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<li class="toctree-l1 current current-page"><a class="current reference internal" href="#">Solving Blackjack with Q-Learning</a></li>
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<article role="main">
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||
<section id="solving-blackjack-with-q-learning">
|
||
<h1>Solving Blackjack with Q-Learning<a class="headerlink" href="#solving-blackjack-with-q-learning" title="Permalink to this heading">#</a></h1>
|
||
<a class="reference internal image-reference" href="../../_images/blackjack_AE_loop.jpg"><img alt="agent-environment-diagram" src="../../_images/blackjack_AE_loop.jpg" style="width: 650px;" /></a>
|
||
<p>In this tutorial, we’ll explore and solve the <em>Blackjack-v1</em>
|
||
environment.</p>
|
||
<p><strong>Blackjack</strong> is one of the most popular casino card games that is also
|
||
infamous for being beatable under certain conditions. This version of
|
||
the game uses an infinite deck (we draw the cards with replacement), so
|
||
counting cards won’t be a viable strategy in our simulated game.</p>
|
||
<p><strong>Objective</strong>: To win, your card sum should be greater than than the
|
||
dealers without exceeding 21.</p>
|
||
<p><strong>Approach</strong>: To solve this environment by yourself, you can pick your
|
||
favorite discrete RL algorithm. The presented solution uses <em>Q-learning</em>
|
||
(a model-free RL algorithm).</p>
|
||
<section id="imports-and-environment-setup">
|
||
<h2>Imports and Environment Setup<a class="headerlink" href="#imports-and-environment-setup" title="Permalink to this heading">#</a></h2>
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Till Zemann</span>
|
||
<span class="c1"># License: MIT License</span>
|
||
|
||
<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
|
||
|
||
<span class="kn">import</span> <span class="nn">gym</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">seaborn</span> <span class="k">as</span> <span class="nn">sns</span>
|
||
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>
|
||
<span class="kn">from</span> <span class="nn">matplotlib.patches</span> <span class="kn">import</span> <span class="n">Patch</span>
|
||
|
||
<span class="c1"># Let's start by creating the blackjack environment.</span>
|
||
<span class="c1"># Note: We are going to follow the rules from Sutton & Barto.</span>
|
||
<span class="c1"># Other versions of the game can be found below for you to experiment.</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">"Blackjack-v1"</span><span class="p">,</span> <span class="n">sab</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
<div class="highlight-py notranslate"><div class="highlight"><pre><span></span># Other possible environment configurations:
|
||
|
||
env = gym.make('Blackjack-v1', natural=True, sab=False)``
|
||
|
||
env = gym.make('Blackjack-v1', natural=False, sab=False)``
|
||
</pre></div>
|
||
</div>
|
||
</section>
|
||
<section id="observing-the-environment">
|
||
<h2>Observing the environment<a class="headerlink" href="#observing-the-environment" title="Permalink to this heading">#</a></h2>
|
||
<p>First of all, we call <code class="docutils literal notranslate"><span class="pre">env.reset()</span></code> to start an episode. This function
|
||
resets the environment to a starting position and returns an initial
|
||
<code class="docutils literal notranslate"><span class="pre">observation</span></code>. We usually also set <code class="docutils literal notranslate"><span class="pre">done</span> <span class="pre">=</span> <span class="pre">False</span></code>. This variable
|
||
will be useful later to check if a game is terminated. In this tutorial
|
||
we will use the terms observation and state synonymously but in more
|
||
complex problems a state might differ from the observation it is based
|
||
on.</p>
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># reset the environment to get the first observation</span>
|
||
<span class="n">done</span> <span class="o">=</span> <span class="kc">False</span>
|
||
<span class="n">observation</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">reset</span><span class="p">()</span>
|
||
|
||
<span class="nb">print</span><span class="p">(</span><span class="n">observation</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>Note that our observation is a 3-tuple consisting of 3 discrete values:</p>
|
||
<ul class="simple">
|
||
<li><p>The players current sum</p></li>
|
||
<li><p>Value of the dealers face-up card</p></li>
|
||
<li><p>Boolean whether the player holds a usable ace (An ace is usable if it
|
||
counts as 11 without busting)</p></li>
|
||
</ul>
|
||
</section>
|
||
<section id="executing-an-action">
|
||
<h2>Executing an action<a class="headerlink" href="#executing-an-action" title="Permalink to this heading">#</a></h2>
|
||
<p>After receiving our first observation, we are only going to use the
|
||
<code class="docutils literal notranslate"><span class="pre">env.step(action)</span></code> function to interact with the environment. This
|
||
function takes an action as input and executes it in the environment.
