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<p class="caption"><span class="caption-text">Notes</span></p>
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<li class="toctree-l1"><a class="reference internal" href="notes/amp_examples.html">Automatic Mixed Precision examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/autograd.html">Autograd mechanics</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/broadcasting.html">Broadcasting semantics</a></li>
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<div class="section" id="module-torch.optim">
<span id="torch-optim"></span><h1>torch.optim<a class="headerlink" href="#module-torch.optim" title="Permalink to this headline">¶</a></h1>
<p><a class="reference internal" href="#module-torch.optim" title="torch.optim"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.optim</span></code></a> is a package implementing various optimization algorithms.
Most commonly used methods are already supported, and the interface is general
enough, so that more sophisticated ones can be also easily integrated in the
future.</p>
<div class="section" id="how-to-use-an-optimizer">
<h2>How to use an optimizer<a class="headerlink" href="#how-to-use-an-optimizer" title="Permalink to this headline">¶</a></h2>
<p>To use <a class="reference internal" href="#module-torch.optim" title="torch.optim"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.optim</span></code></a> you have to construct an optimizer object, that will hold
the current state and will update the parameters based on the computed gradients.</p>
<div class="section" id="constructing-it">
<h3>Constructing it<a class="headerlink" href="#constructing-it" title="Permalink to this headline">¶</a></h3>
<p>To construct an <a class="reference internal" href="#torch.optim.Optimizer" title="torch.optim.Optimizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Optimizer</span></code></a> you have to give it an iterable containing the
parameters (all should be <code class="xref py py-class docutils literal notranslate"><span class="pre">Variable</span></code> s) to optimize. Then,
you can specify optimizer-specific options such as the learning rate, weight decay, etc.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>If you need to move a model to GPU via <code class="docutils literal notranslate"><span class="pre">.cuda()</span></code>, please do so before
constructing optimizers for it. Parameters of a model after <code class="docutils literal notranslate"><span class="pre">.cuda()</span></code> will
be different objects with those before the call.</p>
<p>In general, you should make sure that optimized parameters live in
consistent locations when optimizers are constructed and used.</p>
</div>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">optimizer</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">(),</span> <span class="n">lr</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">momentum</span><span class="o">=</span><span class="mf">0.9</span><span class="p">)</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">Adam</span><span class="p">([</span><span class="n">var1</span><span class="p">,</span> <span class="n">var2</span><span class="p">],</span> <span class="n">lr</span><span class="o">=</span><span class="mf">0.0001</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="per-parameter-options">
<h3>Per-parameter options<a class="headerlink" href="#per-parameter-options" title="Permalink to this headline">¶</a></h3>
<p><a class="reference internal" href="#torch.optim.Optimizer" title="torch.optim.Optimizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Optimizer</span></code></a> s also support specifying per-parameter options. To do this, instead
of passing an iterable of <code class="xref py py-class docutils literal notranslate"><span class="pre">Variable</span></code> s, pass in an iterable of
<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.9)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a> s. Each of them will define a separate parameter group, and should contain
a <code class="docutils literal notranslate"><span class="pre">params</span></code> key, containing a list of parameters belonging to it. Other keys
should match the keyword arguments accepted by the optimizers, and will be used
as optimization options for this group.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>You can still pass options as keyword arguments. They will be used as
defaults, in the groups that didn’t override them. This is useful when you
only want to vary a single option, while keeping all others consistent
between parameter groups.</p>
</div>
<p>For example, this is very useful when one wants to specify per-layer learning rates:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">optim</span><span class="o">.</span><span class="n">SGD</span><span class="p">([</span>
<span class="p">{</span><span class="s1">'params'</span><span class="p">:</span> <span class="n">model</span><span class="o">.</span><span class="n">base</span><span class="o">.</span><span class="n">parameters</span><span class="p">()},</span>
