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

03/19/2019

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by   Arun Sai Suggala, et al.

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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'.