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<h1 id="neural-episodic-control">Neural Episodic Control</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/1703.01988">Neural Episodic Control</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\nec.png" width=500>
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</p>
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<h2 id="algorithm-description">Algorithm Description</h2>
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<h3 id="choosing-an-action">Choosing an action</h3>
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<ol>
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<li>Use the current state as an input to the online network and extract the state embedding, which is the intermediate output from the middleware. </li>
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<li>For each possible action <script type="math/tex">a_i</script>, run the DND head using the state embedding and the selected action <script type="math/tex">a_i</script> as inputs. The DND is queried and returns the <script type="math/tex"> P </script> nearest neighbor keys and values. The keys and values are used to calculate and return the action <script type="math/tex"> Q </script> value from the network. </li>
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<li>Pass all the <script type="math/tex"> Q </script> values to the exploration policy and choose an action accordingly. </li>
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<li>Store the state embeddings and actions taken during the current episode in a small buffer <script type="math/tex">B</script>, in order to accumulate transitions until it is possible to calculate the total discounted returns over the entire episode.</li>
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</ol>
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<h3 id="finalizing-an-episode">Finalizing an episode</h3>
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<p>For each step in the episode, the state embeddings and the taken actions are stored in the buffer <script type="math/tex">B</script>. When the episode is finished, the replay buffer calculates the <script type="math/tex"> N </script>-step total return of each transition in the buffer, bootstrapped using the maximum <script type="math/tex">Q</script> value of the <script type="math/tex">N</script>-th transition. Those values are inserted along with the total return into the DND, and the buffer <script type="math/tex">B</script> is reset.</p>
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<h3 id="training-the-network">Training the network</h3>
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<p>Train the network only when the DND has enough entries for querying.</p>
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<p>To train the network, the current states are used as the inputs and the <script type="math/tex">N</script>-step returns are used as the targets. The <script type="math/tex">N</script>-step return used takes into account <script type="math/tex"> N </script> consecutive steps, and bootstraps the last value from the network if necessary:
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<script type="math/tex; mode=display"> y_t=\sum_{j=0}^{N-1}\gamma^j r(s_{t+j},a_{t+j} ) +\gamma^N max_a Q(s_{t+N},a) </script>
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