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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="first admonition-title">Note</p>
<p>If you need to move a model to GPU via <cite>.cuda()</cite>, please do so before
constructing optimizers for it. Parameters of a model after <cite>.cuda()</cite> will
be different objects with those before the call.</p>
<p class="last">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 v3.7)"><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="first admonition-title">Note</p>
<p class="last">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">
<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="descclassname">torch.optim.</code><code class="descname">Optimizer</code><span class="sig-paren">(</span><em>params</em>, <em>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="first admonition-title">Warning</p>
<p class="last">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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><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 v3.7)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a> s. Specifies what Tensors should be optimized.</li>
<li><strong>defaults</strong> – (dict): a dict containing default values of optimization
options (used when a parameter group doesn’t specify them).</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.Optimizer.add_param_group">
<code class="descname">add_param_group</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>param_group</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.7)"><em>dict</em></a>) – Specifies what Tensors should be optimized along with group</li>
<li><strong>optimization options.</strong> (<em>specific</em>) – </li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.load_state_dict">
<code class="descname">load_state_dict</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>state_dict</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.7)"><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>.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.state_dict">
<code class="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 v3.7)"><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="first docutils">
<dt>state - a dict holding current optimization state. Its content</dt>
<dd>differs between optimizer classes.</dd>
</dl>
</li>
<li>param_groups - a dict containing all parameter groups</li>
</ul>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>closure</strong> (<em>callable</em>) – A closure that reevaluates the model and
returns the loss. Optional for most optimizers.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.zero_grad">
<code class="descname">zero_grad</code><span class="sig-paren">(</span><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>Clears 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.</p>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Adadelta">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">Adadelta</code><span class="sig-paren">(</span><em>params</em>, <em>lr=1.0</em>, <em>rho=0.9</em>, <em>eps=1e-06</em>, <em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</li>
<li><strong>rho</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – coefficient used for computing a running average
of squared gradients (default: 0.9)</li>
<li><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-6)</li>
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – coefficient that scale delta before it is applied
to the parameters (default: 1.0)</li>
<li><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.Adadelta.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Adagrad">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">Adagrad</code><span class="sig-paren">(</span><em>params</em>, <em>lr=0.01</em>, <em>lr_decay=0</em>, <em>weight_decay=0</em>, <em>initial_accumulator_value=0</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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</li>
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-2)</li>
<li><strong>lr_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate decay (default: 0)</li>
<li><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.Adagrad.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Adam">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">Adam</code><span class="sig-paren">(</span><em>params</em>, <em>lr=0.001</em>, <em>betas=(0.9</em>, <em>0.999)</em>, <em>eps=1e-08</em>, <em>weight_decay=0</em>, <em>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>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</li>
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-3)</li>
<li><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 v3.7)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><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))</li>
<li><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-8)</li>
<li><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</li>
<li><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)</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.Adam.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.SparseAdam">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">SparseAdam</code><span class="sig-paren">(</span><em>params</em>, <em>lr=0.001</em>, <em>betas=(0.9</em>, <em>0.999)</em>, <em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</li>
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-3)</li>
<li><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 v3.7)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><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))</li>
<li><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-8)</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.SparseAdam.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Adamax">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">Adamax</code><span class="sig-paren">(</span><em>params</em>, <em>lr=0.002</em>, <em>betas=(0.9</em>, <em>0.999)</em>, <em>eps=1e-08</em>, <em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</li>
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 2e-3)</li>
<li><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 v3.7)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – coefficients used for computing
running averages of gradient and its square</li>
<li><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-8)</li>