<span class="p">{</span><span class="s1">'params'</span><span class="p">:</span> <span class="n">model</span><span class="o">.</span><span class="n">classifier</span><span class="o">.</span><span class="n">parameters</span><span class="p">(),</span> <span class="s1">'lr'</span><span class="p">:</span> <span class="mf">1e-3</span><span class="p">}</span>
<span class="p">],</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">momentum</span><span class="o">=</span><span class="mf">0.9</span><span class="p">)</span>
</pre></div>
</div>
<p>This means that <code class="docutils literal notranslate"><span class="pre">model.base</span></code>’s parameters will use the default learning rate of <code class="docutils literal notranslate"><span class="pre">1e-2</span></code>,
<code class="docutils literal notranslate"><span class="pre">model.classifier</span></code>’s parameters will use a learning rate of <code class="docutils literal notranslate"><span class="pre">1e-3</span></code>, and a momentum of
<code class="docutils literal notranslate"><span class="pre">0.9</span></code> will be used for all parameters.</p>
</div>
<div class="section" id="taking-an-optimization-step">
<h3>Taking an optimization step<a class="headerlink" href="#taking-an-optimization-step" title="Permalink to this headline">¶</a></h3>
<p>All optimizers implement a <a class="reference internal" href="#torch.optim.Optimizer.step" title="torch.optim.Optimizer.step"><code class="xref py py-func docutils literal notranslate"><span class="pre">step()</span></code></a> method, that updates the
parameters. It can be used in two ways:</p>
<div class="section" id="optimizer-step">
<h4><code class="docutils literal notranslate"><span class="pre">optimizer.step()</span></code><a class="headerlink" href="#optimizer-step" title="Permalink to this headline">¶</a></h4>
<p>This is a simplified version supported by most optimizers. The function can be
called once the gradients are computed using e.g.
<code class="xref py py-func docutils literal notranslate"><span class="pre">backward()</span></code>.</p>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="nb">input</span><span class="p">,</span> <span class="n">target</span> <span class="ow">in</span> <span class="n">dataset</span><span class="p">:</span>
<span class="n">optimizer</span><span class="o">.</span><span class="n">zero_grad</span><span class="p">()</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">loss_fn</span><span class="p">(</span><span class="n">output</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
<span class="n">loss</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="n">optimizer</span><span class="o">.</span><span class="n">step</span><span class="p">()</span>
</pre></div>
</div>
</div>
<div class="section" id="optimizer-step-closure">
<h4><code class="docutils literal notranslate"><span class="pre">optimizer.step(closure)</span></code><a class="headerlink" href="#optimizer-step-closure" title="Permalink to this headline">¶</a></h4>
<p>Some optimization algorithms such as Conjugate Gradient and LBFGS need to
reevaluate the function multiple times, so you have to pass in a closure that
allows them to recompute your model. The closure should clear the gradients,
compute the loss, and return it.</p>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="nb">input</span><span class="p">,</span> <span class="n">target</span> <span class="ow">in</span> <span class="n">dataset</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">closure</span><span class="p">():</span>
<span class="n">optimizer</span><span class="o">.</span><span class="n">zero_grad</span><span class="p">()</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">loss_fn</span><span class="p">(</span><span class="n">output</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
<span class="n">loss</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="k">return</span> <span class="n">loss</span>
<span class="n">optimizer</span><span class="o">.</span><span class="n">step</span><span class="p">(</span><span class="n">closure</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="section" id="algorithms">
<span id="optimizer-algorithms"></span><h2>Algorithms<a class="headerlink" href="#algorithms" title="Permalink to this headline">¶</a></h2>
<dl class="class">
<dt id="torch.optim.Optimizer">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">Optimizer</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">defaults</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer" title="Permalink to this definition">¶</a></dt>
<dd><p>Base class for all optimizers.</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>Parameters need to be specified as collections that have a deterministic
ordering that is consistent between runs. Examples of objects that don’t
