An Efficient Stochastic Approximation Algorithm for Stochastic Saddle Point Problems

  • Arkadi Nemirovski
  • Reuven Y. Rubinstein
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 46)


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.


Modeling Uncertainty Stochastic Approximation Search Point Saddle Point Problem Minimax Problem 
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Copyright information

© Springer Science + Business Media, Inc. 2002

Authors and Affiliations

  • Arkadi Nemirovski
  • Reuven Y. Rubinstein
    • 1
  1. 1.Faculty of Industrial Engineering and ManagementTechnion—Israel Institute of TechnologyHaifaIsrael

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