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arXiv · 1709.04136

Recursive Exponential Weighting for Online Non-convex Optimization

Lin Yang·Cheng Tan·Wing Shing Wong
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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.

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Lin Yang, Cheng Tan, Wing Shing Wong. 2017-09-13. Recursive Exponential Weighting for Online Non-convex Optimization. https://arxiv.org/abs/1709.04136

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