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arXiv · 2001.10114

Second-order Online Nonconvex Optimization

Antoine Lesage-Landry·Joshua A. Taylor·Iman Shames
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Abstract

We present the online Newton's method, a single-step second-order method for online nonconvex optimization. We analyze its performance and obtain a dynamic regret bound that is linear in the cumulative variation between round optima. We show that if the variation between round optima is limited, the method leads to a constant regret bound. In the general case, the online Newton's method outperforms online convex optimization algorithms for convex functions and performs similarly to a specialized algorithm for strongly convex functions. We simulate the performance of the online Newton's method on a nonlinear, nonconvex moving target localization example and find that it outperforms a first-order approach.

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Antoine Lesage-Landry, Joshua A. Taylor, Iman Shames. 2020-01-27. Second-order Online Nonconvex Optimization. https://doi.org/10.1109/tac.2020.3040372

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