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<section class="sphx-glr-example-title" id="frozenlake-benchmark">
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<span id="sphx-glr-tutorials-training-agents-frozenlake-tuto-py"></span><h1>Frozenlake benchmark<a class="headerlink" href="#frozenlake-benchmark" title="Link to this heading">#</a></h1>
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<p>In this post we’ll compare a bunch of different map sizes on the
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<a class="reference external" href="https://gymnasium.farama.org/environments/toy_text/frozen_lake/">FrozenLake</a>
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environment from the reinforcement learning
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<a class="reference external" href="https://gymnasium.farama.org/">Gymnasium</a> package using the
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Q-learning algorithm.</p>
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<section id="dependencies">
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<h2>Dependencies<a class="headerlink" href="#dependencies" title="Link to this heading">#</a></h2>
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<p>Let’s first import a few dependencies we’ll need.</p>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Andrea Pierré</span>
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<span class="c1"># License: MIT License</span>
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|
||
|
||
<span class="kn">from</span> <span class="nn">pathlib</span> <span class="kn">import</span> <span class="n">Path</span>
|
||
<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">NamedTuple</span>
|
||
|
||
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
|
||
<span class="kn">import</span> <span class="nn">seaborn</span> <span class="k">as</span> <span class="nn">sns</span>
|
||
<span class="kn">from</span> <span class="nn">tqdm</span> <span class="kn">import</span> <span class="n">tqdm</span>
|
||
|
||
<span class="kn">import</span> <span class="nn">gymnasium</span> <span class="k">as</span> <span class="nn">gym</span>
|
||
<span class="kn">from</span> <span class="nn">gymnasium.envs.toy_text.frozen_lake</span> <span class="kn">import</span> <span class="n">generate_random_map</span>
|
||
|
||
|
||
<span class="n">sns</span><span class="o">.</span><span class="n">set_theme</span><span class="p">()</span>
|
||
|
||
<span class="c1"># %load_ext lab_black</span>
|
||
</pre></div>
|
||
</div>
|
||
</section>
|
||
<section id="parameters-we-ll-use">
|
||
<h2>Parameters we’ll use<a class="headerlink" href="#parameters-we-ll-use" title="Link to this heading">#</a></h2>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Params</span><span class="p">(</span><span class="n">NamedTuple</span><span class="p">):</span>
|
||
<span class="n">total_episodes</span><span class="p">:</span> <span class="nb">int</span> <span class="c1"># Total episodes</span>
|
||
<span class="n">learning_rate</span><span class="p">:</span> <span class="nb">float</span> <span class="c1"># Learning rate</span>
|
||
<span class="n">gamma</span><span class="p">:</span> <span class="nb">float</span> <span class="c1"># Discounting rate</span>
|
||
<span class="n">epsilon</span><span class="p">:</span> <span class="nb">float</span> <span class="c1"># Exploration probability</span>
|
||
<span class="n">map_size</span><span class="p">:</span> <span class="nb">int</span> <span class="c1"># Number of tiles of one side of the squared environment</span>
|
||
<span class="n">seed</span><span class="p">:</span> <span class="nb">int</span> <span class="c1"># Define a seed so that we get reproducible results</span>
|
||
<span class="n">is_slippery</span><span class="p">:</span> <span class="nb">bool</span> <span class="c1"># If true the player will move in intended direction with probability of 1/3 else will move in either perpendicular direction with equal probability of 1/3 in both directions</span>
|
||
<span class="n">n_runs</span><span class="p">:</span> <span class="nb">int</span> <span class="c1"># Number of runs</span>
|
||
<span class="n">action_size</span><span class="p">:</span> <span class="nb">int</span> <span class="c1"># Number of possible actions</span>
|
||
<span class="n">state_size</span><span class="p">:</span> <span class="nb">int</span> <span class="c1"># Number of possible states</span>
|
||
<span class="n">proba_frozen</span><span class="p">:</span> <span class="nb">float</span> <span class="c1"># Probability that a tile is frozen</span>
|
||
<span class="n">savefig_folder</span><span class="p">:</span> <span class="n">Path</span> <span class="c1"># Root folder where plots are saved</span>
|
||
|
||
|
||
<span class="n">params</span> <span class="o">=</span> <span class="n">Params</span><span class="p">(</span>
|
||
<span class="n">total_episodes</span><span class="o">=</span><span class="mi">2000</span><span class="p">,</span>
|
||
<span class="n">learning_rate</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span>
|
||
<span class="n">gamma</span><span class="o">=</span><span class="mf">0.95</span><span class="p">,</span>
|
||
<span class="n">epsilon</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
|
||
<span class="n">map_size</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span>
|
||
<span class="n">seed</span><span class="o">=</span><span class="mi">123</span><span class="p">,</span>
|
||
<span class="n">is_slippery</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
|
||
<span class="n">n_runs</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span>
|
||
<span class="n">action_size</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
|
||
<span class="n">state_size</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
|
||
<span class="n">proba_frozen</span><span class="o">=</span><span class="mf">0.9</span><span class="p">,</span>
|
||
<span class="n">savefig_folder</span><span class="o">=</span><span class="n">Path</span><span class="p">(</span><span class="s2">"../../_static/img/tutorials/"</span><span class="p">),</span>
|
||
<span class="p">)</span>
|
||
<span class="n">params</span>
|
||
|
||
<span class="c1"># Set the seed</span>
|
||
<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="n">params</span><span class="o">.</span><span class="n">seed</span><span class="p">)</span>
|
||
|
||
<span class="c1"># Create the figure folder if it doesn't exist</span>
|
||
