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We present a new algorithm, truncated variance reduction (TruVaR), thattreats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussianprocesses in a unified fashion. The algorithm greedily shrinks a sum oftruncated variances within a set of potential maximizers (BO) or unclassifiedpoints (LSE), which is updated based on confidence bounds. TruVaR is effectivein several important settings that are typically non-trivial to incorporateinto myopic algorithms, including pointwise costs and heteroscedastic noise. Weprovide a general theoretical guarantee for TruVaR covering these aspects, anduse it to recover and strengthen existing results on BO and LSE. Moreover, weprovide a new result for a setting where one can select from a number of noiselevels having associated costs. We demonstrate the effectiveness of thealgorithm on both synthetic and real-world data sets.

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