Near-linear Time Gaussian Process Optimization with Adaptive Batching and Resparsification

• URL: http://arxiv.org/abs/2002.09954v2
• Date: Wed, 26 Feb 2020 09:45:29 GMT
• Title: Near-linear Time Gaussian Process Optimization with Adaptive Batching and Resparsification
• Authors: Daniele Calandriello, Luigi Carratino, Alessandro Lazaric, Michal Valko, Lorenzo Rosasco
• Abstract summary: We introduce BBKB, the first no-regret GP optimization algorithm that provably runs in near-linear time and selects candidates in batches. We show that the same bound can be used to adaptively delay costly updates to the sparse GP approximation, achieving a near-constant per-step amortized cost.
• Score: 119.41129787351092
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gaussian processes (GP) are one of the most successful frameworks to model uncertainty. However, GP optimization (e.g., GP-UCB) suffers from major scalability issues. Experimental time grows linearly with the number of evaluations, unless candidates are selected in batches (e.g., using GP-BUCB) and evaluated in parallel. Furthermore, computational cost is often prohibitive since algorithms such as GP-BUCB require a time at least quadratic in the number of dimensions and iterations to select each batch. In this paper, we introduce BBKB (Batch Budgeted Kernel Bandits), the first no-regret GP optimization algorithm that provably runs in near-linear time and selects candidates in batches. This is obtained with a new guarantee for the tracking of the posterior variances that allows BBKB to choose increasingly larger batches, improving over GP-BUCB. Moreover, we show that the same bound can be used to adaptively delay costly updates to the sparse GP approximation used by BBKB, achieving a near-constant per-step amortized cost. These findings are then confirmed in several experiments, where BBKB is much faster than state-of-the-art methods.

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