Black-box Optimization with Simultaneous Statistical Inference for Optimal Performance

TL;DR

This paper introduces an online algorithm for black-box optimization that simultaneously performs statistical inference, providing reliable confidence intervals for optimal performance in complex systems with limited knowledge.

Contribution

It proposes a novel online method that addresses the lack of a central limit theorem for performance estimates and offers a consistent variance estimator and convergence analysis.

Findings

Algorithm provides asymptotic confidence intervals for performance estimates.

Ensures high reliability in decision-making under limited system knowledge.

Characterizes convergence rate of coverage probabilities.

Abstract

Black-box optimization is often encountered for decision-making in complex systems management, where the knowledge of system is limited. Under these circumstances, it is essential to balance the utilization of new information with computational efficiency. In practice, decision-makers often face the dual tasks of optimization and statistical inference for the optimal performance, in order to achieve it with a high reliability. Our goal is to address the dual tasks in an online fashion. Wu et al (2022) [arXiv preprint: 2210.06737] point out that the sample average of performance estimates generated by the optimization algorithm needs not to admit a central limit theorem. We propose an algorithm that not only tackles this issue, but also provides an online consistent estimator for the variance of the performance. Furthermore, we characterize the convergence rate of the coverage probabilities of the asymptotic confidence intervals.