Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation

TL;DR

TruVaR is a unified algorithm for Bayesian optimization and level-set estimation that adaptively reduces uncertainty, effectively handling complex scenarios like heteroscedastic noise and cost variations, with strong theoretical guarantees and practical success.

Contribution

The paper introduces TruVaR, a novel unified approach for BO and LSE that handles complex noise and cost settings with theoretical guarantees and improved results.

Findings

Effective in heteroscedastic noise settings

Handles pointwise costs in optimization

Demonstrates strong empirical performance

Abstract

We present a new algorithm, truncated variance reduction (TruVaR), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set of potential maximizers (BO) or unclassified points (LSE), which is updated based on confidence bounds. TruVaR is effective in several important settings that are typically non-trivial to incorporate into myopic algorithms, including pointwise costs and heteroscedastic noise. We provide a general theoretical guarantee for TruVaR covering these aspects, and use it to recover and strengthen existing results on BO and LSE. Moreover, we provide a new result for a setting where one can select from a number of noise levels having associated costs. We demonstrate the effectiveness of the algorithm on both synthetic and real-world data sets.