Title: Beyond Exploration–Exploitation: An Identification-Aware Bayesian Optimization Method under Noisy Evaluations
Primary area: optimization
Keywords: black-box optimization, Bayesian optimization, acquisition function, identification problem

Abstract: In this study, we investigate black-box optimization problems with heteroscedastic noise, a setting commonly encountered in hyperparameter tuning for machine learning models. Bayesian optimization (BO) is a popular framework for such problems, with prior work primarily focusing on designing acquisition functions or surrogate models to balance exploration and exploitation. However, a critical yet underexplored issue is the identification problem: BO algorithms often locate promising solutions but fail to reliably identify and return them to users. We take the first step toward addressing this challenge. We formally define the identification error within a standard BO framework and derive a myopic acquisition function that directly minimizes this error. A surprising theoretical result shows that the acquisition function for minimizing identification error is equivalent to the difference between two widely used criteria: the knowledge gradient (KG) and expected improvement (EI). Building on this insight, we propose a novel acquisition function, Identification-Error Aware Acquisition (IDEA), and establish its asymptotic no-regret property. The effectiveness of IDEA is demonstrated on benchmark test functions.

TL;DR: Identification-Aware BO