Convergence of Simulated Annealing Using Kinetic Langevin Dynamics

TL;DR

This paper analyzes the convergence properties of a simulated annealing algorithm based on kinetic Langevin dynamics, providing theoretical guarantees for both continuous and discrete time versions under specific conditions.

Contribution

It offers the first convergence rate results for kinetic Langevin-based simulated annealing, including conditions on the potential, cooling schedule, and discretization.

Findings

Convergence rates established for continuous-time kinetic Langevin annealing.

Convergence rates established for discrete-time kinetic Langevin annealing.

Conditions on potential and parameters ensure algorithm effectiveness.

Abstract

We study the simulated annealing algorithm based on the kinetic Langevin dynamics, in order to find the global minimum of a non-convex potential function. For both the continuous time formulation and a discrete time analogue, we obtain the convergence rate results under technical conditions on the potential function, together with an appropriate choice of the cooling schedule and the time discretization parameters.