Second-Order Online Nonconvex Optimization

Antoine Lesage-Landry, Joshua A. Taylor, Iman Shames

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)4866-4872
Number of pages7
JournalIEEE Transactions on Automatic Control
Volume66
Issue number10
DOIs
StatePublished - Oct 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Keywords

  • Moving target localization
  • Newton's method
  • online nonconvex/convex optimization
  • time-varying optimization

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