satisfy those properties are sets and iterators over values of dictionaries.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>params</strong> (<em>iterable</em>) – an iterable of <a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.Tensor</span></code></a> s or
<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.9)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a> s. Specifies what Tensors should be optimized.</p></li>
<li><p><strong>defaults</strong> – (dict): a dict containing default values of optimization
options (used when a parameter group doesn’t specify them).</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="torch.optim.Optimizer.add_param_group">
<code class="sig-name descname">add_param_group</code><span class="sig-paren">(</span><em class="sig-param">param_group</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer.add_param_group"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer.add_param_group" title="Permalink to this definition">¶</a></dt>
<dd><p>Add a param group to the <a class="reference internal" href="#torch.optim.Optimizer" title="torch.optim.Optimizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Optimizer</span></code></a> s <cite>param_groups</cite>.</p>
<p>This can be useful when fine tuning a pre-trained network as frozen layers can be made
trainable and added to the <a class="reference internal" href="#torch.optim.Optimizer" title="torch.optim.Optimizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Optimizer</span></code></a> as training progresses.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>param_group</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.9)"><em>dict</em></a>) – Specifies what Tensors should be optimized along with group</p></li>
<li><p><strong>optimization options.</strong> (<em>specific</em>) – </p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.load_state_dict">
<code class="sig-name descname">load_state_dict</code><span class="sig-paren">(</span><em class="sig-param">state_dict</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer.load_state_dict"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer.load_state_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>Loads the optimizer state.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>state_dict</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.9)"><em>dict</em></a>) – optimizer state. Should be an object returned
from a call to <a class="reference internal" href="#torch.optim.Optimizer.state_dict" title="torch.optim.Optimizer.state_dict"><code class="xref py py-meth docutils literal notranslate"><span class="pre">state_dict()</span></code></a>.</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.state_dict">
<code class="sig-name descname">state_dict</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer.state_dict"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer.state_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the state of the optimizer as a <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.9)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>.</p>
<p>It contains two entries:</p>
<ul class="simple">
<li><dl class="simple">
<dt>state - a dict holding current optimization state. Its content</dt><dd><p>differs between optimizer classes.</p>
</dd>
</dl>
</li>
<li><p>param_groups - a dict containing all parameter groups</p></li>
</ul>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step (parameter update).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em>) – A closure that reevaluates the model and
returns the loss. Optional for most optimizers.</p>
</dd>
</dl>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Unless otherwise specified, this function should not modify the
<code class="docutils literal notranslate"><span class="pre">.grad</span></code> field of the parameters.</p>
</div>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.zero_grad">
<code class="sig-name descname">zero_grad</code><span class="sig-paren">(</span><em class="sig-param">set_to_none: bool = False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer.zero_grad"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer.zero_grad" title="Permalink to this definition">¶</a></dt>
<dd><p>Sets the gradients of all optimized <a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.Tensor</span></code></a> s to zero.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>set_to_none</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.9)"><em>bool</em></a>) – instead of setting to zero, set the grads to None.
This is will in general have lower memory footprint, and can modestly improve performance.
However, it changes certain behaviors. For example:
1. When the user tries to access a gradient and perform manual ops on it,
a None attribute or a Tensor full of 0s will behave differently.
2. If the user requests <code class="docutils literal notranslate"><span class="pre">zero_grad(set_to_none=True)</span></code> followed by a backward pass, <code class="docutils literal notranslate"><span class="pre">.grad</span></code>s
are guaranteed to be None for params that did not receive a gradient.
