optimizer.html



<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
  <meta charset="utf-8">
  
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  
  <title>Optimizer &mdash; PaddlePaddle  documentation</title>
  

    <link rel="stylesheet" href="../../../_static/css/theme.css" type="text/css" />
  

        <link rel="index" title="Index"
              href="../../../genindex.html"/>
        <link rel="search" title="Search" href="../../../search.html"/>
    <link rel="top" title="PaddlePaddle  documentation" href="../../../index.html"/>
        <link rel="up" title="Model Configuration" href="../model_configs.html"/>
        <link rel="next" title="Pooling" href="pooling.html"/>
        <link rel="prev" title="Evaluators" href="evaluators.html"/> 

  <link rel="stylesheet" href="https://cdn.jsdelivr.net/perfect-scrollbar/0.6.14/css/perfect-scrollbar.min.css" type="text/css" />
  <link rel="stylesheet" href="../../../_static/css/override.css" type="text/css" />
  <script>
  var _hmt = _hmt || [];
  (function() {
    var hm = document.createElement("script");
    hm.src = "//hm.baidu.com/hm.js?b9a314ab40d04d805655aab1deee08ba";
    var s = document.getElementsByTagName("script")[0]; 
    s.parentNode.insertBefore(hm, s);
  })();
  </script>

  
  <script src="../../../_static/js/modernizr.min.js"></script>

</head>

<body class="wy-body-for-nav" role="document">

  
  <header class="site-header">
    <div class="site-logo">
      <a href="/"><img src="../../../_static/images/PP_w.png"></a>
    </div>
    <div class="site-nav-links">
      <div class="site-menu">
        <a class="fork-on-github" href="https://github.com/PaddlePaddle/Paddle" target="_blank"><i class="fa fa-github"></i>Fork me on Github</a>
        <div class="language-switcher dropdown">
          <a type="button" data-toggle="dropdown">
            <span>English</span>
            <i class="fa fa-angle-up"></i>
            <i class="fa fa-angle-down"></i>
          </a>
          <ul class="dropdown-menu">
            <li><a href="/doc_cn">中文</a></li>
            <li><a href="/doc">English</a></li>
          </ul>
        </div>
        <ul class="site-page-links">
          <li><a href="/">Home</a></li>
        </ul>
      </div>
      <div class="doc-module">
        
        <ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../../getstarted/index_en.html">GET STARTED</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../howto/index_en.html">HOW TO</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="../../index_en.html">API</a></li>
</ul>

        
<div role="search">
  <form id="rtd-search-form" class="wy-form" action="../../../search.html" method="get">
    <input type="text" name="q" placeholder="Search docs" />
    <input type="hidden" name="check_keywords" value="yes" />
    <input type="hidden" name="area" value="default" />
  </form>
</div>        
      </div>
    </div>
  </header>
  
  <div class="main-content-wrap">

    
    <nav class="doc-menu-vertical" role="navigation">
        
          
          <ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../../getstarted/index_en.html">GET STARTED</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../../getstarted/build_and_install/index_en.html">Install and Build</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../getstarted/build_and_install/docker_install_en.html">PaddlePaddle in Docker Containers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../getstarted/build_and_install/build_from_source_en.html">Installing from Sources</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../../../howto/index_en.html">HOW TO</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/usage/cmd_parameter/index_en.html">Set Command-line Parameters</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../howto/usage/cmd_parameter/use_case_en.html">Use Case</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../howto/usage/cmd_parameter/arguments_en.html">Argument Outline</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../howto/usage/cmd_parameter/detail_introduction_en.html">Detail Description</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/usage/cluster/cluster_train_en.html">PaddlePaddle Distributed Training</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/usage/cluster/cluster_train_en.html#introduction">Introduction</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/usage/cluster/cluster_train_en.html#preparations">Preparations</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/usage/cluster/cluster_train_en.html#command-line-arguments">Command-line arguments</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/usage/cluster/cluster_train_en.html#use-cluster-platforms-or-cluster-management-tools">Use cluster platforms or cluster management tools</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/usage/k8s/k8s_en.html">Paddle On Kubernetes</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/usage/k8s/k8s_aws_en.html">Distributed PaddlePaddle Training on AWS with Kubernetes</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/dev/build_en.html">Build PaddlePaddle from Source Code and Run Unit Test</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/dev/new_layer_en.html">Write New Layers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/dev/contribute_to_paddle_en.html">Contribute Code</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/deep_model/rnn/index_en.html">RNN Models</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../howto/deep_model/rnn/rnn_config_en.html">RNN Configuration</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../../howto/optimization/gpu_profiling_en.html">Tune GPU Performance</a></li>
</ul>
</li>
<li class="toctree-l1 current"><a class="reference internal" href="../../index_en.html">API</a><ul class="current">
<li class="toctree-l2 current"><a class="reference internal" href="../model_configs.html">Model Configuration</a><ul class="current">
<li class="toctree-l3"><a class="reference internal" href="activation.html">Activation</a></li>
<li class="toctree-l3"><a class="reference internal" href="layer.html">Layers</a></li>
<li class="toctree-l3"><a class="reference internal" href="evaluators.html">Evaluators</a></li>
<li class="toctree-l3 current"><a class="current reference internal" href="#">Optimizer</a></li>
<li class="toctree-l3"><a class="reference internal" href="pooling.html">Pooling</a></li>
<li class="toctree-l3"><a class="reference internal" href="networks.html">Networks</a></li>
<li class="toctree-l3"><a class="reference internal" href="attr.html">Parameter Attribute</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../data.html">Data Reader Interface and DataSets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../run_logic.html">Training and Inference</a></li>
</ul>
</li>
</ul>

