Online Non-Convex Learning: Following the Perturbed Leader is Optimal
This provides an optimal regret bound for a classical algorithm in non-convex online learning, which is incremental but improves theoretical guarantees for machine learning practitioners.
The paper tackles the problem of online learning with non-convex losses using an offline optimization oracle, showing that the Follow the Perturbed Leader algorithm achieves an optimal regret rate of O(T^{-1/2}), improving upon the previous best of O(T^{-1/3}).
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'.