3. <code class="docutils literal notranslate"><span class="pre">torch.optim</span></code> optimizers have a different behavior if the gradient is 0 or None
(in one case it does the step with a gradient of 0 and in the other it skips
the step altogether).</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Adadelta">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">Adadelta</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">lr=1.0</em>, <em class="sig-param">rho=0.9</em>, <em class="sig-param">eps=1e-06</em>, <em class="sig-param">weight_decay=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adadelta.html#Adadelta"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adadelta" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements Adadelta algorithm.</p>
<p>It has been proposed in <a class="reference external" href="https://arxiv.org/abs/1212.5701">ADADELTA: An Adaptive Learning Rate Method</a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</p></li>
<li><p><strong>rho</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – coefficient used for computing a running average
of squared gradients (default: 0.9)</p></li>
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-6)</p></li>
<li><p><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – coefficient that scale delta before it is applied
to the parameters (default: 1.0)</p></li>
<li><p><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="torch.optim.Adadelta.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adadelta.html#Adadelta.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adadelta.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Adagrad">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">Adagrad</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">lr=0.01</em>, <em class="sig-param">lr_decay=0</em>, <em class="sig-param">weight_decay=0</em>, <em class="sig-param">initial_accumulator_value=0</em>, <em class="sig-param">eps=1e-10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adagrad.html#Adagrad"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adagrad" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements Adagrad algorithm.</p>
<p>It has been proposed in <a class="reference external" href="http://jmlr.org/papers/v12/duchi11a.html">Adaptive Subgradient Methods for Online Learning
and Stochastic Optimization</a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</p></li>
<li><p><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-2)</p></li>
<li><p><strong>lr_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate decay (default: 0)</p></li>
<li><p><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</p></li>
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-10)</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="torch.optim.Adagrad.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adagrad.html#Adagrad.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adagrad.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Adam">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">Adam</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">lr=0.001</em>, <em class="sig-param">betas=(0.9</em>, <em class="sig-param">0.999)</em>, <em class="sig-param">eps=1e-08</em>, <em class="sig-param">weight_decay=0</em>, <em class="sig-param">amsgrad=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adam.html#Adam"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adam" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements Adam algorithm.</p>
<p>It has been proposed in <a class="reference external" href="https://arxiv.org/abs/1412.6980">Adam: A Method for Stochastic Optimization</a>.
The implementation of the L2 penalty follows changes proposed in
<a class="reference external" href="https://arxiv.org/abs/1711.05101">Decoupled Weight Decay Regularization</a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</p></li>
<li><p><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-3)</p></li>
<li><p><strong>betas</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – coefficients used for computing
running averages of gradient and its square (default: (0.9, 0.999))</p></li>
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-8)</p></li>
<li><p><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</p></li>
<li><p><strong>amsgrad</strong> (<em>boolean</em><em>, </em><em>optional</em>) – whether to use the AMSGrad variant of this
algorithm from the paper <a class="reference external" href="https://openreview.net/forum?id=ryQu7f-RZ">On the Convergence of Adam and Beyond</a>
(default: False)</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="torch.optim.Adam.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adam.html#Adam.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adam.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.AdamW">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">AdamW</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">lr=0.001</em>, <em class="sig-param">betas=(0.9</em>, <em class="sig-param">0.999)</em>, <em class="sig-param">eps=1e-08</em>, <em class="sig-param">weight_decay=0.01</em>, <em class="sig-param">amsgrad=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adamw.html#AdamW"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.AdamW" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements AdamW algorithm.</p>
<p>The original Adam algorithm was proposed in <a class="reference external" href="https://arxiv.org/abs/1412.6980">Adam: A Method for Stochastic Optimization</a>.