        
    </nav>
    
    <section class="doc-content-wrap">

      
<div role="navigation" aria-label="breadcrumbs navigation">
  <ul class="wy-breadcrumbs">
      
        <li><a href="../../index_en.html">API</a> > </li>
      
        <li><a href="../model_configs.html">Model Configuration</a> > </li>
      
    <li>Optimizer</li>
  </ul>
</div>
      
      <div class="wy-nav-content" id="doc-content">
        <div class="rst-content">
          <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
           <div itemprop="articleBody">
            
  <div class="section" id="optimizer">
<h1>Optimizer<a class="headerlink" href="#optimizer" title="Permalink to this headline">¶</a></h1>
<div class="section" id="momentum">
<h2>Momentum<a class="headerlink" href="#momentum" title="Permalink to this headline">¶</a></h2>
<p>Optimizers(update equation) for SGD method.</p>
<p>TODO(yuyang18): Complete comments.</p>
<dl class="class">
<dt>
<em class="property">class </em><code class="descclassname">paddle.v2.optimizer.</code><code class="descname">Momentum</code><span class="sig-paren">(</span><em>momentum=None</em>, <em>sparse=False</em>, <em>**kwargs</em><span class="sig-paren">)</span></dt>
<dd><p>SGD Optimizer.</p>
<p>SGD is an optimization method, trying to find a neural network that
minimize the &#8220;cost/error&#8221; of it by iteration. In paddle&#8217;s implementation
SGD Optimizer is synchronized, which means all gradients will be wait to
calculate and reduced into one gradient, then do optimize operation.</p>
<p>The neural network consider the learning problem of minimizing an objective
function, that has the form of a sum</p>
<div class="math">
\[Q(w) = \sum_{i}^{n} Q_i(w)\]</div>
<p>The value of function Q sometimes is the cost of neural network (Mean
Square Error between prediction and label for example). The function Q is
parametrised by w, the weight/bias of neural network. And weights is what to
be learned. The i is the i-th observation in (trainning) data.</p>
<p>So, the SGD method will optimize the weight by</p>
<div class="math">
\[w = w - \eta \nabla Q(w) = w - \eta \sum_{i}^{n} \nabla Q_i(w)\]</div>
<p>where <span class="math">\(\eta\)</span> is learning rate. And <span class="math">\(n\)</span> is batch size.</p>
</dd></dl>

</div>
<div class="section" id="adam">
<h2>Adam<a class="headerlink" href="#adam" title="Permalink to this headline">¶</a></h2>
<p>Optimizers(update equation) for SGD method.</p>
<p>TODO(yuyang18): Complete comments.</p>
<dl class="class">
<dt>
<em class="property">class </em><code class="descclassname">paddle.v2.optimizer.</code><code class="descname">Adam</code><span class="sig-paren">(</span><em>beta1=0.9</em>, <em>beta2=0.999</em>, <em>epsilon=1e-08</em>, <em>**kwargs</em><span class="sig-paren">)</span></dt>
<dd><p>Adam optimizer.
The details of please refer <a class="reference external" href="https://arxiv.org/abs/1412.6980">Adam: A Method for Stochastic Optimization</a></p>
<div class="math">
\[\begin{split}m(w, t) &amp; = \beta_1 m(w, t-1) + (1 - \beta_1) \nabla Q_i(w) \\
v(w, t) &amp; = \beta_2 v(w, t-1) + (1 - \beta_2)(\nabla Q_i(w)) ^2 \\
w &amp; = w - \frac{\eta}{\sqrt{v(w,t) + \epsilon}}\end{split}\]</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>beta1</strong> (<em>float</em>) &#8211; the <span class="math">\(\beta_1\)</span> in equation.</li>
<li><strong>beta2</strong> (<em>float</em>) &#8211; the <span class="math">\(\beta_2\)</span> in equation.</li>
<li><strong>epsilon</strong> (<em>float</em>) &#8211; the <span class="math">\(\epsilon\)</span> in equation. It is used to prevent
divided by zero.</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>

