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Accelerated Stochastic Algorithms for Convex-Concave Saddle-Point Problems

Author

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  • Renbo Zhao

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142)

Abstract

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this problem. When the gradient noises obey sub-Gaussian distributions, the oracle complexity of our restart scheme is strictly better than any of the existing methods, even in the deterministic case. Furthermore, for each problem parameter of interest, whenever the lower bound exists, the oracle complexity of our restart scheme is either optimal or nearly optimal (up to a log factor). The subroutine used in this scheme is itself a new stochastic algorithm developed for the problem where the saddle function is nonstrongly convex in the primal variable. This new algorithm, which is based on the primal-dual hybrid gradient framework, achieves the state-of-the-art oracle complexity and may be of independent interest.

Suggested Citation

  • Renbo Zhao, 2022. "Accelerated Stochastic Algorithms for Convex-Concave Saddle-Point Problems," Mathematics of Operations Research, INFORMS, vol. 47(2), pages 1443-1473, May.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:2:p:1443-1473
    DOI: 10.1287/moor.2021.1175
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