The AdamW variant was proposed in <a class="reference external" href="https://arxiv.org/abs/1711.05101">Decoupled Weight Decay Regularization</a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</p></li>
<li><p><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-3)</p></li>
<li><p><strong>betas</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – coefficients used for computing
running averages of gradient and its square (default: (0.9, 0.999))</p></li>
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-8)</p></li>
<li><p><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay coefficient (default: 1e-2)</p></li>
<li><p><strong>amsgrad</strong> (<em>boolean</em><em>, </em><em>optional</em>) – whether to use the AMSGrad variant of this
algorithm from the paper <a class="reference external" href="https://openreview.net/forum?id=ryQu7f-RZ">On the Convergence of Adam and Beyond</a>
(default: False)</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="torch.optim.AdamW.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adamw.html#AdamW.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.AdamW.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.SparseAdam">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">SparseAdam</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">lr=0.001</em>, <em class="sig-param">betas=(0.9</em>, <em class="sig-param">0.999)</em>, <em class="sig-param">eps=1e-08</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/sparse_adam.html#SparseAdam"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.SparseAdam" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements lazy version of Adam algorithm suitable for sparse tensors.</p>
<p>In this variant, only moments that show up in the gradient get updated, and
only those portions of the gradient get applied to the parameters.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</p></li>
<li><p><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-3)</p></li>
<li><p><strong>betas</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – coefficients used for computing
running averages of gradient and its square (default: (0.9, 0.999))</p></li>
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-8)</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="torch.optim.SparseAdam.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/sparse_adam.html#SparseAdam.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.SparseAdam.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Adamax">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">Adamax</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">lr=0.002</em>, <em class="sig-param">betas=(0.9</em>, <em class="sig-param">0.999)</em>, <em class="sig-param">eps=1e-08</em>, <em class="sig-param">weight_decay=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adamax.html#Adamax"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adamax" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements Adamax algorithm (a variant of Adam based on infinity norm).</p>
<p>It has been proposed in <a class="reference external" href="https://arxiv.org/abs/1412.6980">Adam: A Method for Stochastic Optimization</a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</p></li>
<li><p><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 2e-3)</p></li>
<li><p><strong>betas</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – coefficients used for computing
running averages of gradient and its square</p></li>
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-8)</p></li>
<li><p><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="torch.optim.Adamax.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adamax.html#Adamax.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adamax.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.ASGD">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">ASGD</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">lr=0.01</em>, <em class="sig-param">lambd=0.0001</em>, <em class="sig-param">alpha=0.75</em>, <em class="sig-param">t0=1000000.0</em>, <em class="sig-param">weight_decay=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/asgd.html#ASGD"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.ASGD" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements Averaged Stochastic Gradient Descent.</p>
<p>It has been proposed in <a class="reference external" href="https://dl.acm.org/citation.cfm?id=131098">Acceleration of stochastic approximation by
averaging</a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</p></li>
<li><p><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-2)</p></li>
<li><p><strong>lambd</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – decay term (default: 1e-4)</p></li>
<li><p><strong>alpha</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – power for eta update (default: 0.75)</p></li>
<li><p><strong>t0</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – point at which to start averaging (default: 1e6)</p></li>
<li><p><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="torch.optim.ASGD.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/asgd.html#ASGD.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.ASGD.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.LBFGS">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">LBFGS</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">lr=1</em>, <em class="sig-param">max_iter=20</em>, <em class="sig-param">max_eval=None</em>, <em class="sig-param">tolerance_grad=1e-07</em>, <em class="sig-param">tolerance_change=1e-09</em>, <em class="sig-param">history_size=100</em>, <em class="sig-param">line_search_fn=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/lbfgs.html#LBFGS"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.LBFGS" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements L-BFGS algorithm, heavily inspired by <cite>minFunc
<https://www.cs.ubc.ca/~schmidtm/Software/minFunc.html></cite>.</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>This optimizer doesn’t support per-parameter options and parameter
groups (there can be only one).</p>
</div>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>Right now all parameters have to be on a single device. This will be
improved in the future.</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This is a very memory intensive optimizer (it requires additional
