Learning in Non-convex Games with an Optimization Oracle
This addresses a foundational computational problem in machine learning for researchers and practitioners dealing with non-convex optimization, though it is incremental as it builds on prior oracle models.
The paper tackles the computational gap between online and statistical learning in non-convex settings by strengthening the optimization oracle model, showing they become computationally equivalent for Lipschitz and bounded functions, and applies this to efficiently compute equilibria in non-convex games like GANs.
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.