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

*Proceedings of the 31st International Conference on Algorithmic Learning Theory*, PMLR 117:845-861, 2020.

#### 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 $O(T^{-1/2})$ in this setting. This improves upon the previous best-known regret rate of $O(T^{-1/3})$ 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”.