On the Second-order Convergence Properties of Random Search Methods

Author name not available (Why is that?)

Publication date: 25 October 2021

Abstract: We study the theoretical convergence properties of random-search methods when optimizing non-convex objective functions without having access to derivatives. We prove that standard random-search methods that do not rely on second-order information converge to a second-order stationary point. However, they suffer from an exponential complexity in terms of the input dimension of the problem. In order to address this issue, we propose a novel variant of random search that exploits negative curvature by only relying on function evaluations. We prove that this approach converges to a second-order stationary point at a much faster rate than vanilla methods: namely, the complexity in terms of the number of function evaluations is only linear in the problem dimension. We test our algorithm empirically and find good agreements with our theoretical results.

Has companion code repository: https://github.com/adamsolomou/second-order-random-search

This page was built for publication: On the Second-order Convergence Properties of Random Search Methods

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6381248)