Recursive Exponential Weighting for Online Non-convex Optimization

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( √ 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( √ T ), matching the well-known regret lower bound. To the best of our knowledge, this is the first online algorithm with provable O( √ T ) regret for the online non-convex optimization problem.