|
||
Because that action changes the state of the environment, it returns
|
||
four useful variables to us. These are:</p>
|
||
<ul class="simple">
|
||
<li><p><code class="docutils literal notranslate"><span class="pre">next_state</span></code>: This is the observation that the agent will receive
|
||
after taking the action.</p></li>
|
||
<li><p><code class="docutils literal notranslate"><span class="pre">reward</span></code>: This is the reward that the agent will receive after
|
||
taking the action.</p></li>
|
||
<li><p><code class="docutils literal notranslate"><span class="pre">terminated</span></code>: This is a boolean variable that indicates whether or
|
||
not the episode is over.</p></li>
|
||
<li><p><code class="docutils literal notranslate"><span class="pre">truncated</span></code>: This is a boolean variable that also indicates whether
|
||
the episode ended by early truncation.</p></li>
|
||
<li><p><code class="docutils literal notranslate"><span class="pre">info</span></code>: This is a dictionary that might contain additional
|
||
information about the environment.</p></li>
|
||
</ul>
|
||
<p>The <code class="docutils literal notranslate"><span class="pre">next_state</span></code>, <code class="docutils literal notranslate"><span class="pre">reward</span></code>, and <code class="docutils literal notranslate"><span class="pre">done</span></code> variables are
|
||
self-explanatory, but the <code class="docutils literal notranslate"><span class="pre">info</span></code> variable requires some additional
|
||
explanation. This variable contains a dictionary that might have some
|
||
extra information about the environment, but in the Blackjack-v1
|
||
environment you can ignore it. For example in Atari environments the
|
||
info dictionary has a <code class="docutils literal notranslate"><span class="pre">ale.lives</span></code> key that tells us how many lives the
|
||
agent has left. If the agent has 0 lives, then the episode is over.</p>
|
||
<p>Blackjack-v1 doesn’t have a <code class="docutils literal notranslate"><span class="pre">env.render()</span></code> function to render the
|
||
environment, but in other environments you can use this function to
|
||
watch the agent play. Important to note is that using <code class="docutils literal notranslate"><span class="pre">env.render()</span></code>
|
||
is optional - the environment is going to work even if you don’t render
|
||
it, but it can be helpful to see an episode rendered out to get an idea
|
||
of how the current policy behaves. Note that it is not a good idea to
|
||
call this function in your training loop because rendering slows down
|
||
training by a lot. Rather try to build an extra loop to evaluate and
|
||
showcase the agent after training.</p>
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># sample a random action from all valid actions</span>
|
||
<span class="n">action</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">sample</span><span class="p">()</span>
|
||
|
||
<span class="c1"># execute the action in our environment and receive infos from the environment</span>
|
||
<span class="n">observation</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="nb">print</span><span class="p">(</span><span class="s2">"observation:"</span><span class="p">,</span> <span class="n">observation</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"reward:"</span><span class="p">,</span> <span class="n">reward</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"terminated:"</span><span class="p">,</span> <span class="n">terminated</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"truncated:"</span><span class="p">,</span> <span class="n">truncated</span><span class="p">)</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="s2">"info:"</span><span class="p">,</span> <span class="n">info</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>Once <code class="docutils literal notranslate"><span class="pre">terminated</span> <span class="pre">=</span> <span class="pre">True</span></code> or <code class="docutils literal notranslate"><span class="pre">truncated=True</span></code>, we should stop the
|
||
current episode and begin a new one with <code class="docutils literal notranslate"><span class="pre">env.reset()</span></code>. If you
|
||
continue executing act`ons without resetting the environment, it still
|
||
responds but the output won’t be useful for training (it might even be
|
||
harmful if the agent learns on invalid data).</p>
|
||
</section>
|
||
<section id="building-an-agent">
|
||
<h2>Building an agent<a class="headerlink" href="#building-an-agent" title="Permalink to this heading">#</a></h2>
|
||
<p>Let’s build a <code class="docutils literal notranslate"><span class="pre">Q-learning</span> <span class="pre">agent</span></code> to solve <em>Blackjack-v1</em>! We’ll need
|
||
some functions for picking an action and updating the agents action
|
||
values. To ensure that the agents expores the environment, one possible
|
||
solution is the <code class="docutils literal notranslate"><span class="pre">epsilon-greedy</span></code> strategy, where we pick a random
|
||