<span class="n">params</span><span class="o">.</span><span class="n">savefig_folder</span><span class="o">.</span><span class="n">mkdir</span><span class="p">(</span><span class="n">parents</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">exist_ok</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
</section>
|
||
<section id="the-frozenlake-environment">
|
||
<h2>The FrozenLake environment<a class="headerlink" href="#the-frozenlake-environment" title="Link to this heading">#</a></h2>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">env</span> <span class="o">=</span> <span class="n">gym</span><span class="o">.</span><span class="n">make</span><span class="p">(</span>
|
||
<span class="s2">"FrozenLake-v1"</span><span class="p">,</span>
|
||
<span class="n">is_slippery</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">is_slippery</span><span class="p">,</span>
|
||
<span class="n">render_mode</span><span class="o">=</span><span class="s2">"rgb_array"</span><span class="p">,</span>
|
||
<span class="n">desc</span><span class="o">=</span><span class="n">generate_random_map</span><span class="p">(</span>
|
||
<span class="n">size</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">map_size</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">proba_frozen</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">seed</span>
|
||
<span class="p">),</span>
|
||
<span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
<section id="creating-the-q-table">
|
||
<h3>Creating the Q-table<a class="headerlink" href="#creating-the-q-table" title="Link to this heading">#</a></h3>
|
||
<p>In this tutorial we’ll be using Q-learning as our learning algorithm and
|
||
<span class="math notranslate nohighlight">\(\epsilon\)</span>-greedy to decide which action to pick at each step. You
|
||
can have a look at the <a class="reference external" href="#References">References section</a> for some
|
||
refreshers on the theory. Now, let’s create our Q-table initialized at
|
||
zero with the states number as rows and the actions number as columns.</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">params</span> <span class="o">=</span> <span class="n">params</span><span class="o">.</span><span class="n">_replace</span><span class="p">(</span><span class="n">action_size</span><span class="o">=</span><span class="n">env</span><span class="o">.</span><span class="n">action_space</span><span class="o">.</span><span class="n">n</span><span class="p">)</span>
|
||
<span class="n">params</span> <span class="o">=</span> <span class="n">params</span><span class="o">.</span><span class="n">_replace</span><span class="p">(</span><span class="n">state_size</span><span class="o">=</span><span class="n">env</span><span class="o">.</span><span class="n">observation_space</span><span class="o">.</span><span class="n">n</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Action size: </span><span class="si">{</span><span class="n">params</span><span class="o">.</span><span class="n">action_size</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"State size: </span><span class="si">{</span><span class="n">params</span><span class="o">.</span><span class="n">state_size</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
|
||
|
||
<span class="k">class</span> <span class="nc">Qlearning</span><span class="p">:</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">learning_rate</span><span class="p">,</span> <span class="n">gamma</span><span class="p">,</span> <span class="n">state_size</span><span class="p">,</span> <span class="n">action_size</span><span class="p">):</span>
|
||
<span class="bp">self</span><span class="o">.</span><span class="n">state_size</span> <span class="o">=</span> <span class="n">state_size</span>
|
||
<span class="bp">self</span><span class="o">.</span><span class="n">action_size</span> <span class="o">=</span> <span class="n">action_size</span>
|
||
<span class="bp">self</span><span class="o">.</span><span class="n">learning_rate</span> <span class="o">=</span> <span class="n">learning_rate</span>
|
||
<span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">=</span> <span class="n">gamma</span>
|
||
<span class="bp">self</span><span class="o">.</span><span class="n">reset_qtable</span><span class="p">()</span>
|
||
|
||
<span class="k">def</span> <span class="nf">update</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">state</span><span class="p">,</span> <span class="n">action</span><span class="p">,</span> <span class="n">reward</span><span class="p">,</span> <span class="n">new_state</span><span class="p">):</span>
|
||
<span class="w"> </span><span class="sd">"""Update Q(s,a):= Q(s,a) + lr [R(s,a) + gamma * max Q(s',a') - Q(s,a)]"""</span>
|
||
<span class="n">delta</span> <span class="o">=</span> <span class="p">(</span>
|
||
<span class="n">reward</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">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">qtable</span><span class="p">[</span><span class="n">new_state</span><span class="p">,</span> <span class="p">:])</span>
|
||
<span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">qtable</span><span class="p">[</span><span class="n">state</span><span class="p">,</span> <span class="n">action</span><span class="p">]</span>
|
||
<span class="p">)</span>
|
||
<span class="n">q_update</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">qtable</span><span class="p">[</span><span class="n">state</span><span class="p">,</span> <span class="n">action</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">learning_rate</span> <span class="o">*</span> <span class="n">delta</span>
|
||
<span class="k">return</span> <span class="n">q_update</span>
|
||
|
||
<span class="k">def</span> <span class="nf">reset_qtable</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
<span class="w"> </span><span class="sd">"""Reset the Q-table."""</span>
|
||
<span class="bp">self</span><span class="o">.</span><span class="n">qtable</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">state_size</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">action_size</span><span class="p">))</span>
|
||
|
||
|
||
<span class="k">class</span> <span class="nc">EpsilonGreedy</span><span class="p">:</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">epsilon</span><span class="p">):</span>
|
||
<span class="bp">self</span><span class="o">.</span><span class="n">epsilon</span> <span class="o">=</span> <span class="n">epsilon</span>
|
||
|
||
<span class="k">def</span> <span class="nf">choose_action</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">action_space</span><span class="p">,</span> <span class="n">state</span><span class="p">,</span> <span class="n">qtable</span><span class="p">):</span>
