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<h1>Generalized Advantage Estimation (GAE)</h1>
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<p>This is a <a href="https://pytorch.org">PyTorch</a> implementation of paper
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<a href="https://arxiv.org/abs/1506.02438">Generalized Advantage Estimation</a>.</p>
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<div class="highlight"><pre><span class="lineno">13</span><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span></pre></div>
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<div class="highlight"><pre><span class="lineno">16</span><span class="k">class</span> <span class="nc">GAE</span><span class="p">:</span></pre></div>
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<div class="highlight"><pre><span class="lineno">17</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">n_workers</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">worker_steps</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">gamma</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">lambda_</span><span class="p">:</span> <span class="nb">float</span><span class="p">):</span>
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<span class="lineno">18</span> <span class="bp">self</span><span class="o">.</span><span class="n">lambda_</span> <span class="o">=</span> <span class="n">lambda_</span>
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<span class="lineno">19</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">=</span> <span class="n">gamma</span>
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<span class="lineno">20</span> <span class="bp">self</span><span class="o">.</span><span class="n">worker_steps</span> <span class="o">=</span> <span class="n">worker_steps</span>
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<span class="lineno">21</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_workers</span> <span class="o">=</span> <span class="n">n_workers</span></pre></div>
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<div class='docs doc-strings'>
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<a href='#section-3'>#</a>
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<h3>Calculate advantages</h3>
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<p>
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<script type="math/tex; mode=display">\begin{align}
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\hat{A_t^{(1)}} &= r_t + \gamma V(s_{t+1}) - V(s)
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\\
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\hat{A_t^{(2)}} &= r_t + \gamma r_{t+1} +\gamma^2 V(s_{t+2}) - V(s)
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\\
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...
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\\
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\hat{A_t^{(\infty)}} &= r_t + \gamma r_{t+1} +\gamma^2 r_{t+1} + ... - V(s)
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\end{align}</script>
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</p>
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<p>$\hat{A_t^{(1)}}$ is high bias, low variance, whilst
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$\hat{A_t^{(\infty)}}$ is unbiased, high variance.</p>
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<p>We take a weighted average of $\hat{A_t^{(k)}}$ to balance bias and variance.
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This is called Generalized Advantage Estimation.
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<script type="math/tex; mode=display">\hat{A_t} = \hat{A_t^{GAE}} = \sum_k w_k \hat{A_t^{(k)}}</script>
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We set $w_k = \lambda^{k-1}$, this gives clean calculation for
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$\hat{A_t}$</p>
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<p>
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<script type="math/tex; mode=display">\begin{align}
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\delta_t &= r_t + \gamma V(s_{t+1}) - V(s_t)$
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\\
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\hat{A_t} &= \delta_t + \gamma \lambda \delta_{t+1} + ... +
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(\gamma \lambda)^{T - t + 1} \delta_{T - 1}$
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\\
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&= \delta_t + \gamma \lambda \hat{A_{t+1}}
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\end{align}</script>
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</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">23</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">done</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">rewards</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">values</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-></span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</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>advantages table</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">56</span> <span class="n">advantages</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">n_workers</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">worker_steps</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
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<span class="lineno">57</span> <span class="n">last_advantage</span> <span class="o">=</span> <span class="mi">0</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>$V(s_{t+1})$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">60</span> <span class="n">last_value</span> <span class="o">=</span> <span class="n">values</span><span class="p">[:,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span>
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<span class="lineno">61</span>
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<span class="lineno">62</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">worker_steps</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>mask if episode completed after step $t$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">64</span> <span class="n">mask</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">-</span> <span class="n">done</span><span class="p">[:,</span> <span class="n">t</span><span class="p">]</span>
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<span class="lineno">65</span> <span class="n">last_value</span> <span class="o">=</span> <span class="n">last_value</span> <span class="o">*</span> <span class="n">mask</span>
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<span class="lineno">66</span> <span class="n">last_advantage</span> <span class="o">=</span> <span class="n">last_advantage</span> <span class="o">*</span> <span class="n">mask</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>$\delta_t$</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="n">delta</span> <span class="o">=</span> <span class="n">rewards</span><span class="p">[:,</span> <span class="n">t</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">*</span> <span class="n">last_value</span> <span class="o">-</span> <span class="n">values</span><span class="p">[:,</span> <span class="n">t</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>$\hat{A_t} = \delta_t + \gamma \lambda \hat{A_{t+1}}$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">71</span> <span class="n">last_advantage</span> <span class="o">=</span> <span class="n">delta</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">lambda_</span> <span class="o">*</span> <span class="n">last_advantage</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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<p>note that we are collecting in reverse order.
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<em>My initial code was appending to a list and
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I forgot to reverse it later.
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It took me around 4 to 5 hours to find the bug.
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The performance of the model was improving
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slightly during initial runs,
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probably because the samples are similar.</em></p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">80</span> <span class="n">advantages</span><span class="p">[:,</span> <span class="n">t</span><span class="p">]</span> <span class="o">=</span> <span class="n">last_advantage</span>
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<span class="lineno">81</span>
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<span class="lineno">82</span> <span class="n">last_value</span> <span class="o">=</span> <span class="n">values</span><span class="p">[:,</span> <span class="n">t</span><span class="p">]</span>
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<span class="lineno">83</span>
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<span class="lineno">84</span> <span class="k">return</span> <span class="n">advantages</span></pre></div>
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