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An Efficient Stochastic Approximation Algorithm for Stochastic Saddle Point Problems

In: Modeling Uncertainty

Author

Listed:
  • Arkadi Nemirovski
  • Reuven Y. Rubinstein

    (Technion—Israel Institute of Technology)

Abstract

We show that Polyak’s (1990) stochastic approximation algorithm with averaging originally developed for unconstrained minimization of a smooth strongly convex objective function observed with noise can be naturally modified to solve convex-concave stochastic saddle point problems. We also show that the extended algorithm, considered on general families of stochastic convex-concave saddle point problems, possesses a rate of convergence unimprovable in order in the minimax sense. We finally present supporting numerical results for the proposed algorithm.

Suggested Citation

  • Arkadi Nemirovski & Reuven Y. Rubinstein, 2002. "An Efficient Stochastic Approximation Algorithm for Stochastic Saddle Point Problems," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 156-184, Springer.
    • Handle: RePEc:spr:isochp:978-0-306-48102-4_8
    DOI: 10.1007/0-306-48102-2_8
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    Cited by:

    1. Niao He & Anatoli Juditsky & Arkadi Nemirovski, 2015. "Mirror Prox algorithm for multi-term composite minimization and semi-separable problems," Computational Optimization and Applications, Springer, vol. 61(2), pages 275-319, June.

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