Stochastic Zeroth-Order Multi-Gradient Algorithm for Multi-Objective Optimization

Zhihao Li, Qingtao Wu, Moli Zhang (), Lin Wang, Youming Ge and Guoyong Wang
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Zhihao Li: School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China
Qingtao Wu: School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China
Moli Zhang: School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China
Lin Wang: School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China
Youming Ge: School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China
Guoyong Wang: School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang 471023, China

Mathematics, 2025, vol. 13, issue 4, 1-31

Abstract: Multi-objective optimization (MOO) has become an important method in machine learning, which involves solving multiple competing objective problems simultaneously. Nowadays, many MOO algorithms assume that gradient information is easily available and use this information to optimize functions. However, when encountering situations where gradients are not available, such as black-box functions or non-differentiable functions, these algorithms become ineffective. In this paper, we propose a zeroth-order MOO algorithm named SZMG (stochastic zeroth-order multi-gradient algorithm), which approximates the gradient of functions by finite difference methods. Meanwhile, to avoid conflicting gradients between functions and reduce stochastic multi-gradient direction bias caused by stochastic gradients, an SGD-type method is adopted to acquire weight parameters. Under the non-convex setting and mild assumptions, the convergence rate is established for the SZMG algorithm. Simulation results demonstrate the effectiveness of the SZMG algorithm.

Keywords: multi-objective optimization; zeroth-order optimization; stochastic optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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