</div>
<div class="section" id="adamax">
<h2>Adamax<a class="headerlink" href="#adamax" title="Permalink to this headline">¶</a></h2>
<p>Optimizers(update equation) for SGD method.</p>
<p>TODO(yuyang18): Complete comments.</p>
<dl class="class">
<dt>
<em class="property">class </em><code class="descclassname">paddle.v2.optimizer.</code><code class="descname">Adamax</code><span class="sig-paren">(</span><em>beta1=0.9</em>, <em>beta2=0.999</em>, <em>**kwargs</em><span class="sig-paren">)</span></dt>
<dd><p>Adamax optimizer.</p>
<p>The details of please refer this <a class="reference external" href="https://arxiv.org/abs/1412.6980">Adam: A Method for Stochastic Optimization</a></p>
<div class="math">
\[\begin{split}m_t &amp; = \beta_1 * m_{t-1} + (1-\beta_1)* \nabla Q_i(w) \\
u_t &amp; = max(\beta_2*u_{t-1}, abs(\nabla Q_i(w))) \\
w_t &amp; = w_{t-1} - (\eta/(1-\beta_1^t))*m_t/u_t\end{split}\]</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>beta1</strong> (<em>float</em>) &#8211; the <span class="math">\(\beta_1\)</span> in the equation.</li>
<li><strong>beta2</strong> (<em>float</em>) &#8211; the <span class="math">\(\beta_2\)</span> in the equation.</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>

</div>
<div class="section" id="adagrad">
<h2>AdaGrad<a class="headerlink" href="#adagrad" title="Permalink to this headline">¶</a></h2>
<p>Optimizers(update equation) for SGD method.</p>
<p>TODO(yuyang18): Complete comments.</p>
<dl class="class">
<dt>
<em class="property">class </em><code class="descclassname">paddle.v2.optimizer.</code><code class="descname">AdaGrad</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span></dt>
<dd><p>Adagrad(for ADAptive GRAdient algorithm) optimizer.</p>
<p>For details please refer this <a class="reference external" href="http://www.magicbroom.info/Papers/DuchiHaSi10.pdf">Adaptive Subgradient Methods for
Online Learning and Stochastic Optimization</a>.</p>
<div class="math">
\[\begin{split}G &amp;= \sum_{\tau=1}^{t} g_{\tau} g_{\tau}^T \\
w &amp; = w - \eta diag(G)^{-\frac{1}{2}} \circ g\end{split}\]</div>
</dd></dl>

</div>
<div class="section" id="decayedadagrad">
<h2>DecayedAdaGrad<a class="headerlink" href="#decayedadagrad" title="Permalink to this headline">¶</a></h2>
<p>Optimizers(update equation) for SGD method.</p>
<p>TODO(yuyang18): Complete comments.</p>
<dl class="class">
<dt>
<em class="property">class </em><code class="descclassname">paddle.v2.optimizer.</code><code class="descname">DecayedAdaGrad</code><span class="sig-paren">(</span><em>rho=0.95</em>, <em>epsilon=1e-06</em>, <em>**kwargs</em><span class="sig-paren">)</span></dt>
<dd><p>AdaGrad method with decayed sum gradients. The equations of this method
show as follow.</p>
<div class="math">
\[\begin{split}E(g_t^2) &amp;= \rho * E(g_{t-1}^2) + (1-\rho) * g^2 \\
learning\_rate &amp;= 1/sqrt( ( E(g_t^2) + \epsilon )\end{split}\]</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>rho</strong> (<em>float</em>) &#8211; The <span class="math">\(\rho\)</span> parameter in that equation</li>
<li><strong>epsilon</strong> (<em>float</em>) &#8211; The <span class="math">\(\epsilon\)</span> parameter in that equation.</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>