|
||
<span class="w"> </span><span class="sd">"""Choose an action `a` in the current world state (s)."""</span>
|
||
<span class="c1"># First we randomize a number</span>
|
||
<span class="n">explor_exploit_tradeoff</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
|
||
<span class="c1"># Exploration</span>
|
||
<span class="k">if</span> <span class="n">explor_exploit_tradeoff</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">epsilon</span><span class="p">:</span>
|
||
<span class="n">action</span> <span class="o">=</span> <span class="n">action_space</span><span class="o">.</span><span class="n">sample</span><span class="p">()</span>
|
||
|
||
<span class="c1"># Exploitation (taking the biggest Q-value for this state)</span>
|
||
<span class="k">else</span><span class="p">:</span>
|
||
<span class="c1"># Break ties randomly</span>
|
||
<span class="c1"># If all actions are the same for this state we choose a random one</span>
|
||
<span class="c1"># (otherwise `np.argmax()` would always take the first one)</span>
|
||
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">qtable</span><span class="p">[</span><span class="n">state</span><span class="p">,</span> <span class="p">:])</span> <span class="o">==</span> <span class="n">qtable</span><span class="p">[</span><span class="n">state</span><span class="p">,</span> <span class="mi">0</span><span class="p">]:</span>
|
||
<span class="n">action</span> <span class="o">=</span> <span class="n">action_space</span><span class="o">.</span><span class="n">sample</span><span class="p">()</span>
|
||
<span class="k">else</span><span class="p">:</span>
|
||
<span class="n">action</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">qtable</span><span class="p">[</span><span class="n">state</span><span class="p">,</span> <span class="p">:])</span>
|
||
<span class="k">return</span> <span class="n">action</span>
|
||
</pre></div>
|
||
</div>
|
||
</section>
|
||
<section id="running-the-environment">
|
||
<h3>Running the environment<a class="headerlink" href="#running-the-environment" title="Link to this heading">#</a></h3>
|
||
<p>Let’s instantiate the learner and the explorer.</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">learner</span> <span class="o">=</span> <span class="n">Qlearning</span><span class="p">(</span>
|
||
<span class="n">learning_rate</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">learning_rate</span><span class="p">,</span>
|
||
<span class="n">gamma</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">gamma</span><span class="p">,</span>
|
||
<span class="n">state_size</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">state_size</span><span class="p">,</span>
|
||
<span class="n">action_size</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">action_size</span><span class="p">,</span>
|
||
<span class="p">)</span>
|
||
<span class="n">explorer</span> <span class="o">=</span> <span class="n">EpsilonGreedy</span><span class="p">(</span>
|
||
<span class="n">epsilon</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">epsilon</span><span class="p">,</span>
|
||
<span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>This will be our main function to run our environment until the maximum
|
||
number of episodes <code class="docutils literal notranslate"><span class="pre">params.total_episodes</span></code>. To account for
|
||
stochasticity, we will also run our environment a few times.</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">run_env</span><span class="p">():</span>
|
||
<span class="n">rewards</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="n">params</span><span class="o">.</span><span class="n">total_episodes</span><span class="p">,</span> <span class="n">params</span><span class="o">.</span><span class="n">n_runs</span><span class="p">))</span>
|
||
<span class="n">steps</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="n">params</span><span class="o">.</span><span class="n">total_episodes</span><span class="p">,</span> <span class="n">params</span><span class="o">.</span><span class="n">n_runs</span><span class="p">))</span>
|
||
<span class="n">episodes</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">params</span><span class="o">.</span><span class="n">total_episodes</span><span class="p">)</span>
|
||
<span class="n">qtables</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="n">params</span><span class="o">.</span><span class="n">n_runs</span><span class="p">,</span> <span class="n">params</span><span class="o">.</span><span class="n">state_size</span><span class="p">,</span> <span class="n">params</span><span class="o">.</span><span class="n">action_size</span><span class="p">))</span>
|
||
<span class="n">all_states</span> <span class="o">=</span> <span class="p">[]</span>
|
||
<span class="n">all_actions</span> <span class="o">=</span> <span class="p">[]</span>
|
||
|
||
<span class="k">for</span> <span class="n">run</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">params</span><span class="o">.</span><span class="n">n_runs</span><span class="p">):</span> <span class="c1"># Run several times to account for stochasticity</span>
|
||
<span class="n">learner</span><span class="o">.</span><span class="n">reset_qtable</span><span class="p">()</span> <span class="c1"># Reset the Q-table between runs</span>
|
||
|
||
<span class="k">for</span> <span class="n">episode</span> <span class="ow">in</span> <span class="n">tqdm</span><span class="p">(</span>
|
||
<span class="n">episodes</span><span class="p">,</span> <span class="n">desc</span><span class="o">=</span><span class="sa">f</span><span class="s2">"Run </span><span class="si">{</span><span class="n">run</span><span class="si">}</span><span class="s2">/</span><span class="si">{</span><span class="n">params</span><span class="o">.</span><span class="n">n_runs</span><span class="si">}</span><span class="s2"> - Episodes"</span><span class="p">,</span> <span class="n">leave</span><span class="o">=</span><span class="kc">False</span>
|
||
<span class="p">):</span>
|
||
<span class="n">state</span> <span class="o">=</span> <span class="n">env</span><span class="o">.</span><span class="n">reset</span><span class="p">(</span><span class="n">seed</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">seed</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># Reset the environment</span>
|
||
<span class="n">step</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<span class="n">done</span> <span class="o">=</span> <span class="kc">False</span>
|
||
