如果此参数组正在使用<code class="highlight"><span></span><span class="n">amsgrad</span></code>
|
||
</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">88</span> <span class="k">if</span> <span class="n">group</span><span class="p">[</span><span class="s1">'amsgrad'</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>得到<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="mop">max</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</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="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;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 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="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">...</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</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-left:-0.03588em;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 coloredeq eqbc" style=""><span class="mord mathnormal mtight" style="">t</span></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="mclose">)</span></span></span></span></span>。</p>
|
||
<p>🗒 本文使用了这个符号<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"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord">^</span></span></span></span></span></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-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqbc" style=""><span class="mord mathnormal mtight" style="">t</span></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>，我们在这里不使用这种符号，因为它与亚当对偏差校正指数移动平均线使用相同的符号混淆了。</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">94</span> <span class="n">v_max</span> <span class="o">=</span> <span class="n">state</span><span class="p">[</span><span class="s1">'max_exp_avg_sq'</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>计算<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 eqc" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;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="">1</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="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;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="">2</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="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="">...</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:0.03588em">v</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-left:-0.03588em;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 mathnormal mtight coloredeq eqbc" style="">t</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">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="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</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:-0.03588em;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 mathnormal mtight coloredeq eqbc" style="">t</span></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" style="">)</span></span></span></span></span></span>。</p>
|
||
<p>🤔 我觉得你应该取/保持偏差校正的平方梯度的第二个指数平均值的最大值。但这也是<a href="https://github.com/pytorch/pytorch/blob/19f4c5110e8bcad5e7e75375194262fca0a6293a/torch/optim/functional.py#L90">在 PyTorch 中实现</a>它的方式。我想这并不重要，因为偏差校正只会增加值，而且只会在训练的最初几个步骤中产生实际差异。</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">103</span> <span class="n">torch</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">v_max</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">v_max</span><span class="p">)</span>
|
||
<span class="lineno">104</span>
|
||
<span class="lineno">105</span> <span class="k">return</span> <span class="n">m</span><span class="p">,</span> <span class="n">v_max</span>
|
||
<span class="lineno">106</span> <span class="k">else</span><span class="p">:</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-12'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-12'>#</a>
|
||
</div>
|
||
<p>如果参数组未使用，则回退到 <em>Adam</em><code class="highlight"><span></span><span class="n">amsgrad</span></code>
|
||
</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">108</span> <span class="k">return</span> <span class="n">m</span><span class="p">,</span> <span class="n">v</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-13'>
|
||
<div class='docs doc-strings'>
|
||
<div class='section-link'>
|
||
<a href='#section-13'>#</a>
|
||
</div>
|
||
<h2>合成实验</h2>
|
||
<p>这是论文中描述的合成实验，它显示了<em>亚当</em>失败的情景。</p>
|
||
<p>本文（和亚当）将优化问题描述为最小化函数<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 eqf" style=""><span class="mord mathbb" style="">E</span><span class="mopen" style="">[</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqbb" style="margin-right:0.10764em">f</span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</span></span><span class="mclose" style="">)]</span></span></span></span></span></span>相对于参数的预期值<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 coloredeq eqs" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span></span></span></span></span></span>。在随机训练设置中，我们无法掌握<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbb" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span></span></span></span></span></span>它自身的函数；也就是说，当你优化时，NN<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbb" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span></span></span></span></span></span> 将是整批数据的函数。我们实际评估的是一个小批量，所以实际的功能是随机指标的实现<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbb" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span></span></span></span></span></span>。这就是我们谈论预期值的原因。因此，让函数实现<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord coloredeq eqbb" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><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">1</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="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqbb" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><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">2</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="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">...</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqbb" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><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" style="margin-right:0.13889em;">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></span></span></span>适用于训练的每个时间步。</p>
|
||
