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Volume 36, Issue 3
Parallel Stochastic Newton Method

Mojmír Mutný & Peter Richtárik

DOI: 10.4208/jcm.1708-m2017-0113

J. Comp. Math., 36 (2018), pp. 404-425.

Published online: 2018-06

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  • Abstract

We propose a parallel stochastic Newton method (PSN) for minimizing unconstrained smooth convex functions. We analyze the method in the strongly convex case, and give conditions under which acceleration can be expected when compared to its serial counterpart. We show how PSN can be applied to the large quadratic function minimization in general, and empirical risk minimization problems. We demonstrate the practical efficiency of the method through numerical experiments and models of simple matrix classes.

  • Keywords

optimization, parallel methods, Newton's method, stochastic algorithms.

  • AMS Subject Headings

65K05, 65Y05, 68W10, 68W20.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mojmir.mutny@inf.ethz.ch (Mojmír Mutný)

peter.richtarik@ed.ac.uk (Peter Richtárik)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-404, author = {Mutný , Mojmír and Richtárik , Peter}, title = {Parallel Stochastic Newton Method}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {3}, pages = {404--425}, abstract = {

We propose a parallel stochastic Newton method (PSN) for minimizing unconstrained smooth convex functions. We analyze the method in the strongly convex case, and give conditions under which acceleration can be expected when compared to its serial counterpart. We show how PSN can be applied to the large quadratic function minimization in general, and empirical risk minimization problems. We demonstrate the practical efficiency of the method through numerical experiments and models of simple matrix classes.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1708-m2017-0113}, url = {http://global-sci.org/intro/article_detail/jcm/12268.html} }
TY - JOUR T1 - Parallel Stochastic Newton Method AU - Mutný , Mojmír AU - Richtárik , Peter JO - Journal of Computational Mathematics VL - 3 SP - 404 EP - 425 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1708-m2017-0113 UR - https://global-sci.org/intro/article_detail/jcm/12268.html KW - optimization, parallel methods, Newton's method, stochastic algorithms. AB -

We propose a parallel stochastic Newton method (PSN) for minimizing unconstrained smooth convex functions. We analyze the method in the strongly convex case, and give conditions under which acceleration can be expected when compared to its serial counterpart. We show how PSN can be applied to the large quadratic function minimization in general, and empirical risk minimization problems. We demonstrate the practical efficiency of the method through numerical experiments and models of simple matrix classes.

Mutný , Mojmír and Richtárik , Peter. (2018). Parallel Stochastic Newton Method. Journal of Computational Mathematics. 36 (3). 404-425. doi:10.4208/jcm.1708-m2017-0113
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