<span class="n">total_rewards</span> <span class="o">=</span> <span class="mi">0</span>
|
||
|
||
<span class="k">while</span> <span class="ow">not</span> <span class="n">done</span><span class="p">:</span>
|
||
<span class="n">action</span> <span class="o">=</span> <span class="n">explorer</span><span class="o">.</span><span class="n">choose_action</span><span class="p">(</span>
|
||
<span class="n">action_space</span><span class="o">=</span><span class="n">env</span><span class="o">.</span><span class="n">action_space</span><span class="p">,</span> <span class="n">state</span><span class="o">=</span><span class="n">state</span><span class="p">,</span> <span class="n">qtable</span><span class="o">=</span><span class="n">learner</span><span class="o">.</span><span class="n">qtable</span>
|
||
<span class="p">)</span>
|
||
|
||
<span class="c1"># Log all states and actions</span>
|
||
<span class="n">all_states</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
|
||
<span class="n">all_actions</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">action</span><span class="p">)</span>
|
||
|
||
<span class="c1"># Take the action (a) and observe the outcome state(s') and reward (r)</span>
|
||
<span class="n">new_state</span><span class="p">,</span> <span class="n">reward</span><span class="p">,</span> <span class="n">terminated</span><span class="p">,</span> <span class="n">truncated</span><span class="p">,</span> <span class="n">info</span> <span class="o">=</span> <span class="n">env</span><span class="o">.</span><span class="n">step</span><span class="p">(</span><span class="n">action</span><span class="p">)</span>
|
||
|
||
<span class="n">done</span> <span class="o">=</span> <span class="n">terminated</span> <span class="ow">or</span> <span class="n">truncated</span>
|
||
|
||
<span class="n">learner</span><span class="o">.</span><span class="n">qtable</span><span class="p">[</span><span class="n">state</span><span class="p">,</span> <span class="n">action</span><span class="p">]</span> <span class="o">=</span> <span class="n">learner</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
|
||
<span class="n">state</span><span class="p">,</span> <span class="n">action</span><span class="p">,</span> <span class="n">reward</span><span class="p">,</span> <span class="n">new_state</span>
|
||
<span class="p">)</span>
|
||
|
||
<span class="n">total_rewards</span> <span class="o">+=</span> <span class="n">reward</span>
|
||
<span class="n">step</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
|
||
<span class="c1"># Our new state is state</span>
|
||
<span class="n">state</span> <span class="o">=</span> <span class="n">new_state</span>
|
||
|
||
<span class="c1"># Log all rewards and steps</span>
|
||
<span class="n">rewards</span><span class="p">[</span><span class="n">episode</span><span class="p">,</span> <span class="n">run</span><span class="p">]</span> <span class="o">=</span> <span class="n">total_rewards</span>
|
||
<span class="n">steps</span><span class="p">[</span><span class="n">episode</span><span class="p">,</span> <span class="n">run</span><span class="p">]</span> <span class="o">=</span> <span class="n">step</span>
|
||
<span class="n">qtables</span><span class="p">[</span><span class="n">run</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">learner</span><span class="o">.</span><span class="n">qtable</span>
|
||
|
||
<span class="k">return</span> <span class="n">rewards</span><span class="p">,</span> <span class="n">steps</span><span class="p">,</span> <span class="n">episodes</span><span class="p">,</span> <span class="n">qtables</span><span class="p">,</span> <span class="n">all_states</span><span class="p">,</span> <span class="n">all_actions</span>
|
||
</pre></div>
|
||
</div>
|
||
</section>
|
||
<section id="visualization">
|
||
<h3>Visualization<a class="headerlink" href="#visualization" title="Link to this heading">#</a></h3>
|
||
<p>To make it easy to plot the results with Seaborn, we’ll save the main
|
||
results of the simulation in Pandas dataframes.</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">postprocess</span><span class="p">(</span><span class="n">episodes</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="n">rewards</span><span class="p">,</span> <span class="n">steps</span><span class="p">,</span> <span class="n">map_size</span><span class="p">):</span>
|
||
<span class="w"> </span><span class="sd">"""Convert the results of the simulation in dataframes."""</span>
|
||
<span class="n">res</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span>
|
||
<span class="n">data</span><span class="o">=</span><span class="p">{</span>
|
||
<span class="s2">"Episodes"</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">tile</span><span class="p">(</span><span class="n">episodes</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">n_runs</span><span class="p">),</span>
|
||
<span class="s2">"Rewards"</span><span class="p">:</span> <span class="n">rewards</span><span class="o">.</span><span class="n">flatten</span><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="s2">"F"</span><span class="p">),</span>
|
||
<span class="s2">"Steps"</span><span class="p">:</span> <span class="n">steps</span><span class="o">.</span><span class="n">flatten</span><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="s2">"F"</span><span class="p">),</span>
|
||
<span class="p">}</span>
|
||
<span class="p">)</span>
|
||
<span class="n">res</span><span class="p">[</span><span class="s2">"cum_rewards"</span><span class="p">]</span> <span class="o">=</span> <span class="n">rewards</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="s2">"F"</span><span class="p">)</span>
|
||
<span class="n">res</span><span class="p">[</span><span class="s2">"map_size"</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">map_size</span><span class="si">}</span><span class="s2">x</span><span class="si">{</span><span class="n">map_size</span><span class="si">}</span><span class="s2">"</span><span class="p">,</span> <span class="n">res</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||
|
||
<span class="n">st</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="p">{</span><span class="s2">"Episodes"</span><span class="p">:</span> <span class="n">episodes</span><span class="p">,</span> <span class="s2">"Steps"</span><span class="p">:</span> <span class="n">steps</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)})</span>
|
||