action with the percentage <code class="docutils literal notranslate"><span class="pre">epsilon</span></code> and the greedy action (currently
|
||
valued as the best) <code class="docutils literal notranslate"><span class="pre">1</span> <span class="pre">-</span> <span class="pre">epsilon</span></code>.</p>
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">BlackjackAgent</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">lr</span><span class="o">=</span><span class="mf">1e-3</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">epsilon_decay</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">):</span>
|
||
<span class="sd">"""</span>
|
||
<span class="sd"> Initialize an Reinforcement Learning agent with an empty dictionary</span>
|
||
<span class="sd"> of state-action values (q_values), a learning rate and an epsilon.</span>
|
||
<span class="sd"> """</span>
|
||
<span class="bp">self</span><span class="o">.</span><span class="n">q_values</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span>
|
||
<span class="k">lambda</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</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">n</span><span class="p">)</span>
|
||
<span class="p">)</span> <span class="c1"># maps a state to action values</span>
|
||
<span class="bp">self</span><span class="o">.</span><span class="n">lr</span> <span class="o">=</span> <span class="n">lr</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="bp">self</span><span class="o">.</span><span class="n">epsilon_decay</span> <span class="o">=</span> <span class="n">epsilon_decay</span>
|
||
|
||
<span class="k">def</span> <span class="nf">get_action</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="sd">"""</span>
|
||
<span class="sd"> Returns the best action with probability (1 - epsilon)</span>
|
||
<span class="sd"> and a random action with probability epsilon to ensure exploration.</span>
|
||
<span class="sd"> """</span>
|
||
<span class="c1"># with probability epsilon return a random action to explore the environment</span>
|
||
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</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">env</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"># with probability (1 - epsilon) act greedily (exploit)</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="bp">self</span><span class="o">.</span><span class="n">q_values</span><span class="p">[</span><span class="n">state</span><span class="p">])</span>
|
||
<span class="k">return</span> <span class="n">action</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">next_state</span><span class="p">,</span> <span class="n">done</span><span class="p">):</span>
|
||
<span class="sd">"""</span>
|
||
<span class="sd"> Updates the Q-value of an action.</span>
|
||
<span class="sd"> """</span>
|
||
<span class="n">old_q_value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">q_values</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">max_future_q</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">q_values</span><span class="p">[</span><span class="n">next_state</span><span class="p">])</span>
|
||
<span class="n">target</span> <span class="o">=</span> <span class="n">reward</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">lr</span> <span class="o">*</span> <span class="n">max_future_q</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">done</span><span class="p">)</span>
|
||
<span class="bp">self</span><span class="o">.</span><span class="n">q_values</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="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">lr</span><span class="p">)</span> <span class="o">*</span> <span class="n">old_q_value</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">lr</span> <span class="o">*</span> <span class="n">target</span>
|
||
|
||
<span class="k">def</span> <span class="nf">decay_epsilon</span><span class="p">(</span><span class="bp">self</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="bp">self</span><span class="o">.</span><span class="n">epsilon</span> <span class="o">-</span> <span class="n">epsilon_decay</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>To train the agent, we will let the agent play one episode (one complete
|
||
game is called an episode) at a time and then update it’s Q-values after
|
||
each episode. The agent will have to experience a lot of episodes to
|
||
explore the environment sufficiently.</p>
|
||
<p>Now we should be ready to build the training loop.</p>
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># hyperparameters</span>
|
||
<span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">1e-3</span>
|
||
<span class="n">start_epsilon</span> <span class="o">=</span> <span class="mf">0.8</span>
|
||
<span class="n">n_episodes</span> <span class="o">=</span> <span class="mi">200_000</span>
|
||
<span class="n">epsilon_decay</span> <span class="o">=</span> <span class="n">start_epsilon</span> <span class="o">/</span> <span class="n">n_episodes</span> <span class="c1"># less exploration over time</span>
|
||
|
||
<span class="n">agent</span> <span class="o">=</span> <span class="n">BlackjackAgent</span><span class="p">(</span>
