Consensus-Based Optimization for Saddle Point Problems
Optimization and Control
2024-08-05 v2 Numerical Analysis
Classical Analysis and ODEs
Dynamical Systems
Numerical Analysis
Abstract
In this paper, we propose consensus-based optimization for saddle point problems (CBO-SP), a novel multi-particle metaheuristic derivative-free optimization method capable of provably finding global Nash equilibria. Following the idea of swarm intelligence, the method employs a group of interacting particles, which perform a minimization over one variable and a maximization over the other. This paradigm permits a passage to the mean-field limit, which makes the method amenable to theoretical analysis and allows to obtain rigorous convergence guarantees under reasonable assumptions about the initialization and the objective function, which most notably include nonconvex-nonconcave objectives.
Cite
@article{arxiv.2212.12334,
title = {Consensus-Based Optimization for Saddle Point Problems},
author = {Hui Huang and Jinniao Qiu and Konstantin Riedl},
journal= {arXiv preprint arXiv:2212.12334},
year = {2024}
}