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<div class="section" id="acer">
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<h1>ACER<a class="headerlink" href="#acer" 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/1611.01224">Sample Efficient Actor-Critic with Experience Replay</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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<a class="reference internal image-reference" href="../../../_images/acer.png"><img alt="../../../_images/acer.png" class="align-center" src="../../../_images/acer.png" style="width: 500px;" /></a>
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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="choosing-an-action-discrete-actions">
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<h3>Choosing an action - Discrete actions<a class="headerlink" href="#choosing-an-action-discrete-actions" title="Permalink to this headline">¶</a></h3>
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<p>The policy network is used in order to predict action probabilites. While training, a sample is taken from a categorical
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distribution assigned with these probabilities. When testing, the action with the highest probability is used.</p>
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</div>
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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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<p>Each iteration perform one on-policy update with a batch of the last <span class="math notranslate nohighlight">\(T_{max}\)</span> transitions,
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and <span class="math notranslate nohighlight">\(n\)</span> (replay ratio) off-policy updates from batches of <span class="math notranslate nohighlight">\(T_{max}\)</span> transitions sampled from the replay buffer.</p>
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<p>Each update perform the following procedure:</p>
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<ol class="arabic">
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<li><p><strong>Calculate state values:</strong></p>
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<div class="math notranslate nohighlight">
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\[V(s_t) = \mathbb{E}_{a \sim \pi} [Q(s_t,a)]\]</div>
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</li>
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<li><p><strong>Calculate Q retrace:</strong></p>
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<blockquote>
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<div><div class="math notranslate nohighlight">
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\[Q^{ret}(s_t,a_t) = r_t +\gamma \bar{\rho}_{t+1}[Q^{ret}(s_{t+1},a_{t+1}) - Q(s_{t+1},a_{t+1})] + \gamma V(s_{t+1})\]</div>
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<div class="math notranslate nohighlight">
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\[\text{where} \quad \bar{\rho}_{t} = \min{\left\{c,\rho_t\right\}},\quad \rho_t=\frac{\pi (a_t \mid s_t)}{\mu (a_t \mid s_t)}\]</div>
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</div></blockquote>
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</li>
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<li><p><strong>Accumulate gradients:</strong></p>
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<blockquote>
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<div><p><span class="math notranslate nohighlight">\(\bullet\)</span> <strong>Policy gradients (with bias correction):</strong></p>
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<blockquote>
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<div><div class="math notranslate nohighlight">
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\[\begin{split}\hat{g}_t^{policy} & = & \bar{\rho}_{t} \nabla \log \pi (a_t \mid s_t) [Q^{ret}(s_t,a_t) - V(s_t)] \\
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& & + \mathbb{E}_{a \sim \pi} \left(\left[\frac{\rho_t(a)-c}{\rho_t(a)}\right] \nabla \log \pi (a \mid s_t) [Q(s_t,a) - V(s_t)] \right)\end{split}\]</div>
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</div></blockquote>
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<p><span class="math notranslate nohighlight">\(\bullet\)</span> <strong>Q-Head gradients (MSE):</strong></p>
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<blockquote>
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<div><div class="math notranslate nohighlight">
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\[\begin{split}\hat{g}_t^{Q} = (Q^{ret}(s_t,a_t) - Q(s_t,a_t)) \nabla Q(s_t,a_t)\\\end{split}\]</div>
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</div></blockquote>
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</div></blockquote>
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</li>
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<li><p><strong>(Optional) Trust region update:</strong> change the policy loss gradient w.r.t network output:</p>
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<blockquote>
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<div><div class="math notranslate nohighlight">
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\[\hat{g}_t^{trust-region} = \hat{g}_t^{policy} - \max \left\{0, \frac{k^T \hat{g}_t^{policy} - \delta}{\lVert k \rVert_2^2}\right\} k\]</div>
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<div class="math notranslate nohighlight">
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\[\text{where} \quad k = \nabla D_{KL}[\pi_{avg} \parallel \pi]\]</div>
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<p>The average policy network is an exponential moving average of the parameters of the network (<span class="math notranslate nohighlight">\(\theta_{avg}=\alpha\theta_{avg}+(1-\alpha)\theta\)</span>).
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The goal of the trust region update is to the difference between the updated policy and the average policy to ensure stability.</p>
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</div></blockquote>
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</li>
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</ol>
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<dl class="class">
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<dt id="rl_coach.agents.acer_agent.ACERAlgorithmParameters">
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<em class="property">class </em><code class="sig-prename descclassname">rl_coach.agents.acer_agent.</code><code class="sig-name descname">ACERAlgorithmParameters</code><a class="reference internal" href="../../../_modules/rl_coach/agents/acer_agent.html#ACERAlgorithmParameters"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#rl_coach.agents.acer_agent.ACERAlgorithmParameters" 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>num_steps_between_gradient_updates</strong> – (int)
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Every num_steps_between_gradient_updates transitions will be considered as a single batch and use for
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accumulating gradients. This is also the number of steps used for bootstrapping according to the n-step formulation.</p></li>
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<li><p><strong>ratio_of_replay</strong> – (int)
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The number of off-policy training iterations in each ACER iteration.</p></li>
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<li><p><strong>num_transitions_to_start_replay</strong> – (int)
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Number of environment steps until ACER starts to train off-policy from the experience replay.
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This emulates a heat-up phase where the agents learns only on-policy until there are enough transitions in
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the experience replay to start the off-policy training.</p></li>
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<li><p><strong>rate_for_copying_weights_to_target</strong> – (float)
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The rate of the exponential moving average for the average policy which is used for the trust region optimization.
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The target network in this algorithm is used as the average policy.</p></li>
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<li><p><strong>importance_weight_truncation</strong> – (float)
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The clipping constant for the importance weight truncation (not used in the Q-retrace calculation).</p></li>
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<li><p><strong>use_trust_region_optimization</strong> – (bool)
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If set to True, the gradients of the network will be modified with a term dependant on the KL divergence between
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the average policy and the current one, to bound the change of the policy during the network update.</p></li>
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<li><p><strong>max_KL_divergence</strong> – (float)
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The upper bound parameter for the trust region optimization, use_trust_region_optimization needs to be set true
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for this parameter to have an effect.</p></li>
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<li><p><strong>beta_entropy</strong> – (float)
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An entropy regulaization term can be added to the loss function in order to control exploration. This term
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is weighted using the beta value defined by beta_entropy.</p></li>
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</ul>
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</dd>
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</dl>
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</dd></dl>
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</div>
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