Recursive Exponential Weighting for Online Non-convex Optimization

TL;DR

This paper introduces a recursive exponential weighting algorithm for online non-convex optimization that achieves the optimal regret bound of O(√T), significantly advancing the theoretical understanding of non-convex online learning.

Contribution

It presents the first online algorithm with provable O(√T) regret for non-convex optimization, using a novel recursive structure.

Findings

Achieves O(√T) regret, matching the lower bound.

First online algorithm with provable regret bounds for non-convex problems.

Introduces a recursive structure to exponential weighting algorithms.

Abstract

In this paper, we investigate the online non-convex optimization problem which generalizes the classic {online convex optimization problem by relaxing the convexity assumption on the cost function. For this type of problem, the classic exponential weighting online algorithm has recently been shown to attain a sub-linear regret of $O(\sqrt{T\log T})$. In this paper, we introduce a novel recursive structure to the online algorithm to define a recursive exponential weighting algorithm that attains a regret of $O(\sqrt{T})$, matching the well-known regret lower bound. To the best of our knowledge, this is the first online algorithm with provable $O(\sqrt{T})$ regret for the online non-convex optimization problem.