An Efficient Stochastic Approximation Algorithm for Stochastic Saddle Point Problems

Arkadi Nemirovski and Reuven Y. Rubinstein
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Reuven Y. Rubinstein: Technion—Israel Institute of Technology

Chapter Chapter 8 in Modeling Uncertainty, 2002, pp 156-184 from Springer

Abstract: 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.

Keywords: Modeling Uncertainty; Stochastic Approximation; Search Point; Saddle Point Problem; Minimax Problem (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-0-306-48102-4_8

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DOI: 10.1007/0-306-48102-2_8

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