<p>我们将优化器的性能作为遗憾来衡量，<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0954490000000003em;vertical-align:-1.267113em;"></span><span class="mord coloredeq eqb" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqx" style="margin-right:0.00773em">R</span><span class="mopen coloredeq eqx" style="">(</span><span class="mord mathnormal coloredeq eqx" style="margin-right:0.13889em">T</span><span class="mclose coloredeq eqx" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style="">1</span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op" style="">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">[</span></span></span><span class="mord" style=""><span class="mord coloredeq eqd" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbb" style="margin-right:0.10764em">f</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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 coloredeq eqd" style="">(</span><span class="mord coloredeq eqd" style=""><span class="mord coloredeq eqn" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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 eqd" style="">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin coloredeq eqd" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord coloredeq eqd" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbb" style="margin-right:0.10764em">f</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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 coloredeq eqd" style="">(</span><span class="mord coloredeq eqd" style=""><span class="mord coloredeq eqm" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</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" style=""><span class="mbin mtight" style="">∗</span></span></span></span></span></span></span></span></span><span class="mclose coloredeq eqd" style="">)</span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">]</span></span></span></span></span></span></span></span></span>其中<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 coloredeq eqn" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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>是时间步的参数<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord coloredeq eqbc" style=""><span class="mord mathnormal" style="">t</span></span></span></span></span></span>，<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 coloredeq eqm" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.688696em;"><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="mbin mtight" style="">∗</span></span></span></span></span></span></span></span></span></span></span></span></span>是最佳的最小化的参数<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 eqf" style=""><span class="mord mathbb" style="">E</span><span class="mopen" style="">[</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqbb" style="margin-right:0.10764em">f</span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</span></span><span class="mclose" style="">)]</span></span></span></span></span></span>。</p>
|
||
<p>现在让我们来定义综合问题，</p>
|
||
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.30003em;vertical-align:-1.400015em;"></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:1.900015em;"><span style="top:-3.9000150000000002em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord coloredeq eqt" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbb" style="margin-right:0.10764em">f</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqbd" style="">x</span></span><span class="mclose" style="">)</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="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em;"><span style="top:-3.69em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord">1010</span><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal" style="">x</span></span><span class="mpunct">,</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord">−</span><span class="mord">10</span><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal" style="">x</span></span><span class="mpunct">,</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.19em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em;"><span style="top:-3.69em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord text"><span class="mord coloredeq eqbb" style=""><span class="mord" style="">f</span></span><span class="mord">or </span></span><span class="mord coloredeq eqbc" style=""><span class="mord mathnormal" style="">t</span></span><span class="mspace allowbreak"></span><span class="mspace" style="margin-right:0.6666666666666666em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">mod</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">101</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">1</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord text"><span class="mord">o</span><span class="mord coloredeq eqbc" style=""><span class="mord" style="">t</span></span><span class="mord">herwise</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.19em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.400015em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>在哪里<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.78041em;vertical-align:-0.13597em;"></span><span class="mord coloredeq eqh" style=""><span class="mord" style="">−</span><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqbd" style="">x</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style="">+</span><span class="mord" style="">1</span></span></span></span></span></span>。最佳的解决方案是<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord coloredeq eqv" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbd" style="">x</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style="">−</span><span class="mord" style="">1</span></span></span></span></span></span>。</p>
|
||
<p>这段代码将尝试运行<em>亚当</em>和<em>阿姆斯格</em>拉德来解决这个问题。</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">111</span><span class="k">def</span> <span class="nf">_synthetic_experiment</span><span class="p">(</span><span class="n">is_adam</span><span class="p">:</span> <span class="nb">bool</span><span class="p">):</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-14'>
|
||
<div class='docs'>
|
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<div class='section-link'>
|
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<a href='#section-14'>#</a>
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</div>
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<p>定义<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 eqbd" style=""><span class="mord mathnormal" style="">x</span></span></span></span></span></span>参数</p>
|
||
|
||
</div>
|
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<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">153</span> <span class="n">x</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Parameter</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="mf">.0</span><span class="p">]))</span></pre></div>
|
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</div>
|
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</div>
|
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<div class='section' id='section-15'>
|
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<div class='docs'>
|
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<div class='section-link'>
|
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<a href='#section-15'>#</a>
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</div>
|
