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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> <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 “cost/error” of it by iteration. In paddle’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> <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"> \[\begin{split}m(w, t) & = \beta_1 m(w, t-1) + (1 - \beta_1) \nabla Q_i(w) \\ v(w, t) & = \beta_2 v(w, t-1) + (1 - \beta_2)(\nabla Q_i(w)) ^2 \\ w & = w - \frac{\eta}{\sqrt{v(w,t) + \epsilon}}\end{split}\]</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>) – the <span class="math">\(\beta_1\)</span> in equation.</li> <li><strong>beta2</strong> (<em>float</em>) – the <span class="math">\(\beta_2\)</span> in equation.</li> <li><strong>epsilon</strong> (<em>float</em>) – 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> <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"> \[\begin{split}m_t & = \beta_1 * m_{t-1} + (1-\beta_1)* \nabla Q_i(w) \\ u_t & = max(\beta_2*u_{t-1}, abs(\nabla Q_i(w))) \\ w_t & = w_{t-1} - (\eta/(1-\beta_1^t))*m_t/u_t\end{split}\]</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>) – the <span class="math">\(\beta_1\)</span> in the equation.</li> <li><strong>beta2</strong> (<em>float</em>) – 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> <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"> \[\begin{split}G &= \sum_{\tau=1}^{t} g_{\tau} g_{\tau}^T \\ w & = w - \eta diag(G)^{-\frac{1}{2}} \circ g\end{split}\]</div> </dd></dl> </div> <div class="section" id="decayedadagrad"> <h2>DecayedAdaGrad<a class="headerlink" href="#decayedadagrad" title="Permalink to this headline">¶</a></h2> <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"> \[\begin{split}E(g_t^2) &= \rho * E(g_{t-1}^2) + (1-\rho) * g^2 \\ learning\_rate &= 1/sqrt( ( E(g_t^2) + \epsilon )\end{split}\]</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>) – The <span class="math">\(\rho\)</span> parameter in that equation</li> <li><strong>epsilon</strong> (<em>float</em>) – 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> <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"> \[\begin{split}E(g_t^2) &= \rho * E(g_{t-1}^2) + (1-\rho) * g^2 \\ learning\_rate &= sqrt( ( E(dx_{t-1}^2) + \epsilon ) / ( \ E(g_t^2) + \epsilon ) ) \\ E(dx_t^2) &= \rho * E(dx_{t-1}^2) + (1-\rho) * (-g*learning\_rate)^2\end{split}\]</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>) – <span class="math">\(\rho\)</span> in equation</li> <li><strong>epsilon</strong> (<em>float</em>) – <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> <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"> \[\begin{split}v(w, t) & = \rho v(w, t-1) + (1 - \rho)(\nabla Q_{i}(w))^2 \\ w & = w - \frac{\eta} {\sqrt{v(w,t) + \epsilon}} \nabla Q_{i}(w)\end{split}\]</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>) – the <span class="math">\(\rho\)</span> in the equation. The forgetting factor.</li> <li><strong>epsilon</strong> (<em>float</em>) – 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> © 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>