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</div>
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<h1>Deep Q Network (DQN) Model</h1>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">10</span><span></span><span class="kn">import</span> <span class="nn">torch</span>
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<span class="lineno">11</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">12</span>
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<span class="lineno">13</span><span class="kn">from</span> <span class="nn">labml_helpers.module</span> <span class="kn">import</span> <span class="n">Module</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>Dueling Network ⚔️ Model for $Q$ Values</h2>
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<p>We are using a <a href="https://arxiv.org/abs/1511.06581">dueling network</a>
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to calculate Q-values.
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Intuition behind dueling network architecture is that in most states
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the action doesn’t matter,
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and in some states the action is significant. Dueling network allows
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this to be represented very well.</p>
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<p>
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<script type="math/tex; mode=display">\begin{align}
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Q^\pi(s,a) &= V^\pi(s) + A^\pi(s, a)
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\\
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\mathop{\mathbb{E}}_{a \sim \pi(s)}
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\Big[
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A^\pi(s, a)
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\Big]
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&= 0
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\end{align}</script>
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</p>
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<p>So we create two networks for $V$ and $A$ and get $Q$ from them.
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<script type="math/tex; mode=display">
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Q(s, a) = V(s) +
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\Big(
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A(s, a) - \frac{1}{|\mathcal{A}|} \sum_{a' \in \mathcal{A}} A(s, a')
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\Big)
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</script>
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We share the initial layers of the $V$ and $A$ networks.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">16</span><span class="k">class</span> <span class="nc">Model</span><span class="p">(</span><span class="n">Module</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'>
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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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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">47</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
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<span class="lineno">48</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
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<span class="lineno">49</span> <span class="bp">self</span><span class="o">.</span><span class="n">conv</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</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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<p>The first convolution layer takes a
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$84\times84$ frame and produces a $20\times20$ frame</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">52</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="n">in_channels</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">out_channels</span><span class="o">=</span><span class="mi">32</span><span class="p">,</span> <span class="n">kernel_size</span><span class="o">=</span><span class="mi">8</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">4</span><span class="p">),</span>
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<span class="lineno">53</span> <span class="n">nn</span><span class="o">.</span><span class="n">ReLU</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'>
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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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<p>The second convolution layer takes a
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$20\times20$ frame and produces a $9\times9$ frame</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">57</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="n">in_channels</span><span class="o">=</span><span class="mi">32</span><span class="p">,</span> <span class="n">out_channels</span><span class="o">=</span><span class="mi">64</span><span class="p">,</span> <span class="n">kernel_size</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">2</span><span class="p">),</span>
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<span class="lineno">58</span> <span class="n">nn</span><span class="o">.</span><span class="n">ReLU</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>The third convolution layer takes a
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$9\times9$ frame and produces a $7\times7$ frame</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">62</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="n">in_channels</span><span class="o">=</span><span class="mi">64</span><span class="p">,</span> <span class="n">out_channels</span><span class="o">=</span><span class="mi">64</span><span class="p">,</span> <span class="n">kernel_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span>
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<span class="lineno">63</span> <span class="n">nn</span><span class="o">.</span><span class="n">ReLU</span><span class="p">(),</span>
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<span class="lineno">64</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>A fully connected layer takes the flattened
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frame from third convolution layer, and outputs
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$512$ features</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">69</span> <span class="bp">self</span><span class="o">.</span><span class="n">lin</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">in_features</span><span class="o">=</span><span class="mi">7</span> <span class="o">*</span> <span class="mi">7</span> <span class="o">*</span> <span class="mi">64</span><span class="p">,</span> <span class="n">out_features</span><span class="o">=</span><span class="mi">512</span><span class="p">)</span>
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<span class="lineno">70</span> <span class="bp">self</span><span class="o">.</span><span class="n">activation</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">ReLU</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'>
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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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<p>This head gives the state value $V$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">73</span> <span class="bp">self</span><span class="o">.</span><span class="n">state_value</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span>
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<span class="lineno">74</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">in_features</span><span class="o">=</span><span class="mi">512</span><span class="p">,</span> <span class="n">out_features</span><span class="o">=</span><span class="mi">256</span><span class="p">),</span>
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<span class="lineno">75</span> <span class="n">nn</span><span class="o">.</span><span class="n">ReLU</span><span class="p">(),</span>
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<span class="lineno">76</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">in_features</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span> <span class="n">out_features</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span>
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<span class="lineno">77</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-8'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-8'>#</a>
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</div>
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<p>This head gives the action value $A$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">79</span> <span class="bp">self</span><span class="o">.</span><span class="n">action_value</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span>
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<span class="lineno">80</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">in_features</span><span class="o">=</span><span class="mi">512</span><span class="p">,</span> <span class="n">out_features</span><span class="o">=</span><span class="mi">256</span><span class="p">),</span>
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<span class="lineno">81</span> <span class="n">nn</span><span class="o">.</span><span class="n">ReLU</span><span class="p">(),</span>
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<span class="lineno">82</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">in_features</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span> <span class="n">out_features</span><span class="o">=</span><span class="mi">4</span><span class="p">),</span>
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<span class="lineno">83</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-9'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-9'>#</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">85</span> <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obs</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>
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</div>
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</div>
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<div class='section' id='section-10'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-10'>#</a>
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</div>
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<p>Convolution</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">87</span> <span class="n">h</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">conv</span><span class="p">(</span><span class="n">obs</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-11'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-11'>#</a>
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</div>
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<p>Reshape for linear layers</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">89</span> <span class="n">h</span> <span class="o">=</span> <span class="n">h</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">7</span> <span class="o">*</span> <span class="mi">7</span> <span class="o">*</span> <span class="mi">64</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-12'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-12'>#</a>
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</div>
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<p>Linear layer</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">92</span> <span class="n">h</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">activation</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">lin</span><span class="p">(</span><span class="n">h</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-13'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-13'>#</a>
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</div>
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<p>$A$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">95</span> <span class="n">action_value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">action_value</span><span class="p">(</span><span class="n">h</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-14'>
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<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>$V$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">97</span> <span class="n">state_value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">state_value</span><span class="p">(</span><span class="n">h</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>$A(s, a) - \frac{1}{|\mathcal{A}|} \sum_{a’ \in \mathcal{A}} A(s, a’)$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">100</span> <span class="n">action_score_centered</span> <span class="o">=</span> <span class="n">action_value</span> <span class="o">-</span> <span class="n">action_value</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdim</span><span class="o">=</span><span class="kc">True</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-16'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-16'>#</a>
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</div>
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<p>$Q(s, a) =V(s) + \Big(A(s, a) - \frac{1}{|\mathcal{A}|} \sum_{a’ \in \mathcal{A}} A(s, a’)\Big)$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">102</span> <span class="n">q</span> <span class="o">=</span> <span class="n">state_value</span> <span class="o">+</span> <span class="n">action_score_centered</span>
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<span class="lineno">103</span>
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<span class="lineno">104</span> <span class="k">return</span> <span class="n">q</span></pre></div>
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