|
||
<span class="n">lr</span><span class="o">=</span><span class="n">learning_rate</span><span class="p">,</span> <span class="n">epsilon</span><span class="o">=</span><span class="n">start_epsilon</span><span class="p">,</span> <span class="n">epsilon_decay</span><span class="o">=</span><span class="n">epsilon_decay</span>
|
||
<span class="p">)</span>
|
||
|
||
|
||
<span class="k">def</span> <span class="nf">train</span><span class="p">(</span><span class="n">agent</span><span class="p">,</span> <span class="n">n_episodes</span><span class="p">):</span>
|
||
<span class="k">for</span> <span class="n">episode</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_episodes</span><span class="p">):</span>
|
||
|
||
<span class="c1"># reset the environment</span>
|
||
<span class="n">state</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">reset</span><span class="p">()</span>
|
||
<span class="n">done</span> <span class="o">=</span> <span class="kc">False</span>
|
||
|
||
<span class="c1"># play one episode</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">agent</span><span class="o">.</span><span class="n">get_action</span><span class="p">(</span><span class="n">observation</span><span class="p">)</span>
|
||
<span class="n">next_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="p">(</span>
|
||
<span class="n">terminated</span> <span class="ow">or</span> <span class="n">truncated</span>
|
||
<span class="p">)</span> <span class="c1"># if the episode terminated or was truncated early, set done to True</span>
|
||
<span class="n">agent</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">next_state</span><span class="p">,</span> <span class="n">done</span><span class="p">)</span>
|
||
<span class="n">state</span> <span class="o">=</span> <span class="n">next_state</span>
|
||
|
||
<span class="n">agent</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">next_state</span><span class="p">,</span> <span class="n">done</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>Great, let’s train!</p>
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">train</span><span class="p">(</span><span class="n">agent</span><span class="p">,</span> <span class="n">n_episodes</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
</section>
|
||
<section id="visualizing-the-results">
|
||
<h2>Visualizing the results<a class="headerlink" href="#visualizing-the-results" title="Permalink to this heading">#</a></h2>
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">create_grids</span><span class="p">(</span><span class="n">agent</span><span class="p">,</span> <span class="n">usable_ace</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||
|
||
<span class="c1"># convert our state-action values to state values</span>
|
||
<span class="c1"># and build a policy dictionary that maps observations to actions</span>
|
||
<span class="n">V</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">float</span><span class="p">)</span>
|
||
<span class="n">policy</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">int</span><span class="p">)</span>
|
||
<span class="k">for</span> <span class="n">obs</span><span class="p">,</span> <span class="n">action_values</span> <span class="ow">in</span> <span class="n">agent</span><span class="o">.</span><span class="n">q_values</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
|
||
<span class="n">V</span><span class="p">[</span><span class="n">obs</span><span class="p">]</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="n">action_values</span><span class="p">)</span>
|
||
<span class="n">policy</span><span class="p">[</span><span class="n">obs</span><span class="p">]</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">action_values</span><span class="p">)</span>
|
||
|
||
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span>
|
||
<span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">22</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">11</span><span class="p">)</span> <span class="c1"># players count</span>
|
||
<span class="p">)</span> <span class="c1"># dealers face-up card</span>
|
||
|
||
<span class="c1"># create the value grid for plotting</span>
|
||
<span class="n">Z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">apply_along_axis</span><span class="p">(</span>
|
||
<span class="k">lambda</span> <span class="n">obs</span><span class="p">:</span> <span class="n">V</span><span class="p">[(</span><span class="n">obs</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">obs</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">usable_ace</span><span class="p">)],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">arr</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">dstack</span><span class="p">([</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">])</span>
|
||
<span class="p">)</span>
|
||
<span class="n">value_grid</span> <span class="o">=</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span>
|
||
|
||
<span class="c1"># create the policy grid for plotting</span>
|
||
<span class="n">policy_grid</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">apply_along_axis</span><span class="p">(</span>
