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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.
Author Information
Ilija Bogunovic (EPFL Lausanne)
Jonathan Scarlett (EPFL)
Andreas Krause (ETH Zurich)
Volkan Cevher (EPFL)
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2009 Spotlight: Online Learning of Assignments »
Matthew Streeter · Daniel Golovin · Andreas Krause -
2009 Poster: Learning with Compressible Priors »
Volkan Cevher -
2008 Poster: Sparse Signal Recovery Using Markov Random Fields »
Volkan Cevher · Marco F Duarte · Chinmay Hegde · Richard Baraniuk -
2008 Spotlight: Sparse Signal Recovery Using Markov Random Fields »
Volkan Cevher · Marco F Duarte · Chinmay Hegde · Richard Baraniuk -
2007 Spotlight: Selecting Observations against Adversarial Objectives »
Andreas Krause · H. Brendan McMahan · Carlos Guestrin · Anupam Gupta -
2007 Poster: Selecting Observations against Adversarial Objectives »
Andreas Krause · H. Brendan McMahan · Carlos Guestrin · Anupam Gupta