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<p>最佳，<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.688696em;vertical-align:0em;"></span><span class="mord"><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal" style="">x</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.688696em;"><span style="top:-3.063em;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="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:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">−</span><span class="mord">1</span></span></span></span></span></p>
|
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|
||
</div>
|
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<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">155</span> <span class="n">x_star</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Parameter</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="mi">1</span><span class="p">]),</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-16'>
|
||
<div class='docs doc-strings'>
|
||
<div class='section-link'>
|
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<a href='#section-16'>#</a>
|
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</div>
|
||
<h3><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 eqt" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbb" style="margin-right:0.10764em">f</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqbd" style="">x</span></span><span class="mclose" style="">)</span></span></span></span></span></span></h3>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">157</span> <span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">t</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">x_</span><span class="p">:</span> <span class="n">nn</span><span class="o">.</span><span class="n">Parameter</span><span class="p">):</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-17'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-17'>#</a>
|
||
</div>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">161</span> <span class="k">if</span> <span class="n">t</span> <span class="o">%</span> <span class="mi">101</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||
<span class="lineno">162</span> <span class="k">return</span> <span class="p">(</span><span class="mi">1010</span> <span class="o">*</span> <span class="n">x_</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
|
||
<span class="lineno">163</span> <span class="k">else</span><span class="p">:</span>
|
||
<span class="lineno">164</span> <span class="k">return</span> <span class="p">(</span><span class="o">-</span><span class="mi">10</span> <span class="o">*</span> <span class="n">x_</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-18'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-18'>#</a>
|
||
</div>
|
||
<p>初始化相关的优化器</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">167</span> <span class="k">if</span> <span class="n">is_adam</span><span class="p">:</span>
|
||
<span class="lineno">168</span> <span class="n">optimizer</span> <span class="o">=</span> <span class="n">Adam</span><span class="p">([</span><span class="n">x</span><span class="p">],</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">betas</span><span class="o">=</span><span class="p">(</span><span class="mf">0.9</span><span class="p">,</span> <span class="mf">0.99</span><span class="p">))</span>
|
||
<span class="lineno">169</span> <span class="k">else</span><span class="p">:</span>
|
||
<span class="lineno">170</span> <span class="n">optimizer</span> <span class="o">=</span> <span class="n">AMSGrad</span><span class="p">([</span><span class="n">x</span><span class="p">],</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">betas</span><span class="o">=</span><span class="p">(</span><span class="mf">0.9</span><span class="p">,</span> <span class="mf">0.99</span><span class="p">))</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-19'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-19'>#</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 eqx" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="mopen" style="">(</span><span class="mord mathnormal" style="margin-right:0.13889em">T</span><span class="mclose" style="">)</span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">172</span> <span class="n">total_regret</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<span class="lineno">173</span>
|
||
<span class="lineno">174</span> <span class="kn">from</span> <span class="nn">labml</span> <span class="kn">import</span> <span class="n">monit</span><span class="p">,</span> <span class="n">tracker</span><span class="p">,</span> <span class="n">experiment</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-20'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-20'>#</a>
|
||
</div>
|
||
<p>创建实验以记录结果</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">177</span> <span class="k">with</span> <span class="n">experiment</span><span class="o">.</span><span class="n">record</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s1">'synthetic'</span><span class="p">,</span> <span class="n">comment</span><span class="o">=</span><span class="s1">'Adam'</span> <span class="k">if</span> <span class="n">is_adam</span> <span class="k">else</span> <span class="s1">'AMSGrad'</span><span class="p">):</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-21'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-21'>#</a>
|
||
</div>
|
||
<p>跑步跑<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">7</span></span></span></span></span></span></span></span></span></span></span></span>步</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">179</span> <span class="k">for</span> <span class="n">step</span> <span class="ow">in</span> <span class="n">monit</span><span class="o">.</span><span class="n">loop</span><span class="p">(</span><span class="mi">10_000_000</span><span class="p">):</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-22'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-22'>#</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 eqd" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbb" style="margin-right:0.10764em">f</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqn" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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" style="">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbb" style="margin-right:0.10764em">f</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqm" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.688696em;"><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="mbin mtight" style="">∗</span></span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">181</span> <span class="n">regret</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">step</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="o">-</span> <span class="n">func</span><span class="p">(</span><span class="n">step</span><span class="p">,</span> <span class="n">x_star</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-23'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-23'>#</a>