<span class="n">st</span><span class="p">[</span><span class="s2">"map_size"</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">map_size</span><span class="si">}</span><span class="s2">x</span><span class="si">{</span><span class="n">map_size</span><span class="si">}</span><span class="s2">"</span><span class="p">,</span> <span class="n">st</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||
<span class="k">return</span> <span class="n">res</span><span class="p">,</span> <span class="n">st</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>We want to plot the policy the agent has learned in the end. To do that
|
||
we will: 1. extract the best Q-values from the Q-table for each state,
|
||
2. get the corresponding best action for those Q-values, 3. map each
|
||
action to an arrow so we can visualize it.</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">qtable_directions_map</span><span class="p">(</span><span class="n">qtable</span><span class="p">,</span> <span class="n">map_size</span><span class="p">):</span>
|
||
<span class="w"> </span><span class="sd">"""Get the best learned action & map it to arrows."""</span>
|
||
<span class="n">qtable_val_max</span> <span class="o">=</span> <span class="n">qtable</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">map_size</span><span class="p">,</span> <span class="n">map_size</span><span class="p">)</span>
|
||
<span class="n">qtable_best_action</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">qtable</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">map_size</span><span class="p">,</span> <span class="n">map_size</span><span class="p">)</span>
|
||
<span class="n">directions</span> <span class="o">=</span> <span class="p">{</span><span class="mi">0</span><span class="p">:</span> <span class="s2">"←"</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span> <span class="s2">"↓"</span><span class="p">,</span> <span class="mi">2</span><span class="p">:</span> <span class="s2">"→"</span><span class="p">,</span> <span class="mi">3</span><span class="p">:</span> <span class="s2">"↑"</span><span class="p">}</span>
|
||
<span class="n">qtable_directions</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">qtable_best_action</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">str</span><span class="p">)</span>
|
||
<span class="n">eps</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="nb">float</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span> <span class="c1"># Minimum float number on the machine</span>
|
||
<span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">val</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">qtable_best_action</span><span class="o">.</span><span class="n">flatten</span><span class="p">()):</span>
|
||
<span class="k">if</span> <span class="n">qtable_val_max</span><span class="o">.</span><span class="n">flatten</span><span class="p">()[</span><span class="n">idx</span><span class="p">]</span> <span class="o">></span> <span class="n">eps</span><span class="p">:</span>
|
||
<span class="c1"># Assign an arrow only if a minimal Q-value has been learned as best action</span>
|
||
<span class="c1"># otherwise since 0 is a direction, it also gets mapped on the tiles where</span>
|
||
<span class="c1"># it didn't actually learn anything</span>
|
||
<span class="n">qtable_directions</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">directions</span><span class="p">[</span><span class="n">val</span><span class="p">]</span>
|
||
<span class="n">qtable_directions</span> <span class="o">=</span> <span class="n">qtable_directions</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">map_size</span><span class="p">,</span> <span class="n">map_size</span><span class="p">)</span>
|
||
<span class="k">return</span> <span class="n">qtable_val_max</span><span class="p">,</span> <span class="n">qtable_directions</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>With the following function, we’ll plot on the left the last frame of
|
||
the simulation. If the agent learned a good policy to solve the task, we
|
||
expect to see it on the tile of the treasure in the last frame of the
|
||
video. On the right we’ll plot the policy the agent has learned. Each
|
||
arrow will represent the best action to choose for each tile/state.</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">plot_q_values_map</span><span class="p">(</span><span class="n">qtable</span><span class="p">,</span> <span class="n">env</span><span class="p">,</span> <span class="n">map_size</span><span class="p">):</span>
|
||
<span class="w"> </span><span class="sd">"""Plot the last frame of the simulation and the policy learned."""</span>
|
||
<span class="n">qtable_val_max</span><span class="p">,</span> <span class="n">qtable_directions</span> <span class="o">=</span> <span class="n">qtable_directions_map</span><span class="p">(</span><span class="n">qtable</span><span class="p">,</span> <span class="n">map_size</span><span class="p">)</span>
|
||
|
||
<span class="c1"># Plot the last frame</span>
|
||
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">nrows</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">ncols</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
|
||
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">env</span><span class="o">.</span><span class="n">render</span><span class="p">())</span>
|
||
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
|
||
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Last frame"</span><span class="p">)</span>
|
||
|
||
<span class="c1"># Plot the policy</span>
|
||
<span class="n">sns</span><span class="o">.</span><span class="n">heatmap</span><span class="p">(</span>
|
||
<span class="n">qtable_val_max</span><span class="p">,</span>
|
||
<span class="n">annot</span><span class="o">=</span><span class="n">qtable_directions</span><span class="p">,</span>
|
||
<span class="n">fmt</span><span class="o">=</span><span class="s2">""</span><span class="p">,</span>
|
||
<span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
|
||
<span class="n">cmap</span><span class="o">=</span><span class="n">sns</span><span class="o">.</span><span class="n">color_palette</span><span class="p">(</span><span class="s2">"Blues"</span><span class="p">,</span> <span class="n">as_cmap</span><span class="o">=</span><span class="kc">True</span><span class="p">),</span>
|
||
<span class="n">linewidths</span><span class="o">=</span><span class="mf">0.7</span><span class="p">,</span>
|
||
<span class="n">linecolor</span><span class="o">=</span><span class="s2">"black"</span><span class="p">,</span>
|
||
<span class="n">xticklabels</span><span class="o">=</span><span class="p">[],</span>
|
||
<span class="n">yticklabels</span><span class="o">=</span><span class="p">[],</span>
