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Finite-sum smooth optimization with SARAH

Author

Listed:
  • Lam M. Nguyen

    (IBM Research, Thomas J. Watson Research Center)

  • Marten Dijk

    (Computer Security Group)

  • Dzung T. Phan

    (IBM Research, Thomas J. Watson Research Center)

  • Phuong Ha Nguyen

    (eBay Inc.)

  • Tsui-Wei Weng

    (University of California San Diego)

  • Jayant R. Kalagnanam

    (IBM Research, Thomas J. Watson Research Center)

Abstract

We introduce NC-SARAH for non-convex optimization as a practical modified version of the original SARAH algorithm that was developed for convex optimization. NC-SARAH is the first to achieve two crucial performance properties at the same time—allowing flexible minibatch sizes and large step sizes to achieve fast convergence in practice as verified by experiments. NC-SARAH has a close to optimal asymptotic convergence rate equal to existing prior variants of SARAH called SPIDER and SpiderBoost that either use an order of magnitude smaller step size or a fixed minibatch size. For convex optimization, we propose SARAH++ with sublinear convergence for general convex and linear convergence for strongly convex problems; and we provide a practical version for which numerical experiments on various datasets show an improved performance.

Suggested Citation

  • Lam M. Nguyen & Marten Dijk & Dzung T. Phan & Phuong Ha Nguyen & Tsui-Wei Weng & Jayant R. Kalagnanam, 2022. "Finite-sum smooth optimization with SARAH," Computational Optimization and Applications, Springer, vol. 82(3), pages 561-593, July.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:3:d:10.1007_s10589-022-00375-x
    DOI: 10.1007/s10589-022-00375-x
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