|
||
<span class="k">lambda</span> <span class="n">obs</span><span class="p">:</span> <span class="n">policy</span><span class="p">[(</span><span class="n">obs</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">obs</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">usable_ace</span><span class="p">)],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">arr</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">dstack</span><span class="p">([</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">])</span>
|
||
<span class="p">)</span>
|
||
<span class="k">return</span> <span class="n">value_grid</span><span class="p">,</span> <span class="n">policy_grid</span>
|
||
|
||
|
||
<span class="k">def</span> <span class="nf">create_plots</span><span class="p">(</span><span class="n">value_grid</span><span class="p">,</span> <span class="n">policy_grid</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s2">"N/A"</span><span class="p">):</span>
|
||
|
||
<span class="c1"># create a new figure with 2 subplots (left: state values, right: policy)</span>
|
||
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span> <span class="o">=</span> <span class="n">value_grid</span>
|
||
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">figaspect</span><span class="p">(</span><span class="mf">0.4</span><span class="p">))</span>
|
||
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="n">title</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">16</span><span class="p">)</span>
|
||
|
||
<span class="c1"># plot the state values</span>
|
||
<span class="n">ax1</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">projection</span><span class="o">=</span><span class="s2">"3d"</span><span class="p">)</span>
|
||
<span class="n">ax1</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">rstride</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">cstride</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s2">"viridis"</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s2">"none"</span><span class="p">)</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">xticks</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">22</span><span class="p">),</span> <span class="nb">range</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">22</span><span class="p">))</span>
|
||
<span class="n">plt</span><span class="o">.</span><span class="n">yticks</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">11</span><span class="p">),</span> <span class="p">[</span><span class="s2">"A"</span><span class="p">]</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">11</span><span class="p">)))</span>
|
||
<span class="n">ax1</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"State values: "</span> <span class="o">+</span> <span class="n">title</span><span class="p">)</span>
|
||
<span class="n">ax1</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Player sum"</span><span class="p">)</span>
|
||
<span class="n">ax1</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">"Dealer showing"</span><span class="p">)</span>
|
||
<span class="n">ax1</span><span class="o">.</span><span class="n">zaxis</span><span class="o">.</span><span class="n">set_rotate_label</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
|
||
<span class="n">ax1</span><span class="o">.</span><span class="n">set_zlabel</span><span class="p">(</span><span class="s2">"Value"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">14</span><span class="p">,</span> <span class="n">rotation</span><span class="o">=</span><span class="mi">90</span><span class="p">)</span>
|
||
<span class="n">ax1</span><span class="o">.</span><span class="n">view_init</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">220</span><span class="p">)</span>
|
||
|
||
<span class="c1"># plot the policy</span>
|
||
<span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||
<span class="n">ax2</span> <span class="o">=</span> <span class="n">sns</span><span class="o">.</span><span class="n">heatmap</span><span class="p">(</span><span class="n">policy_grid</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">annot</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s2">"Accent_r"</span><span class="p">,</span> <span class="n">cbar</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
|
||
<span class="n">ax2</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Policy: "</span> <span class="o">+</span> <span class="n">title</span><span class="p">)</span>
|
||
<span class="n">ax2</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Player sum"</span><span class="p">)</span>
|
||
<span class="n">ax2</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">"Dealer showing"</span><span class="p">)</span>
|
||
<span class="n">ax2</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">22</span><span class="p">))</span>
|
||
<span class="n">ax2</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">([</span><span class="s2">"A"</span><span class="p">]</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">11</span><span class="p">)),</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
|
||
|
||
