Learning in Non-convex Games with an Optimization Oracle

TL;DR

This paper shows that with a slightly enhanced offline optimization oracle, online learning in non-convex adversarial settings becomes computationally equivalent to statistical learning, enabling efficient equilibrium computation in non-convex games like GANs.

Contribution

It introduces a strengthened oracle model that bridges the computational gap between online and statistical learning in non-convex settings.

Findings

Online learning becomes computationally equivalent to statistical learning with the new oracle model.

The approach enables efficient equilibrium computation in non-convex games such as GANs.

The results apply to Lipschitz and bounded non-convex functions.

Abstract

We consider online learning in an adversarial, non-convex setting under the assumption that the learner has an access to an offline optimization oracle. In the general setting of prediction with expert advice, Hazan et al. (2016) established that in the optimization-oracle model, online learning requires exponentially more computation than statistical learning. In this paper we show that by slightly strengthening the oracle model, the online and the statistical learning models become computationally equivalent. Our result holds for any Lipschitz and bounded (but not necessarily convex) function. As an application we demonstrate how the offline oracle enables efficient computation of an equilibrium in non-convex games, that include GAN (generative adversarial networks) as a special case.