Simulated Annealing: Rigorous finite-time guarantees for optimization on continuous domains

TL;DR

This paper extends simulated annealing to continuous domains, providing finite-time guarantees for global optimization, and connects it with Markov chain Monte Carlo convergence theory.

Contribution

It introduces a new formulation of simulated annealing that guarantees finite-time performance for continuous optimization problems.

Findings

Universal guarantees for bounded domains

Connection to MCMC convergence theory

Inspired by finite-time learning concepts

Abstract

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.