Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation
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.
Cite
@article{arxiv.1610.07379,
title = {Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation},
author = {Ilija Bogunovic and Jonathan Scarlett and Andreas Krause and Volkan Cevher},
journal= {arXiv preprint arXiv:1610.07379},
year = {2016}
}
Comments
Accepted to NIPS 2016