<code class="docutils literal notranslate"><span class="pre">param_bytes</span> <span class="pre">*</span> <span class="pre">(history_size</span> <span class="pre">+</span> <span class="pre">1)</span></code> bytes). If it doesn’t fit in memory
try reducing the history size, or use a different algorithm.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a>) – learning rate (default: 1)</p></li>
<li><p><strong>max_iter</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a>) – maximal number of iterations per optimization step
(default: 20)</p></li>
<li><p><strong>max_eval</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a>) – maximal number of function evaluations per optimization
step (default: max_iter * 1.25).</p></li>
<li><p><strong>tolerance_grad</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a>) – termination tolerance on first order optimality
(default: 1e-5).</p></li>
<li><p><strong>tolerance_change</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a>) – termination tolerance on function
value/parameter changes (default: 1e-9).</p></li>
<li><p><strong>history_size</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a>) – update history size (default: 100).</p></li>
<li><p><strong>line_search_fn</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a>) – either ‘strong_wolfe’ or None (default: None).</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="torch.optim.LBFGS.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/lbfgs.html#LBFGS.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.LBFGS.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em>) – A closure that reevaluates the model
and returns the loss.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.RMSprop">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">RMSprop</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">lr=0.01</em>, <em class="sig-param">alpha=0.99</em>, <em class="sig-param">eps=1e-08</em>, <em class="sig-param">weight_decay=0</em>, <em class="sig-param">momentum=0</em>, <em class="sig-param">centered=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/rmsprop.html#RMSprop"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.RMSprop" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements RMSprop algorithm.</p>
<p>Proposed by G. Hinton in his
<a class="reference external" href="https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf">course</a>.</p>
<p>The centered version first appears in <a class="reference external" href="https://arxiv.org/pdf/1308.0850v5.pdf">Generating Sequences
With Recurrent Neural Networks</a>.</p>
<p>The implementation here takes the square root of the gradient average before
adding epsilon (note that TensorFlow interchanges these two operations). The effective
learning rate is thus <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><msqrt><mi>v</mi></msqrt><mo>+</mo><mi>ϵ</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\alpha/(\sqrt{v} + \epsilon)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.05028em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mord">/</span><span class="mopen">(</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8002800000000001em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span></span></span><span style="top:-2.76028em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.23972em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">ϵ</span><span class="mclose">)</span></span></span></span>
</span> where <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span></span></span></span>
</span>
is the scheduled learning rate and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span></span></span></span>
</span> is the weighted moving average
of the squared gradient.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</p></li>
<li><p><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-2)</p></li>
<li><p><strong>momentum</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – momentum factor (default: 0)</p></li>
<li><p><strong>alpha</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – smoothing constant (default: 0.99)</p></li>
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-8)</p></li>
<li><p><strong>centered</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.9)"><em>bool</em></a><em>, </em><em>optional</em>) – if <code class="docutils literal notranslate"><span class="pre">True</span></code>, compute the centered RMSProp,
the gradient is normalized by an estimation of its variance</p></li>
<li><p><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="torch.optim.RMSprop.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/rmsprop.html#RMSprop.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.RMSprop.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Rprop">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">Rprop</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">lr=0.01</em>, <em class="sig-param">etas=(0.5</em>, <em class="sig-param">1.2)</em>, <em class="sig-param">step_sizes=(1e-06</em>, <em class="sig-param">50)</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/rprop.html#Rprop"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Rprop" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements the resilient backpropagation algorithm.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</p></li>
<li><p><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-2)</p></li>
<li><p><strong>etas</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – pair of (etaminus, etaplis), that
are multiplicative increase and decrease factors
(default: (0.5, 1.2))</p></li>
<li><p><strong>step_sizes</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – a pair of minimal and
maximal allowed step sizes (default: (1e-6, 50))</p></li>
</ul>
</dd>
</dl>
<dl class="method">
<dt id="torch.optim.Rprop.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/rprop.html#Rprop.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Rprop.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.SGD">
