Stochastic Approximation Proximal Method of Multipliers for Convex Stochastic Programming

Liwei Zhang (), Yule Zhang (), Xiantao Xiao () and Jia Wu ()
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Liwei Zhang: Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, 116023 Dalian, China
Yule Zhang: Department of Statistics, School of Science, Dalian Maritime University, 116026 Dalian, China
Xiantao Xiao: Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, 116023 Dalian, China
Jia Wu: Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, 116023 Dalian, China

Mathematics of Operations Research, 2023, vol. 48, issue 1, 177-193

Abstract: This paper considers the problem of minimizing a convex expectation function over a closed convex set, coupled with a set of inequality convex expectation constraints. We present a new stochastic approximation proximal method of multipliers to solve this convex stochastic optimization problem. We analyze regrets of the proposed method for solving convex stochastic optimization problems. Under mild conditions, we show that this method exhibits sublinear regret for both objective reduction and constraint violation if parameters in the algorithm are properly chosen. Moreover, we investigate the high probability performance of the proposed method under the standard light-tail assumption.

Keywords: Primary: 90C30; secondary: 90C15; 49M37; stochastic approximation; proximal method of multipliers; objective regret; constraint violation regret; high probability regret bound; convex stochastic optimization (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:1:p:177-193

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