Efficient Nonmyopic Bayesian Optimization via One-Shot Multi-Step Trees

December 7, 2020

Abstract

Bayesian optimization is a sequential decision making framework for optimizing expensive-to-evaluate black-box functions. Computing a full lookahead policy amounts to solving a highly intractable stochastic dynamic program. Myopic approaches, such as expected improvement, are often adopted in practice, but they ignore the long-term impact of the immediate decision. Existing nonmyopic approaches are mostly heuristic and/or computationally expensive. In this paper, we provide the first efficient implementation of general multi-step lookahead Bayesian optimization, formulated as a sequence of nested optimization problems within a multi-step scenario tree. Instead of solving these problems in a nested way, we equivalently optimize all decision variables in the full tree jointly, in a “one- shot” fashion. Combining this with an efficient method for implementing multi- step Gaussian process “fantasization,” we demonstrate that multi-step expected improvement is computationally tractable and exhibits performance superior to existing methods on a wide range of benchmarks.

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AUTHORS

Written by

Shali Jiang

Daniel R. Jiang

Maximilian Balandat

Brian Karrer

Jacob R. Gardner

Roman Garnett

Publisher

Neural Information Processing Systems (NeurIPS 2020)

Research Topics

Machine learning

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