<span class="c1"># add a legend</span>
|
||
<span class="n">legend_elements</span> <span class="o">=</span> <span class="p">[</span>
|
||
<span class="n">Patch</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s2">"lightgreen"</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s2">"black"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Hit"</span><span class="p">),</span>
|
||
<span class="n">Patch</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s2">"grey"</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s2">"black"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Stick"</span><span class="p">),</span>
|
||
<span class="p">]</span>
|
||
<span class="n">ax2</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">handles</span><span class="o">=</span><span class="n">legend_elements</span><span class="p">,</span> <span class="n">bbox_to_anchor</span><span class="o">=</span><span class="p">(</span><span class="mf">1.3</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
|
||
<span class="k">return</span> <span class="n">fig</span>
|
||
|
||
|
||
<span class="c1"># state values & policy with usable ace (ace counts as 11)</span>
|
||
<span class="n">value_grid</span><span class="p">,</span> <span class="n">policy_grid</span> <span class="o">=</span> <span class="n">create_grids</span><span class="p">(</span><span class="n">agent</span><span class="p">,</span> <span class="n">usable_ace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
<span class="n">fig1</span> <span class="o">=</span> <span class="n">create_plots</span><span class="p">(</span><span class="n">value_grid</span><span class="p">,</span> <span class="n">policy_grid</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s2">"With usable ace"</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>
|
||
<img alt="../../_images/blackjack_with_usable_ace.png" src="../../_images/blackjack_with_usable_ace.png" />
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># state values & policy without usable ace (ace counts as 1)</span>
|
||
<span class="n">value_grid</span><span class="p">,</span> <span class="n">policy_grid</span> <span class="o">=</span> <span class="n">create_grids</span><span class="p">(</span><span class="n">agent</span><span class="p">,</span> <span class="n">usable_ace</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
|
||
<span class="n">fig2</span> <span class="o">=</span> <span class="n">create_plots</span><span class="p">(</span><span class="n">value_grid</span><span class="p">,</span> <span class="n">policy_grid</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s2">"Without usable ace"</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>
|
||
<img alt="../../_images/blackjack_without_usable_ace.png" src="../../_images/blackjack_without_usable_ace.png" />
|
||
<p>It’s good practice to call env.close() at the end of your script,
|
||
so that any used resources by the environment will be closed.</p>
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">env</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>Hopefully this Tutorial helped you get a grip of how to interact with
|
||
OpenAI-Gym environments and sets you on a journey to solve many more RL
|
||
challenges.</p>
|
||
<p>It is recommended that you solve this environment by yourself (project
|
||
based learning is really effective!). You can apply your favorite
|
||
discrete RL algorithm or give Monte Carlo ES a try (covered in <a class="reference external" href="http://incompleteideas.net/book/the-book-2nd.html">Sutton &
|
||
Barto</a>, section
|
||
5.3) - this way you can compare your results directly to the book.</p>
|
||
<p>Best of fun!</p>
|
||
<div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-tutorials-blackjack-tutorial-py">
|
||
<div class="sphx-glr-download sphx-glr-download-python docutils container">
|
||
<p><a class="reference download internal" download="" href="../../_downloads/7784aa5068fc88abcafc19118c52cbb7/blackjack_tutorial.py"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Python</span> <span class="pre">source</span> <span class="pre">code:</span> <span class="pre">blackjack_tutorial.py</span></code></a></p>
|
||
</div>
|
||
<div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
|
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<p><a class="reference download internal" download="" href="../../_downloads/b0e7aa582a7b3c32ccdef133cbd779c5/blackjack_tutorial.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">blackjack_tutorial.ipynb</span></code></a></p>
|
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<li><a class="reference internal" href="#">Solving Blackjack with Q-Learning</a><ul>
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<li><a class="reference internal" href="#imports-and-environment-setup">Imports and Environment Setup</a></li>
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<li><a class="reference internal" href="#observing-the-environment">Observing the environment</a></li>
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<li><a class="reference internal" href="#executing-an-action">Executing an action</a></li>
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