Document Zbl 1516.90060

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Optim. Appl.</a> <a href="/?q=in%3A495574" title="Articles in this Issue">84, No. 2, 531-572 (2023)</a>. </div> <div class="abstract">Summary: We consider a distributed non-convex optimization problem of minimizing the sum of all local cost functions over a network of agents. This problem often appears in large-scale distributed machine learning, known as non-convex empirical risk minimization. In this paper, we propose two accelerated algorithms, named DSGT-HB and DSGT-NAG, which combine the distributed stochastic gradient tracking (DSGT) method with momentum accelerated techniques. Under appropriate assumptions, we prove that both algorithms sublinearly converge to a neighborhood of a first-order stationary point of the distributed non-convex optimization. Moreover, we derive the conditions under which DSGT-HB and DSGT-NAG achieve a network-independent linear speedup. Numerical experiments for a distributed non-convex logistic regression problem on real data sets and a deep neural network on the MNIST database show the superiorities of DSGT-HB and DSGT-NAG compared with DSGT.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7675373">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A90C15" title="MSC2020">90C15</a> </td> <td class="space"> Stochastic programming </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Adistributed+non-convex+optimization">distributed non-convex optimization</a>; <a href="/?q=ut%3Amachine+learning">machine learning</a>; <a href="/?q=ut%3Amomentum+methods">momentum methods</a>; <a href="/?q=ut%3Aoptimization+algorithms">optimization algorithms</a>; <a href="/?q=ut%3Aconvergence+rate">convergence rate</a></div> <div class="software"> <h3>Software:</h3><a href="/software/12859">MNIST</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 1516.90060" data-ciurl="/ci/07675373" data-biburl="/bibtex/07675373.bib" data-amsurl="/amsrefs/07675373.bib" data-xmlurl="/xml/07675373.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07675373.pdf" title="Zbl 1516.90060 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/s10589-022-00432-5" aria-label="DOI for “Distributed stochastic gradient tracking methods with momentum acceleration for non-convex optimization”" title="10.1007/s10589-022-00432-5">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">Tychogiorgos, G.; Gkelias, A.; Leung, KK, A non-convex distributed optimization framework and its application to wireless ad-hoc networks, IEEE Trans. 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