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Poster
Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation
Ilija Bogunovic · Jonathan Scarlett · Andreas Krause · Volkan Cevher

Wed Dec 07 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #92
in Wednesday Posters »

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.

Keywords: Bandit Algorithms · Online Learning · Gaussian Processes
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Author Information

Ilija Bogunovic (EPFL Lausanne)
Jonathan Scarlett (EPFL)
Andreas Krause (ETH Zurich)
Volkan Cevher (EPFL)

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