Time-delay Induced Stochastic Optimization and Extremum Seeking

TL;DR

This paper introduces a new stochastic optimization algorithm utilizing time-delayed perturbations and adaptive step sizes, demonstrating exponential convergence and practical effectiveness through theoretical proofs and numerical simulations.

Contribution

It presents a novel extremum seeking method based on time delays and step size adaptation, with proven convergence properties and validated simulations.

Findings

Proven global exponential convergence in expectation.

Demonstrated practical convergence of trajectory variance.

Validated effectiveness through numerical simulations on various functions.

Abstract

In this paper a novel stochastic optimization and extremum seeking algorithm is presented, one which is based on time-delayed random perturbations and step size adaptation. For the case of a one-dimensional quadratic unconstrained optimization problem, global exponential convergence in expectation and global exponential practical convergence of the variance of the trajectories are proven. The theoretical results are complemented by numerical simulations for one- and multi-dimensional quadratic and non-quadratic objective functions.