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<div class="section" id="categorical-dqn">
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<h1>Categorical DQN<a class="headerlink" href="#categorical-dqn" title="Permalink to this headline">¶</a></h1>
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<p><strong>Actions space:</strong> Discrete</p>
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<p><strong>References:</strong> <a class="reference external" href="https://arxiv.org/abs/1707.06887">A Distributional Perspective on Reinforcement Learning</a></p>
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<div class="section" id="network-structure">
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<h2>Network Structure<a class="headerlink" href="#network-structure" title="Permalink to this headline">¶</a></h2>
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<img alt="../../../_images/distributional_dqn.png" class="align-center" src="../../../_images/distributional_dqn.png" />
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</div>
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<div class="section" id="algorithm-description">
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<h2>Algorithm Description<a class="headerlink" href="#algorithm-description" title="Permalink to this headline">¶</a></h2>
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<div class="section" id="training-the-network">
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<h3>Training the network<a class="headerlink" href="#training-the-network" title="Permalink to this headline">¶</a></h3>
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<ol class="arabic">
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<li><p>Sample a batch of transitions from the replay buffer.</p></li>
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<li><p>The Bellman update is projected to the set of atoms representing the <span class="math notranslate nohighlight">\(Q\)</span> values distribution, such
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that the <span class="math notranslate nohighlight">\(i-th\)</span> component of the projected update is calculated as follows:</p>
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<p><span class="math notranslate nohighlight">\((\Phi \hat{T} Z_{\theta}(s_t,a_t))_i=\sum_{j=0}^{N-1}\Big[1-\frac{\lvert[\hat{T}_{z_{j}}]^{V_{MAX}}_{V_{MIN}}-z_i\rvert}{\Delta z}\Big]^1_0 \ p_j(s_{t+1}, \pi(s_{t+1}))\)</span></p>
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<p>where:
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* <span class="math notranslate nohighlight">\([ \cdot ]\)</span> bounds its argument in the range <span class="math notranslate nohighlight">\([a, b]\)</span>
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* <span class="math notranslate nohighlight">\(\hat{T}_{z_{j}}\)</span> is the Bellman update for atom <span class="math notranslate nohighlight">\(z_j\)</span>: <span class="math notranslate nohighlight">\(\hat{T}_{z_{j}} := r+\gamma z_j\)</span></p>
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</li>
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<li><p>Network is trained with the cross entropy loss between the resulting probability distribution and the target
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probability distribution. Only the target of the actions that were actually taken is updated.</p></li>
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<li><p>Once in every few thousand steps, weights are copied from the online network to the target network.</p></li>
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</ol>
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<dl class="class">
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<dt id="rl_coach.agents.categorical_dqn_agent.CategoricalDQNAlgorithmParameters">
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<em class="property">class </em><code class="descclassname">rl_coach.agents.categorical_dqn_agent.</code><code class="descname">CategoricalDQNAlgorithmParameters</code><a class="reference internal" href="../../../_modules/rl_coach/agents/categorical_dqn_agent.html#CategoricalDQNAlgorithmParameters"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#rl_coach.agents.categorical_dqn_agent.CategoricalDQNAlgorithmParameters" title="Permalink to this definition">¶</a></dt>
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<dd><dl class="field-list simple">
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<dt class="field-odd">Parameters</dt>
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<dd class="field-odd"><ul class="simple">
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<li><p><strong>v_min</strong> – (float)
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The minimal value that will be represented in the network output for predicting the Q value.
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Corresponds to <span class="math notranslate nohighlight">\(v_{min}\)</span> in the paper.</p></li>
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<li><p><strong>v_max</strong> – (float)
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The maximum value that will be represented in the network output for predicting the Q value.
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Corresponds to <span class="math notranslate nohighlight">\(v_{max}\)</span> in the paper.</p></li>
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<li><p><strong>atoms</strong> – (int)
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The number of atoms that will be used to discretize the range between v_min and v_max.
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For the C51 algorithm described in the paper, the number of atoms is 51.</p></li>
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</ul>
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</dd>
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</dl>
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