An Empirical Review of Model-based Adaptive Sampling for Global Optimization of Expensive Black-box Functions

TL;DR

This paper critically reviews model-based adaptive sampling methods for black-box optimization, highlighting their strengths, weaknesses, and the impact of discretization schemes, with empirical insights into their effectiveness across different problem types.

Contribution

It provides a comprehensive classification and analysis of adaptive sampling techniques, introduces EEPA+ as an improved method, and offers empirical evidence on their performance for engineering and algorithm design problems.

Findings

Variance-based sampling is effective for algorithm design problems.

Distance-based sampling performs well for engineering design optimization.

Dynamic discretization improves the performance of acquisition functions.

Abstract

This paper reviews the state-of-the-art model-based adaptive sampling approaches for single-objective black-box optimization (BBO). While BBO literature includes various promising sampling techniques, there is still a lack of comprehensive investigations of the existing research across the vast scope of BBO problems. We first classify BBO problems into two categories: engineering design and algorithm design optimization and discuss their challenges. We then critically discuss and analyze the adaptive model-based sampling techniques focusing on key acquisition functions. We elaborate on the shortcomings of the variance-based sampling techniques for engineering design problems. Moreover, we provide in-depth insights on the impact of the discretization schemes on the performance of acquisition functions. We emphasize the importance of dynamic discretization for distance-based exploration and introduce EEPA+, an improved variant of a previously proposed Pareto-based sampling technique. Our empirical analyses reveal the effectiveness of variance-based techniques for algorithm design and distance-based methods for engineering design optimization problems.