Adaptive State-Dependent Diffusion for Derivative-Free Optimization

TL;DR

This paper introduces a stochastic derivative-free optimization method with adaptive variance that guarantees global convergence without gradient information, outperforming traditional methods like simplex and simulated annealing.

Contribution

It presents a novel state-dependent adaptive variance strategy for derivative-free optimization with proven convergence guarantees.

Findings

Proves global convergence in probability with algebraic rate.

Achieves convergence without explicit gradient or function value comparisons.

Numerical examples demonstrate effectiveness of the method.

Abstract

This paper develops and analyzes a stochastic derivative-free optimization strategy. A key feature is the state-dependent adaptive variance. We prove global convergence in probability with algebraic rate and give the quantitative results in numerical examples. A striking fact is that convergence is achieved without explicit information of the gradient and even without comparing different objective function values as in established methods such as the simplex method and simulated annealing. It can otherwise be compared to annealing with state-dependent temperature.