Bayesian optimization with gradients

Jian Wu, Matthias Poloczek, Andrew Gordon Wilson, Peter I. Frazier

Research output: Contribution to journalConference article

Abstract

Bayesian optimization has been successful at global optimization of expensive-to-evaluate multimodal objective functions. However, unlike most optimization methods, Bayesian optimization typically does not use derivative information. In this paper we show how Bayesian optimization can exploit derivative information to find good solutions with fewer objective function evaluations. In particular, we develop a novel Bayesian optimization algorithm, the derivative-enabled knowledgegradient (d-KG), which is one-step Bayes-optimal, asymptotically consistent, and provides greater one-step value of information than in the derivative-free setting. d-KG accommodates noisy and incomplete derivative information, comes in both sequential and batch forms, and can optionally reduce the computational cost of inference through automatically selected retention of a single directional derivative. We also compute the d-KG acquisition function and its gradient using a novel fast discretization-free technique. We show d-KG provides state-of-the-art performance compared to a wide range of optimization procedures with and without gradients, on benchmarks including logistic regression, deep learning, kernel learning, and k-nearest neighbors.

Original languageEnglish (US)
Pages (from-to)5268-5279
Number of pages12
JournalAdvances in Neural Information Processing Systems
Volume2017-December
StatePublished - 2017
Event31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States
Duration: Dec 4 2017Dec 9 2017

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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    Wu, J., Poloczek, M., Wilson, A. G., & Frazier, P. I. (2017). Bayesian optimization with gradients. Advances in Neural Information Processing Systems, 2017-December, 5268-5279.