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Stochastic ISTA/FISTA Adaptive Step Search Algorithms for Convex Composite Optimization

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  • Lam M. Nguyen

    (IBM Research)

  • Katya Scheinberg

    (Georgia Institute of Technology)

  • Trang H. Tran

    (Cornell University)

Abstract

We develop and analyze stochastic variants of ISTA and a full backtracking FISTA algorithms (Beck and Teboulle in SIAM J Imag Sci 2(1):183–202, 2009; Scheinberg et al. in Found Comput Math 14(3):389–417, 2014) for composite optimization without the assumption that stochastic gradient is an unbiased estimator. This work extends analysis of inexact fixed step ISTA/FISTA in Schmidt et al. (Convergence rates of inexact proximal-gradient methods for convex optimization, 2022. arXiv:1109.2415 ) to the case of stochastic gradient estimates and adaptive step-size parameter chosen by backtracking. It also extends the framework for analyzing stochastic line-search method in Cartis and Scheinberg (Math Program 169(2):337-375, 2018) to the proximal gradient framework as well as to the accelerated first order methods.

Suggested Citation

  • Lam M. Nguyen & Katya Scheinberg & Trang H. Tran, 2025. "Stochastic ISTA/FISTA Adaptive Step Search Algorithms for Convex Composite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 205(1), pages 1-37, April.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:1:d:10.1007_s10957-025-02621-8
    DOI: 10.1007/s10957-025-02621-8
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    References listed on IDEAS

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    1. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2011. "First-order methods of smooth convex optimization with inexact oracle," LIDAM Discussion Papers CORE 2011002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Katya Scheinberg, 2022. "Finite Difference Gradient Approximation: To Randomize or Not?," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2384-2388, September.
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