|
||
</div>
|
||
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.331241em;vertical-align:-0.35001em;"></span><span class="mord coloredeq eqb" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqx" style="margin-right:0.00773em">R</span><span class="mopen coloredeq eqx" style="">(</span><span class="mord mathnormal coloredeq eqx" style="margin-right:0.13889em">T</span><span class="mclose coloredeq eqx" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mop" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;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 mathnormal mtight coloredeq eqbc" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style="">1</span></span></span></span><span style="top:-3.2029em;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="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">[</span></span></span><span class="mord" style=""><span class="mord coloredeq eqd" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbb" style="margin-right:0.10764em">f</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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 coloredeq eqd" style="">(</span><span class="mord coloredeq eqd" style=""><span class="mord coloredeq eqn" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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 eqd" style="">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin coloredeq eqd" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord coloredeq eqd" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbb" style="margin-right:0.10764em">f</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" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbc" style="">t</span></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 coloredeq eqd" style="">(</span><span class="mord coloredeq eqd" style=""><span class="mord coloredeq eqm" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqs" style="margin-right:0.02778em">θ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.688696em;"><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="mbin mtight" style="">∗</span></span></span></span></span></span></span></span></span><span class="mclose coloredeq eqd" style="">)</span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">]</span></span></span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">183</span> <span class="n">total_regret</span> <span class="o">+=</span> <span class="n">regret</span><span class="o">.</span><span class="n">item</span><span class="p">()</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-24'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-24'>#</a>
|
||
</div>
|
||
<p>每 1000 步跟踪一次结果</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">185</span> <span class="k">if</span> <span class="p">(</span><span class="n">step</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="mi">1000</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
||
<span class="lineno">186</span> <span class="n">tracker</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="n">loss</span><span class="o">=</span><span class="n">regret</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">regret</span><span class="o">=</span><span class="n">total_regret</span> <span class="o">/</span> <span class="p">(</span><span class="n">step</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-25'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-25'>#</a>
|
||
</div>
|
||
<p>计算梯度</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">188</span> <span class="n">regret</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-26'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-26'>#</a>
|
||
</div>
|
||
<p>优化</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">190</span> <span class="n">optimizer</span><span class="o">.</span><span class="n">step</span><span class="p">()</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-27'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-27'>#</a>
|
||
</div>
|
||
<p>渐变清晰</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">192</span> <span class="n">optimizer</span><span class="o">.</span><span class="n">zero_grad</span><span class="p">()</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-28'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-28'>#</a>
|
||
</div>
|
||
<p>请确保<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.78041em;vertical-align:-0.13597em;"></span><span class="mord coloredeq eqh" style=""><span class="mord" style="">−</span><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqbd" style="">x</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style="">+</span><span class="mord" style="">1</span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">195</span> <span class="n">x</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">clamp_</span><span class="p">(</span><span class="o">-</span><span class="mf">1.</span><span class="p">,</span> <span class="o">+</span><span class="mf">1.</span><span class="p">)</span>
|
||
<span class="lineno">196</span>
|
||
<span class="lineno">197</span>
|
||
<span class="lineno">198</span><span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span></pre></div>
|
||
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||
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||
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||
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|
||
<div class='section-link'>
|
||
<a href='#section-29'>#</a>
|
||
</div>
|
||
<p>运行合成实验的是<em>亚当</em>。你可以看到亚当聚集在<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 eqbd" style=""><span class="mord mathnormal" style="">x</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><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">+</span><span class="mord">1</span></span></span></span></span></p>
|
||
|
||
</div>
|
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<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">201</span> <span class="n">_synthetic_experiment</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-30'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-30'>#</a>
|
||
</div>
|
||
<p>在 <em>amsGrad</em> 运行合成实验你可以看到 amsGrad 会聚到真正的最优值<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord coloredeq eqv" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbd" style="">x</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style="">−</span><span class="mord" style="">1</span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">204</span> <span class="n">_synthetic_experiment</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span></pre></div>
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