|
||
<span class="n">annot_kws</span><span class="o">=</span><span class="p">{</span><span class="s2">"fontsize"</span><span class="p">:</span> <span class="s2">"xx-large"</span><span class="p">},</span>
|
||
<span class="p">)</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s2">"Learned Q-values</span><span class="se">\n</span><span class="s2">Arrows represent best action"</span><span class="p">)</span>
|
||
<span class="k">for</span> <span class="n">_</span><span class="p">,</span> <span class="n">spine</span> <span class="ow">in</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">spines</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
|
||
<span class="n">spine</span><span class="o">.</span><span class="n">set_visible</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
|
||
<span class="n">spine</span><span class="o">.</span><span class="n">set_linewidth</span><span class="p">(</span><span class="mf">0.7</span><span class="p">)</span>
|
||
<span class="n">spine</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s2">"black"</span><span class="p">)</span>
|
||
<span class="n">img_title</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">"frozenlake_q_values_</span><span class="si">{</span><span class="n">map_size</span><span class="si">}</span><span class="s2">x</span><span class="si">{</span><span class="n">map_size</span><span class="si">}</span><span class="s2">.png"</span>
|
||
<span class="n">fig</span><span class="o">.</span><span class="n">savefig</span><span class="p">(</span><span class="n">params</span><span class="o">.</span><span class="n">savefig_folder</span> <span class="o">/</span> <span class="n">img_title</span><span class="p">,</span> <span class="n">bbox_inches</span><span class="o">=</span><span class="s2">"tight"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>As a sanity check, we will plot the distributions of states and actions
|
||
with the following function:</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">plot_states_actions_distribution</span><span class="p">(</span><span class="n">states</span><span class="p">,</span> <span class="n">actions</span><span class="p">,</span> <span class="n">map_size</span><span class="p">):</span>
|
||
<span class="w"> </span><span class="sd">"""Plot the distributions of states and actions."""</span>
|
||
<span class="n">labels</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"LEFT"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"DOWN"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"RIGHT"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s2">"UP"</span><span class="p">:</span> <span class="mi">3</span><span class="p">}</span>
|
||
|
||
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">nrows</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">ncols</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
|
||
<span class="n">sns</span><span class="o">.</span><span class="n">histplot</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">states</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">kde</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"States"</span><span class="p">)</span>
|
||
<span class="n">sns</span><span class="o">.</span><span class="n">histplot</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">actions</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">labels</span><span class="o">.</span><span class="n">values</span><span class="p">()),</span> <span class="n">labels</span><span class="o">=</span><span class="n">labels</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span>
|
||
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Actions"</span><span class="p">)</span>
|
||
<span class="n">fig</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
|
||
<span class="n">img_title</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">"frozenlake_states_actions_distrib_</span><span class="si">{</span><span class="n">map_size</span><span class="si">}</span><span class="s2">x</span><span class="si">{</span><span class="n">map_size</span><span class="si">}</span><span class="s2">.png"</span>
|
||
<span class="n">fig</span><span class="o">.</span><span class="n">savefig</span><span class="p">(</span><span class="n">params</span><span class="o">.</span><span class="n">savefig_folder</span> <span class="o">/</span> <span class="n">img_title</span><span class="p">,</span> <span class="n">bbox_inches</span><span class="o">=</span><span class="s2">"tight"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>Now we’ll be running our agent on a few increasing maps sizes: -
|
||
<span class="math notranslate nohighlight">\(4 \times 4\)</span>, - <span class="math notranslate nohighlight">\(7 \times 7\)</span>, - <span class="math notranslate nohighlight">\(9 \times 9\)</span>, -
|
||
<span class="math notranslate nohighlight">\(11 \times 11\)</span>.</p>
|
||
<p>Putting it all together:</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">map_sizes</span> <span class="o">=</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">11</span><span class="p">]</span>
|
||
<span class="n">res_all</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">()</span>
|
||
<span class="n">st_all</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">()</span>
|
||
|
||
<span class="k">for</span> <span class="n">map_size</span> <span class="ow">in</span> <span class="n">map_sizes</span><span class="p">:</span>
|
||
<span class="n">env</span> <span class="o">=</span> <span class="n">gym</span><span class="o">.</span><span class="n">make</span><span class="p">(</span>
|
||
<span class="s2">"FrozenLake-v1"</span><span class="p">,</span>
|
||
<span class="n">is_slippery</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">is_slippery</span><span class="p">,</span>
|
||
<span class="n">render_mode</span><span class="o">=</span><span class="s2">"rgb_array"</span><span class="p">,</span>
|
||
<span class="n">desc</span><span class="o">=</span><span class="n">generate_random_map</span><span class="p">(</span>
|
||
<span class="n">size</span><span class="o">=</span><span class="n">map_size</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">proba_frozen</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">seed</span>
|
||
<span class="p">),</span>
|
||
<span class="p">)</span>
|
||
|
||
<span class="n">params</span> <span class="o">=</span> <span class="n">params</span><span class="o">.</span><span class="n">_replace</span><span class="p">(</span><span class="n">action_size</span><span class="o">=</span><span class="n">env</span><span class="o">.</span><span class="n">action_space</span><span class="o">.</span><span class="n">n</span><span class="p">)</span>
