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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.
Reference:
Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation I. Bogunovic, J. Scarlett, A. Krause, V. CevherIn Neural Information Processing Systems (NIPS), 2016
Bibtex Entry:
@inproceedings{bogunovic16truncated,
	Author = {Ilija Bogunovic and Jonathan Scarlett and Andreas Krause and Volkan Cevher},
	Booktitle = {Neural Information Processing Systems (NIPS)},
	Month = {December},
	Title = {Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation},
	Year = {2016}}