<li><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.Adamax.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.ASGD">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">ASGD</code><span class="sig-paren">(</span><em>params</em>, <em>lr=0.01</em>, <em>lambd=0.0001</em>, <em>alpha=0.75</em>, <em>t0=1000000.0</em>, <em>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="http://dl.acm.org/citation.cfm?id=131098">Acceleration of stochastic approximation by
averaging</a>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</li>
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-2)</li>
<li><strong>lambd</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – decay term (default: 1e-4)</li>
<li><strong>alpha</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – power for eta update (default: 0.75)</li>
<li><strong>t0</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – point at which to start averaging (default: 1e6)</li>
<li><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.ASGD.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.LBFGS">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">LBFGS</code><span class="sig-paren">(</span><em>params</em>, <em>lr=1</em>, <em>max_iter=20</em>, <em>max_eval=None</em>, <em>tolerance_grad=1e-05</em>, <em>tolerance_change=1e-09</em>, <em>history_size=100</em>, <em>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.</p>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p class="last">This optimizer doesn’t support per-parameter options and parameter
groups (there can be only one).</p>
</div>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p class="last">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="first admonition-title">Note</p>
<p class="last">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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a>) – learning rate (default: 1)</li>
<li><strong>max_iter</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a>) – maximal number of iterations per optimization step
(default: 20)</li>
<li><strong>max_eval</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a>) – maximal number of function evaluations per optimization
step (default: max_iter * 1.25).</li>
<li><strong>tolerance_grad</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a>) – termination tolerance on first order optimality
(default: 1e-5).</li>
<li><strong>tolerance_change</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a>) – termination tolerance on function
value/parameter changes (default: 1e-9).</li>
<li><strong>history_size</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a>) – update history size (default: 100).</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.LBFGS.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>closure</strong> (<em>callable</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.RMSprop">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">RMSprop</code><span class="sig-paren">(</span><em>params</em>, <em>lr=0.01</em>, <em>alpha=0.99</em>, <em>eps=1e-08</em>, <em>weight_decay=0</em>, <em>momentum=0</em>, <em>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="http://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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</li>
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-2)</li>
<li><strong>momentum</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – momentum factor (default: 0)</li>
<li><strong>alpha</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – smoothing constant (default: 0.99)</li>
<li><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-8)</li>
<li><strong>centered</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><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</li>
<li><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.RMSprop.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Rprop">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">Rprop</code><span class="sig-paren">(</span><em>params</em>, <em>lr=0.01</em>, <em>etas=(0.5</em>, <em>1.2)</em>, <em>step_sizes=(1e-06</em>, <em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</li>
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-2)</li>
<li><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 v3.7)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><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))</li>
<li><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 v3.7)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – a pair of minimal and
maximal allowed step sizes (default: (1e-6, 50))</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.Rprop.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.SGD">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">SGD</code><span class="sig-paren">(</span><em>params</em>, <em>lr=<required parameter></em>, <em>momentum=0</em>, <em>dampening=0</em>, <em>weight_decay=0</em>, <em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</li>
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a>) – learning rate</li>
<li><strong>momentum</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – momentum factor (default: 0)</li>
<li><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</li>
<li><strong>dampening</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – dampening for momentum (default: 0)</li>
<li><strong>nesterov</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>optional</em>) – enables Nesterov momentum (default: False)</li>
</ul>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Example</p>
<div class="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="first 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">
\[v = \rho * v + g \\
p = p - lr * v
\]</div>
<p>where p, g, v and <span class="math">\(\rho\)</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">
\[v = \rho * v + lr * g \\
p = p - v
\]</div>
<p class="last">The Nesterov version is analogously modified.</p>
</div>
<dl class="method">
<dt id="torch.optim.SGD.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>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>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>closure</strong> (<em>callable</em><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
</div>
<div class="section" id="how-to-adjust-learning-rate">
<h2>How to adjust Learning Rate<a class="headerlink" href="#how-to-adjust-learning-rate" title="Permalink to this headline">¶</a></h2>