|
||
<span class="n">params</span> <span class="o">=</span> <span class="n">params</span><span class="o">.</span><span class="n">_replace</span><span class="p">(</span><span class="n">state_size</span><span class="o">=</span><span class="n">env</span><span class="o">.</span><span class="n">observation_space</span><span class="o">.</span><span class="n">n</span><span class="p">)</span>
|
||
<span class="n">env</span><span class="o">.</span><span class="n">action_space</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span>
|
||
<span class="n">params</span><span class="o">.</span><span class="n">seed</span>
|
||
<span class="p">)</span> <span class="c1"># Set the seed to get reproducible results when sampling the action space</span>
|
||
<span class="n">learner</span> <span class="o">=</span> <span class="n">Qlearning</span><span class="p">(</span>
|
||
<span class="n">learning_rate</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">learning_rate</span><span class="p">,</span>
|
||
<span class="n">gamma</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">gamma</span><span class="p">,</span>
|
||
<span class="n">state_size</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">state_size</span><span class="p">,</span>
|
||
<span class="n">action_size</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">action_size</span><span class="p">,</span>
|
||
<span class="p">)</span>
|
||
<span class="n">explorer</span> <span class="o">=</span> <span class="n">EpsilonGreedy</span><span class="p">(</span>
|
||
<span class="n">epsilon</span><span class="o">=</span><span class="n">params</span><span class="o">.</span><span class="n">epsilon</span><span class="p">,</span>
|
||
<span class="p">)</span>
|
||
|
||
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Map size: </span><span class="si">{</span><span class="n">map_size</span><span class="si">}</span><span class="s2">x</span><span class="si">{</span><span class="n">map_size</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<span class="n">rewards</span><span class="p">,</span> <span class="n">steps</span><span class="p">,</span> <span class="n">episodes</span><span class="p">,</span> <span class="n">qtables</span><span class="p">,</span> <span class="n">all_states</span><span class="p">,</span> <span class="n">all_actions</span> <span class="o">=</span> <span class="n">run_env</span><span class="p">()</span>
|
||
|
||
<span class="c1"># Save the results in dataframes</span>
|
||
<span class="n">res</span><span class="p">,</span> <span class="n">st</span> <span class="o">=</span> <span class="n">postprocess</span><span class="p">(</span><span class="n">episodes</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="n">rewards</span><span class="p">,</span> <span class="n">steps</span><span class="p">,</span> <span class="n">map_size</span><span class="p">)</span>
|
||
<span class="n">res_all</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">concat</span><span class="p">([</span><span class="n">res_all</span><span class="p">,</span> <span class="n">res</span><span class="p">])</span>
|
||
<span class="n">st_all</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">concat</span><span class="p">([</span><span class="n">st_all</span><span class="p">,</span> <span class="n">st</span><span class="p">])</span>
|
||
<span class="n">qtable</span> <span class="o">=</span> <span class="n">qtables</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="c1"># Average the Q-table between runs</span>
|
||
|
||
<span class="n">plot_states_actions_distribution</span><span class="p">(</span>
|
||
<span class="n">states</span><span class="o">=</span><span class="n">all_states</span><span class="p">,</span> <span class="n">actions</span><span class="o">=</span><span class="n">all_actions</span><span class="p">,</span> <span class="n">map_size</span><span class="o">=</span><span class="n">map_size</span>
|
||
<span class="p">)</span> <span class="c1"># Sanity check</span>
|
||
<span class="n">plot_q_values_map</span><span class="p">(</span><span class="n">qtable</span><span class="p">,</span> <span class="n">env</span><span class="p">,</span> <span class="n">map_size</span><span class="p">)</span>
|
||
|
||
<span class="n">env</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
<section id="map-size-4-times-4">
|
||
<h4>Map size: <span class="math notranslate nohighlight">\(4 \times 4\)</span><a class="headerlink" href="#map-size-4-times-4" title="Link to this heading">#</a></h4>
|
||
<p><img alt="States actions histogram 4x4 map" src="../../../_images/frozenlake_states_actions_distrib_4x4.png" /> <img alt="Q-values 4x4 map" src="../../../_images/frozenlake_q_values_4x4.png" /></p>
|
||
</section>
|
||
<section id="map-size-7-times-7">
|
||
<h4>Map size: <span class="math notranslate nohighlight">\(7 \times 7\)</span><a class="headerlink" href="#map-size-7-times-7" title="Link to this heading">#</a></h4>
|
||
<p><img alt="States actions histogram 7x7 map" src="../../../_images/frozenlake_states_actions_distrib_7x7.png" /> <img alt="Q-values 7x7 map" src="../../../_images/frozenlake_q_values_7x7.png" /></p>
|
||
</section>
|
||
<section id="map-size-9-times-9">
|
||
<h4>Map size: <span class="math notranslate nohighlight">\(9 \times 9\)</span><a class="headerlink" href="#map-size-9-times-9" title="Link to this heading">#</a></h4>
|
||
<p><img alt="States actions histogram 9x9 map" src="../../../_images/frozenlake_states_actions_distrib_9x9.png" /> <img alt="Q-values 9x9 map" src="../../../_images/frozenlake_q_values_9x9.png" /></p>
|
||
</section>
|
||
<section id="map-size-11-times-11">
|
||
<h4>Map size: <span class="math notranslate nohighlight">\(11 \times 11\)</span><a class="headerlink" href="#map-size-11-times-11" title="Link to this heading">#</a></h4>
|
||
<p><img alt="States actions histogram 11x11 map" src="../../../_images/frozenlake_states_actions_distrib_11x11.png" /> <img alt="Q-values 11x11 map" src="../../../_images/frozenlake_q_values_11x11.png" /></p>
|
||
<p>The <code class="docutils literal notranslate"><span class="pre">DOWN</span></code> and <code class="docutils literal notranslate"><span class="pre">RIGHT</span></code> actions get chosen more often, which makes
|
||
sense as the agent starts at the top left of the map and needs to find
|
||
its way down to the bottom right. Also the bigger the map, the less
|
||
states/tiles further away from the starting state get visited.</p>
|
||
<p>To check if our agent is learning, we want to plot the cumulated sum of