<em class="property">class </em><code class="sig-prename descclassname">torch.optim.</code><code class="sig-name descname">SGD</code><span class="sig-paren">(</span><em class="sig-param">params</em>, <em class="sig-param">lr=<required parameter></em>, <em class="sig-param">momentum=0</em>, <em class="sig-param">dampening=0</em>, <em class="sig-param">weight_decay=0</em>, <em class="sig-param">nesterov=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/sgd.html#SGD"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.SGD" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements stochastic gradient descent (optionally with momentum).</p>
<p>Nesterov momentum is based on the formula from
<a class="reference external" href="http://www.cs.toronto.edu/%7Ehinton/absps/momentum.pdf">On the importance of initialization and momentum in deep learning</a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</p></li>
<li><p><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a>) – learning rate</p></li>
<li><p><strong>momentum</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – momentum factor (default: 0)</p></li>
<li><p><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</p></li>
<li><p><strong>dampening</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a><em>, </em><em>optional</em>) – dampening for momentum (default: 0)</p></li>
<li><p><strong>nesterov</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.9)"><em>bool</em></a><em>, </em><em>optional</em>) – enables Nesterov momentum (default: False)</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">optimizer</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">optim</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">(),</span> <span class="n">lr</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">momentum</span><span class="o">=</span><span class="mf">0.9</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">optimizer</span><span class="o">.</span><span class="n">zero_grad</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">loss_fn</span><span class="p">(</span><span class="n">model</span><span class="p">(</span><span class="nb">input</span><span class="p">),</span> <span class="n">target</span><span class="p">)</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">optimizer</span><span class="o">.</span><span class="n">step</span><span class="p">()</span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The implementation of SGD with Momentum/Nesterov subtly differs from
Sutskever et. al. and implementations in some other frameworks.</p>
<p>Considering the specific case of Momentum, the update can be written as</p>
<div class="math">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>v</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>μ</mi><mo>∗</mo><msub><mi>v</mi><mi>t</mi></msub><mo>+</mo><msub><mi>g</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub><mo separator="true">,</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>p</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><msub><mi>p</mi><mi>t</mi></msub><mo>−</mo><mtext>lr</mtext><mo>∗</mo><msub><mi>v</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub><mo separator="true">,</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}
v_{t+1} & = \mu * v_{t} + g_{t+1}, \\
p_{t+1} & = p_{t} - \text{lr} * v_{t+1},
\end{aligned}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000000000000004em;vertical-align:-1.2500000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7500000000000002em;"><span style="top:-3.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.2500000000000002em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7500000000000002em;"><span style="top:-3.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathnormal">μ</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mpunct">,</span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">lr</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mpunct">,</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.2500000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span>
</div><p>where <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">p</span></span></span></span>
</span>, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>g</mi></mrow><annotation encoding="application/x-tex">g</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span></span></span></span>
</span>, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span></span></span></span>
</span> and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi></mrow><annotation encoding="application/x-tex">\mu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">μ</span></span></span></span>
</span> denote the
parameters, gradient, velocity, and momentum respectively.</p>
<p>This is in contrast to Sutskever et. al. and
other frameworks which employ an update of the form</p>
<div class="math">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>v</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>μ</mi><mo>∗</mo><msub><mi>v</mi><mi>t</mi></msub><mo>+</mo><mtext>lr</mtext><mo>∗</mo><msub><mi>g</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub><mo separator="true">,</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>p</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><msub><mi>p</mi><mi>t</mi></msub><mo>−</mo><msub><mi>v</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub><mi mathvariant="normal">.</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}
v_{t+1} & = \mu * v_{t} + \text{lr} * g_{t+1}, \\
p_{t+1} & = p_{t} - v_{t+1}.
\end{aligned}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000000000000004em;vertical-align:-1.2500000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7500000000000002em;"><span style="top:-3.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.2500000000000002em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7500000000000002em;"><span style="top:-3.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathnormal">μ</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">lr</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mpunct">,</span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mord">.</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.2500000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span>
</div><p>The Nesterov version is analogously modified.</p>
</div>
<dl class="method">
<dt id="torch.optim.SGD.step">
<code class="sig-name descname">step</code><span class="sig-paren">(</span><em class="sig-param">closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/sgd.html#SGD.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.SGD.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
</div>