A stochastic linearized proximal method of multipliers for convex stochastic optimization with expectation constraints

• URL: http://arxiv.org/abs/2106.11577v1
• Date: Tue, 22 Jun 2021 07:24:17 GMT
• Title: A stochastic linearized proximal method of multipliers for convex stochastic optimization with expectation constraints
• Authors: Liwei Zhang and Yule Zhang and Jia Wu and Xiantao Xiao
• Abstract summary: We present a computable approximation type algorithm, namely the linearized proximal convex method of multipliers. Some preliminary numerical results demonstrate the performance of the proposed algorithm.
• Score: 8.133190610747974
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal method of multipliers, to solve this convex stochastic optimization problem. This algorithm can be roughly viewed as a hybrid of stochastic approximation and the traditional proximal method of multipliers. Under mild conditions, we show that this algorithm exhibits $O(K^{-1/2})$ expected convergence rates for both objective reduction and constraint violation if parameters in the algorithm are properly chosen, where $K$ denotes the number of iterations. Moreover, we show that, with high probability, the algorithm has $O(\log(K)K^{-1/2})$ constraint violation bound and $O(\log^{3/2}(K)K^{-1/2})$ objective bound. Some preliminary numerical results demonstrate the performance of the proposed algorithm.

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