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<p class="caption" role="heading"><span class="caption-text">Introduction</span></p>
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<article role="main">
<section id="spaces">
<h1>Spaces<a class="headerlink" href="#spaces" title="Permalink to this heading">#</a></h1>
<div class="toctree-wrapper compound">
</div>
<dl class="py class">
<dt class="sig sig-object py" id="gymnasium.spaces.Space">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">gymnasium.spaces.</span></span><span class="sig-name descname"><span class="pre">Space</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">Type</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">str</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">dtype</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seed</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Generator</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#gymnasium.spaces.Space" title="Permalink to this definition">#</a></dt>
<dd><p>Superclass that is used to define observation and action spaces.</p>
<p>Spaces are crucially used in Gym to define the format of valid actions and observations.
They serve various purposes:</p>
<ul class="simple">
<li><p>They clearly define how to interact with environments, i.e. they specify what actions need to look like
and what observations will look like</p></li>
<li><p>They allow us to work with highly structured data (e.g. in the form of elements of <a class="reference internal" href="composite/#gymnasium.spaces.Dict" title="gymnasium.spaces.Dict"><code class="xref py py-class docutils literal notranslate"><span class="pre">Dict</span></code></a> spaces)
and painlessly transform them into flat arrays that can be used in learning code</p></li>
<li><p>They provide a method to sample random elements. This is especially useful for exploration and debugging.</p></li>
</ul>
<p>Different spaces can be combined hierarchically via container spaces (<a class="reference internal" href="composite/#gymnasium.spaces.Tuple" title="gymnasium.spaces.Tuple"><code class="xref py py-class docutils literal notranslate"><span class="pre">Tuple</span></code></a> and <a class="reference internal" href="composite/#gymnasium.spaces.Dict" title="gymnasium.spaces.Dict"><code class="xref py py-class docutils literal notranslate"><span class="pre">Dict</span></code></a>) to build a
more expressive space</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>Custom observation &amp; action spaces can inherit from the <code class="docutils literal notranslate"><span class="pre">Space</span></code>
class. However, most use-cases should be covered by the existing space
classes (e.g. <a class="reference internal" href="fundamental/#gymnasium.spaces.Box" title="gymnasium.spaces.Box"><code class="xref py py-class docutils literal notranslate"><span class="pre">Box</span></code></a>, <a class="reference internal" href="fundamental/#gymnasium.spaces.Discrete" title="gymnasium.spaces.Discrete"><code class="xref py py-class docutils literal notranslate"><span class="pre">Discrete</span></code></a>, etc…), and container classes (:class`Tuple` &amp;
<a class="reference internal" href="composite/#gymnasium.spaces.Dict" title="gymnasium.spaces.Dict"><code class="xref py py-class docutils literal notranslate"><span class="pre">Dict</span></code></a>). Note that parametrized probability distributions (through the
<a class="reference internal" href="#gymnasium.spaces.Space.sample" title="gymnasium.spaces.Space.sample"><code class="xref py py-meth docutils literal notranslate"><span class="pre">Space.sample()</span></code></a> method), and batching functions (in <code class="xref py py-class docutils literal notranslate"><span class="pre">gymnasium.vector.VectorEnv</span></code>), are
only well-defined for instances of spaces provided in gymnasium by default.
