Second-order Online Nonconvex Optimization
Optimization and Control
2020-12-11 v2
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.
Cite
@article{arxiv.2001.10114,
title = {Second-order Online Nonconvex Optimization},
author = {Antoine Lesage-Landry and Joshua A. Taylor and Iman Shames},
journal= {arXiv preprint arXiv:2001.10114},
year = {2020}
}