Efficient Regret Minimization in Non-Convex Games

TL;DR

This paper introduces an efficient approach for regret minimization in non-convex games, enabling convergence to equilibrium through gradient-based methods despite the computational challenges of standard regret minimization.

Contribution

It proposes a new notion of regret suitable for non-convex games and provides gradient-based algorithms that achieve optimal regret and convergence guarantees.

Findings

Achieves optimal regret bounds in non-convex settings

Guarantees convergence to equilibrium using the proposed methods

Introduces a computationally feasible regret notion for non-convex games

Abstract

We consider regret minimization in repeated games with non-convex loss functions. Minimizing the standard notion of regret is computationally intractable. Thus, we define a natural notion of regret which permits efficient optimization and generalizes offline guarantees for convergence to an approximate local optimum. We give gradient-based methods that achieve optimal regret, which in turn guarantee convergence to equilibrium in this framework.