Adaptive Sampling Quasi-Newton Methods for Derivative-Free Stochastic Optimization

TL;DR

This paper introduces an adaptive sampling quasi-Newton method for stochastic zero-order optimization, estimating gradients via finite differences and controlling sample sizes with modified tests, showing promising preliminary results.

Contribution

It presents a novel adaptive sampling quasi-Newton approach for derivative-free stochastic optimization, utilizing modified norm and inner product tests for sample size control.

Findings

Preliminary experiments indicate potential performance improvements.

The method effectively estimates gradients in stochastic zero-order settings.

Sample size control enhances the efficiency of the optimization process.

Abstract

We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic function using finite differences within a common random number framework. We employ modified versions of a norm test and an inner product quasi-Newton test to control the sample sizes used in the stochastic approximations. We provide preliminary numerical experiments to illustrate potential performance benefits of the proposed method.