Document Zbl 1541.62018

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Comput.</a> <a href="/?q=in%3A512972" title="Articles in this Issue">34, No. 3, Paper No. 107, 13 p. (2024)</a>. </div> <div class="abstract">Summary: In the training process of machine learning, the minimization of the empirical risk loss function is often used to measure the difference between the model’s predicted value and the real value. Stochastic gradient descent is very popular for this type of optimization problem, but converges slowly in theoretical analysis. To solve this problem, there are already many algorithms with variance reduction techniques, such as SVRG, SAG, SAGA, etc. Some scholars apply the conjugate gradient method in traditional optimization to these algorithms, such as CGVR, SCGA, SCGN, etc., which can basically achieve linear convergence speed, but these conclusions often need to be established under some relatively strong assumptions. In traditional optimization, the conjugate gradient method often requires the use of line search techniques to achieve good experimental results. In a sense, line search embodies some properties of the conjugate methods. Taking inspiration from this, we apply the modified three-term conjugate gradient method and line search technique to machine learning. In our theoretical analysis, we obtain the same convergence rate as SCGA under weaker conditional assumptions. We also test the convergence of our algorithm using two non-convex machine learning models.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7879270">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62-08" title="MSC2020">62-08</a> </td> <td class="space"> Computational methods for problems pertaining to statistics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65K05" title="MSC2020">65K05</a> </td> <td class="space"> Numerical mathematical programming methods </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C26" title="MSC2020">90C26</a> </td> <td class="space"> Nonconvex programming, global optimization </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C52" title="MSC2020">90C52</a> </td> <td class="space"> Methods of reduced gradient type </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amachine+learning">machine learning</a>; <a href="/?q=ut%3Aempirical+risk+loss+function+minimization">empirical risk loss function minimization</a>; <a href="/?q=ut%3Astochastic+conjugate+gradient">stochastic conjugate gradient</a>; <a href="/?q=ut%3Alinear+convergence">linear convergence</a></div> <div class="software"> <h3>Software:</h3><a href="/software/22205">Adam</a>; <a href="/software/39677">Saga</a>; <a href="/software/49747">AdaBelief</a>; <a href="/software/39429">ADADELTA</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1541.62018" data-ciurl="/ci/07879270" data-biburl="/bibtex/07879270.bib" data-amsurl="/amsrefs/07879270.bib" data-xmlurl="/xml/07879270.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07879270.pdf" title="Zbl 1541.62018 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s11222-024-10409-5" aria-label="DOI for “Stochastic three-term conjugate gradient method with variance technique for non-convex learning”" title="10.1007/s11222-024-10409-5">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Bottou, L.: Large-scale machine learning with stochastic gradient descent//Proceedings of COMPSTAT’2010: 19th international conference on computational statistics Paris France, Aug 22-27, 2010 Keynote, Invited and Contributed Papers. 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