<p><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.optim.lr_scheduler</span></code> provides several methods to adjust the learning
rate based on the number of epochs. <a class="reference internal" href="#torch.optim.lr_scheduler.ReduceLROnPlateau" title="torch.optim.lr_scheduler.ReduceLROnPlateau"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.optim.lr_scheduler.ReduceLROnPlateau</span></code></a>
allows dynamic learning rate reducing based on some validation measurements.</p>
<dl class="class">
<dt id="torch.optim.lr_scheduler.LambdaLR">
<em class="property">class </em><code class="descclassname">torch.optim.lr_scheduler.</code><code class="descname">LambdaLR</code><span class="sig-paren">(</span><em>optimizer</em>, <em>lr_lambda</em>, <em>last_epoch=-1</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/lr_scheduler.html#LambdaLR"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.lr_scheduler.LambdaLR" title="Permalink to this definition">¶</a></dt>
<dd><p>Sets the learning rate of each parameter group to the initial lr
times a given function. When last_epoch=-1, sets initial lr as lr.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>optimizer</strong> (<a class="reference internal" href="#torch.optim.Optimizer" title="torch.optim.Optimizer"><em>Optimizer</em></a>) – Wrapped optimizer.</li>
<li><strong>lr_lambda</strong> (<em>function</em><em> or </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.7)"><em>list</em></a>) – A function which computes a multiplicative
factor given an integer parameter epoch, or a list of such
functions, one for each group in optimizer.param_groups.</li>
<li><strong>last_epoch</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a>) – The index of last epoch. Default: -1.</li>
</ul>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Example</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="c1"># Assuming optimizer has two groups.</span>
<span class="gp">>>> </span><span class="n">lambda1</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">epoch</span><span class="p">:</span> <span class="n">epoch</span> <span class="o">//</span> <span class="mi">30</span>
<span class="gp">>>> </span><span class="n">lambda2</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">epoch</span><span class="p">:</span> <span class="mf">0.95</span> <span class="o">**</span> <span class="n">epoch</span>
<span class="gp">>>> </span><span class="n">scheduler</span> <span class="o">=</span> <span class="n">LambdaLR</span><span class="p">(</span><span class="n">optimizer</span><span class="p">,</span> <span class="n">lr_lambda</span><span class="o">=</span><span class="p">[</span><span class="n">lambda1</span><span class="p">,</span> <span class="n">lambda2</span><span class="p">])</span>
<span class="gp">>>> </span><span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
<span class="gp">>>> </span> <span class="n">scheduler</span><span class="o">.</span><span class="n">step</span><span class="p">()</span>
<span class="gp">>>> </span> <span class="n">train</span><span class="p">(</span><span class="o">...</span><span class="p">)</span>
<span class="gp">>>> </span> <span class="n">validate</span><span class="p">(</span><span class="o">...</span><span class="p">)</span>
</pre></div>
</div>
<dl class="method">
<dt id="torch.optim.lr_scheduler.LambdaLR.load_state_dict">
<code class="descname">load_state_dict</code><span class="sig-paren">(</span><em>state_dict</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/lr_scheduler.html#LambdaLR.load_state_dict"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.lr_scheduler.LambdaLR.load_state_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>Loads the schedulers state.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>state_dict</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.7)"><em>dict</em></a>) – scheduler state. Should be an object returned
from a call to <a class="reference internal" href="#torch.optim.lr_scheduler.LambdaLR.state_dict" title="torch.optim.lr_scheduler.LambdaLR.state_dict"><code class="xref py py-meth docutils literal notranslate"><span class="pre">state_dict()</span></code></a>.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.optim.lr_scheduler.LambdaLR.state_dict">
<code class="descname">state_dict</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/lr_scheduler.html#LambdaLR.state_dict"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.lr_scheduler.LambdaLR.state_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the state of the scheduler as a <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.7)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>.</p>
<p>It contains an entry for every variable in self.__dict__ which
is not the optimizer.
The learning rate lambda functions will only be saved if they are callable objects
and not if they are functions or lambdas.</p>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.lr_scheduler.StepLR">
<em class="property">class </em><code class="descclassname">torch.optim.lr_scheduler.</code><code class="descname">StepLR</code><span class="sig-paren">(</span><em>optimizer</em>, <em>step_size</em>, <em>gamma=0.1</em>, <em>last_epoch=-1</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/lr_scheduler.html#StepLR"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.lr_scheduler.StepLR" title="Permalink to this definition">¶</a></dt>
<dd><p>Decays the learning rate of each parameter group by gamma every
step_size epochs. Notice that such decay can happen simultaneously with
other changes to the learning rate from outside this scheduler. When
last_epoch=-1, sets initial lr as lr.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>optimizer</strong> (<a class="reference internal" href="#torch.optim.Optimizer" title="torch.optim.Optimizer"><em>Optimizer</em></a>) – Wrapped optimizer.</li>
<li><strong>step_size</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a>) – Period of learning rate decay.</li>
<li><strong>gamma</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a>) – Multiplicative factor of learning rate decay.
Default: 0.1.</li>
<li><strong>last_epoch</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a>) – The index of last epoch. Default: -1.</li>
</ul>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Example</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="c1"># Assuming optimizer uses lr = 0.05 for all groups</span>
<span class="gp">>>> </span><span class="c1"># lr = 0.05 if epoch < 30</span>