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.

翻译：本文提出了基于共识的鞍点问题优化方法（CBO-SP），这是一种新型的多粒子元启发式无导数优化方法，能够以可证明的方式找到全局纳什均衡。该方法遵循群体智能思想，采用一组相互作用的粒子，这些粒子对一个变量进行最小化，对另一个变量进行最大化。该范式允许过渡到平均场极限，从而使该方法适用于理论分析，并能在关于初始化和目标函数的合理假设下（其中最值得注意的是非凸-非凹目标）获得严谨的收敛性保证。