Moreover, some implementations of Reinforcement Learning algorithms might
not handle custom spaces properly. Use custom spaces with care.</p>
</div>
<p>Constructor of <a class="reference internal" href="#gymnasium.spaces.Space" title="gymnasium.spaces.Space"><code class="xref py py-class docutils literal notranslate"><span class="pre">Space</span></code></a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>shape</strong> (<em>Optional</em><em>[</em><a class="reference internal" href="composite/#gymnasium.spaces.Sequence" title="gymnasium.spaces.Sequence"><em>Sequence</em></a><em>[</em><em>int</em><em>]</em><em>]</em>) – If elements of the space are numpy arrays, this should specify their shape.</p></li>
<li><p><strong>dtype</strong> (<em>Optional</em><em>[</em><em>Type</em><em> | </em><em>str</em><em>]</em>) – If elements of the space are numpy arrays, this should specify their dtype.</p></li>
<li><p><strong>seed</strong> – Optionally, you can use this argument to seed the RNG that is used to sample from the space</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<section id="general-functions">
<h2>General Functions<a class="headerlink" href="#general-functions" title="Permalink to this heading">#</a></h2>
<p>Each space implements the following functions:</p>
<dl class="py function">
<dt class="sig sig-object py" id="gymnasium.spaces.Space.sample">
<span class="sig-prename descclassname"><span class="pre">gymnasium.spaces.Space.</span></span><span class="sig-name descname"><span class="pre">sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mask</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">T_cov</span></span></span><a class="headerlink" href="#gymnasium.spaces.Space.sample" title="Permalink to this definition">#</a></dt>
<dd><p>Randomly sample an element of this space.</p>
<p>Can be uniform or non-uniform sampling based on boundedness of space.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>mask</strong> – A mask used for sampling, expected <code class="docutils literal notranslate"><span class="pre">dtype=np.int8</span></code> and see sample implementation for expected shape.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>A sampled actions from the space</strong></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="gymnasium.spaces.Space.contains">
<span class="sig-prename descclassname"><span class="pre">gymnasium.spaces.Space.</span></span><span class="sig-name descname"><span class="pre">contains</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="headerlink" href="#gymnasium.spaces.Space.contains" title="Permalink to this definition">#</a></dt>
<dd><p>Return boolean specifying if x is a valid member of this space.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="gymnasium.spaces.Space.shape">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">Space.</span></span><span class="sig-name descname"><span class="pre">shape</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">Tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="p"><span class="pre">...</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#gymnasium.spaces.Space.shape" title="Permalink to this definition">#</a></dt>
<dd><p>Return the shape of the space as an immutable property.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="gymnasium.spaces.Space.dtype">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">gymnasium.spaces.Space.</span></span><span class="sig-name descname"><span class="pre">dtype</span></span><a class="headerlink" href="#gymnasium.spaces.Space.dtype" title="Permalink to this definition">#</a></dt>
<dd><p>Return the data type of this space.</p>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="gymnasium.spaces.Space.seed">
<span class="sig-prename descclassname"><span class="pre">gymnasium.spaces.Space.</span></span><span class="sig-name descname"><span class="pre">seed</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seed</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">list</span></span></span><a class="headerlink" href="#gymnasium.spaces.Space.seed" title="Permalink to this definition">#</a></dt>
<dd><p>Seed the PRNG of this space and possibly the PRNGs of subspaces.</p>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="gymnasium.spaces.Space.to_jsonable">
<span class="sig-prename descclassname"><span class="pre">gymnasium.spaces.Space.</span></span><span class="sig-name descname"><span class="pre">to_jsonable</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_n</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">T_cov</span><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">list</span></span></span><a class="headerlink" href="#gymnasium.spaces.Space.to_jsonable" title="Permalink to this definition">#</a></dt>
<dd><p>Convert a batch of samples from this space to a JSONable data type.</p>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="gymnasium.spaces.Space.from_jsonable">
<span class="sig-prename descclassname"><span class="pre">gymnasium.spaces.Space.</span></span><span class="sig-name descname"><span class="pre">from_jsonable</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_n</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">list</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">T_cov</span><span class="p"><span class="pre">]</span></span></span></span><a class="headerlink" href="#gymnasium.spaces.Space.from_jsonable" title="Permalink to this definition">#</a></dt>
<dd><p>Convert a JSONable data type to a batch of samples from this space.</p>
</dd></dl>
</section>
<section id="fundamental-spaces">
<h2>Fundamental Spaces<a class="headerlink" href="#fundamental-spaces" title="Permalink to this heading">#</a></h2>
<ul class="simple">
<li><p><a class="reference internal" href="fundamental/#gymnasium.spaces.Box" title="gymnasium.spaces.Box"><code class="xref py py-class docutils literal notranslate"><span class="pre">Box</span></code></a> - Supports continuous (and discrete) vectors or matrices, used for vector observations, images, etc</p></li>
