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

Author

Listed:
  • 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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