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<h1 id="persistent-advantage-learning">Persistent Advantage Learning</h1>
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<p><strong>Actions space:</strong> Discrete</p>
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<p><strong>References:</strong> <a href="https://arxiv.org/abs/1512.04860">Increasing the Action Gap: New Operators for Reinforcement Learning</a></p>
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<h2 id="network-structure">Network Structure</h2>
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<p style="text-align: center;">
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<img src="../../design_imgs/dqn.png">
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</p>
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<h2 id="algorithm-description">Algorithm Description</h2>
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<h3 id="training-the-network">Training the network</h3>
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<ol>
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<li>
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<p>Sample a batch of transitions from the replay buffer. </p>
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</li>
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<li>
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<p>Start by calculating the initial target values in the same manner as they are calculated in DDQN
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<script type="math/tex; mode=display"> y_t^{DDQN}=r(s_t,a_t )+\gamma Q(s_{t+1},argmax_a Q(s_{t+1},a)) </script>
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</p>
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</li>
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<li>The action gap <script type="math/tex"> V(s_t )-Q(s_t,a_t) </script> should then be subtracted from each of the calculated targets. To calculate the action gap, run the target network using the current states and get the <script type="math/tex"> Q </script> values for all the actions. Then estimate <script type="math/tex"> V </script> as the maximum predicted <script type="math/tex"> Q </script> value for the current state:
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<script type="math/tex; mode=display"> V(s_t )=max_a Q(s_t,a) </script>
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</li>
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<li>For <em>advantage learning (AL)</em>, reduce the action gap weighted by a predefined parameter <script type="math/tex"> \alpha </script> from the targets <script type="math/tex"> y_t^{DDQN} </script>:
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<script type="math/tex; mode=display"> y_t=y_t^{DDQN}-\alpha \cdot (V(s_t )-Q(s_t,a_t )) </script>
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</li>
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<li>For <em>persistent advantage learning (PAL)</em>, the target network is also used in order to calculate the action gap for the next state:
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<script type="math/tex; mode=display"> V(s_{t+1} )-Q(s_{t+1},a_{t+1}) </script>
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where <script type="math/tex"> a_{t+1} </script> is chosen by running the next states through the online network and choosing the action that has the highest predicted <script type="math/tex"> Q </script> value. Finally, the targets will be defined as -
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<script type="math/tex; mode=display"> y_t=y_t^{DDQN}-\alpha \cdot min(V(s_t )-Q(s_t,a_t ),V(s_{t+1} )-Q(s_{t+1},a_{t+1} )) </script>
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</li>
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<li>
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<p>Train the online network using the current states as inputs, and with the aforementioned targets.</p>
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</li>
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<li>
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<p>Once in every few thousand steps, copy the weights from the online network to the target network.</p>
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</li>
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