<li><p><a class="reference internal" href="fundamental/#gymnasium.spaces.Discrete" title="gymnasium.spaces.Discrete"><code class="xref py py-class docutils literal notranslate"><span class="pre">Discrete</span></code></a> - Supports a single discrete number of values with an optional start for the values</p></li>
<li><p><a class="reference internal" href="fundamental/#gymnasium.spaces.MultiDiscrete" title="gymnasium.spaces.MultiDiscrete"><code class="xref py py-class docutils literal notranslate"><span class="pre">MultiDiscrete</span></code></a> - Supports single or matrices of binary values, used for holding down a button or if an agent has an object</p></li>
<li><p><a class="reference internal" href="fundamental/#gymnasium.spaces.MultiBinary" title="gymnasium.spaces.MultiBinary"><code class="xref py py-class docutils literal notranslate"><span class="pre">MultiBinary</span></code></a> - Supports multiple discrete values with multiple axes, used for controller actions</p></li>
<li><p><a class="reference internal" href="fundamental/#gymnasium.spaces.Text" title="gymnasium.spaces.Text"><code class="xref py py-class docutils literal notranslate"><span class="pre">Text</span></code></a> - Supports strings, used for passing agent messages, mission details, etc</p></li>
</ul>
</section>
<section id="composite-spaces">
<h2>Composite Spaces<a class="headerlink" href="#composite-spaces" title="Permalink to this heading">#</a></h2>
<ul class="simple">
<li><p><a class="reference internal" href="composite/#gymnasium.spaces.Dict" title="gymnasium.spaces.Dict"><code class="xref py py-class docutils literal notranslate"><span class="pre">Dict</span></code></a> - Supports a dictionary of keys and subspaces, used for a fixed number of unordered spaces</p></li>
<li><p><a class="reference internal" href="composite/#gymnasium.spaces.Tuple" title="gymnasium.spaces.Tuple"><code class="xref py py-class docutils literal notranslate"><span class="pre">Tuple</span></code></a> - Supports a tuple of subspaces, used for multiple for a fixed number of ordered spaces</p></li>
<li><p><a class="reference internal" href="composite/#gymnasium.spaces.Sequence" title="gymnasium.spaces.Sequence"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a> - Supports a variable number of instances of a single subspace, used for entities spaces or selecting a variable number of actions</p></li>
<li><p><a class="reference internal" href="composite/#gymnasium.spaces.Graph" title="gymnasium.spaces.Graph"><code class="xref py py-class docutils literal notranslate"><span class="pre">Graph</span></code></a> - Supports graph based actions or observations with discrete or continuous nodes and edge values.</p></li>
</ul>
</section>
<section id="utils">
<h2>Utils<a class="headerlink" href="#utils" title="Permalink to this heading">#</a></h2>
<ul class="simple">
<li><p><a class="reference internal" href="utils/#gymnasium.spaces.utils.flatdim" title="gymnasium.spaces.utils.flatdim"><code class="xref py py-class docutils literal notranslate"><span class="pre">utils.flatdim</span></code></a> - The number of dimensions the flattened space will contain</p></li>
<li><p><a class="reference internal" href="utils/#gymnasium.spaces.utils.flatten_space" title="gymnasium.spaces.utils.flatten_space"><code class="xref py py-class docutils literal notranslate"><span class="pre">utils.flatten_space</span></code></a> - Flattens a space for which the <cite>flattened</cite> space instances will contain</p></li>
<li><p><a class="reference internal" href="utils/#gymnasium.spaces.utils.flatten" title="gymnasium.spaces.utils.flatten"><code class="xref py py-class docutils literal notranslate"><span class="pre">utils.flatten</span></code></a> - Flattens an instance of a space that is contained within the flattened version of the space</p></li>
<li><p><a class="reference internal" href="utils/#gymnasium.spaces.utils.unflatten" title="gymnasium.spaces.utils.unflatten"><code class="xref py py-class docutils literal notranslate"><span class="pre">utils.unflatten</span></code></a> - The reverse of the <cite>flatten_space</cite> function</p></li>
</ul>
</section>
</section>
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<li><a class="reference internal" href="#">Spaces</a><ul>
<li><a class="reference internal" href="#gymnasium.spaces.Space"><code class="docutils literal notranslate"><span class="pre">Space</span></code></a></li>
<li><a class="reference internal" href="#general-functions">General Functions</a><ul>
<li><a class="reference internal" href="#gymnasium.spaces.Space.sample"><code class="docutils literal notranslate"><span class="pre">sample()</span></code></a></li>
<li><a class="reference internal" href="#gymnasium.spaces.Space.contains"><code class="docutils literal notranslate"><span class="pre">contains()</span></code></a></li>
<li><a class="reference internal" href="#gymnasium.spaces.Space.shape"><code class="docutils literal notranslate"><span class="pre">Space.shape</span></code></a></li>
<li><a class="reference internal" href="#gymnasium.spaces.Space.dtype"><code class="docutils literal notranslate"><span class="pre">gymnasium.spaces.Space.dtype</span></code></a></li>
<li><a class="reference internal" href="#gymnasium.spaces.Space.seed"><code class="docutils literal notranslate"><span class="pre">seed()</span></code></a></li>
<li><a class="reference internal" href="#gymnasium.spaces.Space.to_jsonable"><code class="docutils literal notranslate"><span class="pre">to_jsonable()</span></code></a></li>
<li><a class="reference internal" href="#gymnasium.spaces.Space.from_jsonable"><code class="docutils literal notranslate"><span class="pre">from_jsonable()</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#fundamental-spaces">Fundamental Spaces</a></li>
<li><a class="reference internal" href="#composite-spaces">Composite Spaces</a></li>
<li><a class="reference internal" href="#utils">Utils</a></li>
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