|
||
rewards, as well as the number of steps needed until the end of the
|
||
episode. If our agent is learning, we expect to see the cumulated sum of
|
||
rewards to increase and the number of steps to solve the task to
|
||
decrease.</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">plot_steps_and_rewards</span><span class="p">(</span><span class="n">rewards_df</span><span class="p">,</span> <span class="n">steps_df</span><span class="p">):</span>
|
||
<span class="w"> </span><span class="sd">"""Plot the steps and rewards from dataframes."""</span>
|
||
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">nrows</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">ncols</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
|
||
<span class="n">sns</span><span class="o">.</span><span class="n">lineplot</span><span class="p">(</span>
|
||
<span class="n">data</span><span class="o">=</span><span class="n">rewards_df</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="s2">"Episodes"</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="s2">"cum_rewards"</span><span class="p">,</span> <span class="n">hue</span><span class="o">=</span><span class="s2">"map_size"</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||
<span class="p">)</span>
|
||
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">ylabel</span><span class="o">=</span><span class="s2">"Cumulated rewards"</span><span class="p">)</span>
|
||
|
||
<span class="n">sns</span><span class="o">.</span><span class="n">lineplot</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">steps_df</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="s2">"Episodes"</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="s2">"Steps"</span><span class="p">,</span> <span class="n">hue</span><span class="o">=</span><span class="s2">"map_size"</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">ylabel</span><span class="o">=</span><span class="s2">"Averaged steps number"</span><span class="p">)</span>
|
||
|
||
<span class="k">for</span> <span class="n">axi</span> <span class="ow">in</span> <span class="n">ax</span><span class="p">:</span>
|
||
<span class="n">axi</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s2">"map size"</span><span class="p">)</span>
|
||
<span class="n">fig</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
|
||
<span class="n">img_title</span> <span class="o">=</span> <span class="s2">"frozenlake_steps_and_rewards.png"</span>
|
||
<span class="n">fig</span><span class="o">.</span><span class="n">savefig</span><span class="p">(</span><span class="n">params</span><span class="o">.</span><span class="n">savefig_folder</span> <span class="o">/</span> <span class="n">img_title</span><span class="p">,</span> <span class="n">bbox_inches</span><span class="o">=</span><span class="s2">"tight"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
|
||
|
||
<span class="n">plot_steps_and_rewards</span><span class="p">(</span><span class="n">res_all</span><span class="p">,</span> <span class="n">st_all</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
<p><img alt="Steps and rewards" src="../../../_images/frozenlake_steps_and_rewards.png" /></p>
|
||
<p>On the <span class="math notranslate nohighlight">\(4 \times 4\)</span> map, learning converges pretty quickly,
|
||
whereas on the <span class="math notranslate nohighlight">\(7 \times 7\)</span> map, the agent needs <span class="math notranslate nohighlight">\(\sim 300\)</span>
|
||
episodes, on the <span class="math notranslate nohighlight">\(9 \times 9\)</span> map it needs <span class="math notranslate nohighlight">\(\sim 800\)</span>
|
||
episodes, and the <span class="math notranslate nohighlight">\(11 \times 11\)</span> map, it needs <span class="math notranslate nohighlight">\(\sim 1800\)</span>
|
||
episodes to converge. Interestingly, the agent seems to be getting more
|
||
rewards on the <span class="math notranslate nohighlight">\(9 \times 9\)</span> map than on the <span class="math notranslate nohighlight">\(7 \times 7\)</span>
|
||
map, which could mean it didn’t reach an optimal policy on the
|
||
<span class="math notranslate nohighlight">\(7 \times 7\)</span> map.</p>
|
||
<p>In the end, if agent doesn’t get any rewards, rewards don’t get
|
||
propagated in the Q-values, and the agent doesn’t learn anything. In my
|
||
experience on this environment using <span class="math notranslate nohighlight">\(\epsilon\)</span>-greedy and those
|
||
hyperparameters and environment settings, maps having more than
|
||
<span class="math notranslate nohighlight">\(11 \times 11\)</span> tiles start to be difficult to solve. Maybe using a
|
||
different exploration algorithm could overcome this. The other parameter
|
||
having a big impact is the <code class="docutils literal notranslate"><span class="pre">proba_frozen</span></code>, the probability of the tile
|
||
being frozen. With too many holes, i.e. <span class="math notranslate nohighlight">\(p<0.9\)</span>, Q-learning is
|
||
having a hard time in not falling into holes and getting a reward
|
||
signal.</p>
|
||
</section>
|
||
</section>
|
||
</section>
|
||
<section id="references">
|
||
<h2>References<a class="headerlink" href="#references" title="Link to this heading">#</a></h2>
|
||
<ul class="simple">
|
||
<li><p>Code inspired by <a class="reference external" href="https://simoninithomas.github.io/Deep_reinforcement_learning_Course/">Deep Reinforcement Learning
|
||
Course</a>
|
||
by Thomas Simonini (<a class="reference external" href="http://simoninithomas.com/">http://simoninithomas.com/</a>)</p></li>
|
||
<li><p><a class="reference external" href="https://mpatacchiola.github.io/blog/2017/01/15/dissecting-reinforcement-learning-2.html">Dissecting Reinforcement
|
||
Learning-Part.2</a></p></li>
|
||
<li><p><a class="reference external" href="https://www.davidsilver.uk/teaching/">David Silver’s course</a> in
|
||
particular lesson 4 and lesson 5</p></li>
|
||
<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Q-learning">Q-learning article on
|
||
Wikipedia</a></p></li>
|
||
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|
||
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|
||
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|
||
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|
||
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|
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|
||
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|
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|
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