Online Non-Convex Learning: Following the Perturbed Leader is Optimal

Abstract: We study the problem of online learning with non-convex losses, where the learner has access to an offline optimization oracle. We show that the classical Follow the Perturbed Leader (FTPL) algorithm achieves optimal regret rate of $O(T<sup>{-1/2})$ in this setting. This improves upon the previous best-known regret rate of $O(T<sup>{-1/3})$ for FTPL. We further show that an optimistic variant of FTPL achieves better regret bounds when the sequence of losses encountered by the learner is `predictable'.