Simultaneous perturbation stochastic approximation: towards one-measurement per iteration

TL;DR

This paper introduces a new stochastic approximation algorithm that reduces the number of function measurements per iteration from two to one on average, maintaining convergence and effectiveness.

Contribution

The paper presents a novel SPSA variant that requires only one function measurement per iteration, with proven convergence and promising experimental results.

Findings

Proven strong convergence of the new algorithm.

Asymptotic normality established for the estimator.

Experimental results demonstrate effectiveness and potential.

Abstract

When measuring the value of a function to be minimized is not only expensive but also with noise, the popular simultaneous perturbation stochastic approximation (SPSA) algorithm requires only two function values in each iteration. In this paper, we propose a method requiring only one function measurement value per iteration in the average sense. We prove the strong convergence and asymptotic normality of the new algorithm. Experimental results show the effectiveness and potential of our algorithm.