</div>
<div class="section" id="adadelta">
<h2>AdaDelta<a class="headerlink" href="#adadelta" title="Permalink to this headline">¶</a></h2>
<p>Optimizers(update equation) for SGD method.</p>
<p>TODO(yuyang18): Complete comments.</p>
<dl class="class">
<dt>
<em class="property">class </em><code class="descclassname">paddle.v2.optimizer.</code><code class="descname">AdaDelta</code><span class="sig-paren">(</span><em>rho=0.95</em>, <em>epsilon=1e-06</em>, <em>**kwargs</em><span class="sig-paren">)</span></dt>
<dd><p>AdaDelta method. The details of adadelta please refer to this
<a class="reference external" href="http://www.matthewzeiler.com/pubs/googleTR2012/googleTR2012.pdf">ADADELTA: AN ADAPTIVE LEARNING RATE METHOD</a>.</p>
<div class="math">
\[\begin{split}E(g_t^2) &amp;= \rho * E(g_{t-1}^2) + (1-\rho) * g^2 \\
learning\_rate &amp;= sqrt( ( E(dx_{t-1}^2) + \epsilon ) / ( \
                  E(g_t^2) + \epsilon ) ) \\
E(dx_t^2) &amp;= \rho * E(dx_{t-1}^2) + (1-\rho) * (-g*learning\_rate)^2\end{split}\]</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>rho</strong> (<em>float</em>) &#8211; <span class="math">\(\rho\)</span> in equation</li>
<li><strong>epsilon</strong> (<em>float</em>) &#8211; <span class="math">\(\rho\)</span> in equation</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>

</div>
<div class="section" id="rmsprop">
<h2>RMSProp<a class="headerlink" href="#rmsprop" title="Permalink to this headline">¶</a></h2>
<p>Optimizers(update equation) for SGD method.</p>
<p>TODO(yuyang18): Complete comments.</p>
<dl class="class">
<dt>
<em class="property">class </em><code class="descclassname">paddle.v2.optimizer.</code><code class="descname">RMSProp</code><span class="sig-paren">(</span><em>rho=0.95</em>, <em>epsilon=1e-06</em>, <em>**kwargs</em><span class="sig-paren">)</span></dt>
<dd><p>RMSProp(for Root Mean Square Propagation) optimizer. For details please
refer this <a class="reference external" href="http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf">slide</a>.</p>
<p>The equations of this method as follows:</p>
<div class="math">
\[\begin{split}v(w, t) &amp; = \rho v(w, t-1) + (1 - \rho)(\nabla Q_{i}(w))^2 \\
w &amp; = w - \frac{\eta} {\sqrt{v(w,t) + \epsilon}} \nabla Q_{i}(w)\end{split}\]</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>rho</strong> (<em>float</em>) &#8211; the <span class="math">\(\rho\)</span> in the equation. The forgetting factor.</li>
<li><strong>epsilon</strong> (<em>float</em>) &#8211; the <span class="math">\(\epsilon\)</span> in the equation.</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>

</div>
</div>


           </div>
          </div>
          <footer>
  
    <div class="rst-footer-buttons" role="navigation" aria-label="footer navigation">
      
        <a href="pooling.html" class="btn btn-neutral float-right" title="Pooling" accesskey="n">Next <span class="fa fa-arrow-circle-right"></span></a>
      
      
        <a href="evaluators.html" class="btn btn-neutral" title="Evaluators" accesskey="p"><span class="fa fa-arrow-circle-left"></span> Previous</a>
      
    </div>
  

  <hr/>

  <div role="contentinfo">
    <p>
        &copy; Copyright 2016, PaddlePaddle developers.

    </p>
  </div>
  Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/snide/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>. 

</footer>

        </div>
      </div>

    </section>

  </div>
  

    <script type="text/javascript">
        var DOCUMENTATION_OPTIONS = {
            URL_ROOT:'../../../',
            VERSION:'',
            COLLAPSE_INDEX:false,
            FILE_SUFFIX:'.html',
            HAS_SOURCE:  true,
            SOURCELINK_SUFFIX: ".txt",
        };
    </script>
      <script type="text/javascript" src="../../../_static/jquery.js"></script>
      <script type="text/javascript" src="../../../_static/underscore.js"></script>
      <script type="text/javascript" src="../../../_static/doctools.js"></script>
      <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
       
  
    <script type="text/javascript" src="../../../_static/js/theme.js"></script>
  
  
  <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha384-Tc5IQib027qvyjSMfHjOMaLkfuWVxZxUPnCJA7l2mCWNIpG9mGCD8wGNIcPD7Txa" crossorigin="anonymous"></script>
  <script src="https://cdn.jsdelivr.net/perfect-scrollbar/0.6.14/js/perfect-scrollbar.jquery.min.js"></script>
  <script src="../../../_static/js/paddle_doc_init.js"></script> 

</body>
</html>