Adaptive Sampling Stochastic Multigradient Algorithm for Stochastic Multiobjective Optimization

Yong Zhao (), Wang Chen () and Xinmin Yang ()
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Yong Zhao: Chongqing Jiaotong University
Wang Chen: Chongqing Normal University
Xinmin Yang: Chongqing Normal University

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 1, No 8, 215-241

Abstract: Abstract In this paper, we propose an adaptive sampling stochastic multigradient algorithm for solving stochastic multiobjective optimization problems. Instead of requiring additional storage or computation of full gradients, the proposed method reduces variance by adaptively controlling the sample size used. Without the convexity assumption on the objective functions, we obtain that the proposed algorithm converges to Pareto stationary points in almost surely. We then analyze the convergence rates of the proposed algorithm. Numerical experiments are presented to demonstrate the effectiveness of the proposed algorithm.

Keywords: Stochastic multiobjective optimization; Stochastic multigradient algorithm; Adaptive sampling; Convergence rate; 90C06; 90C15; 90C29 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02334-w

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