Constrained Stochastic Multi-Objective Optimization

Biqian Feng, Xiyang Zhang, Cheng Gong, Tiancan Feng, Xiaoyuan Zhang, Tse-Tin Chan

Keywords: Multiobjective optimization

Abstract: This paper aims to address the constrained stochastic multi-objective optimization (CSMOO) problem, where both objectives and constraints involve expectations over random variables. Firstly, to tackle the computational challenge of exact expectation evaluations, we propose two approximation schemes: stochastic approximation, which updates the entire problem using new samples at each iteration, and block stochastic approximation, which updates only subsets of variables iteratively. Secondly, to handle potential infeasibility in the surrogate problems, we develop two strategies: a feasible update reformulation and a rigorously justified penalty scheme equivalent to the original problem. Our framework provides asymptotic convergence guarantees to stationary points that satisfy Fritz John conditions. Experiments on synthetic and real-world wireless communication benchmarks demonstrate superior convergence, stability, and constraint satisfaction over state-of-the-art methods.

Primary Area: optimization

Submission Number: 2416