Sequential and Parallel Constrained Max-value Entropy Search via Information Lower Bound
Shion Takeno, Tomoyuki Tamura, Kazuki Shitara, Masayuki Karasuyama
Abstract
Max-value entropy search (MES) is one of the state-of-the-art approaches in Bayesian optimization (BO). In this paper, we propose a novel variant of MES for constrained problems, called Constrained MES via Information lower BOund (CMES-IBO), that is based on a Monte Carlo (MC) estimator of a lower bound of a mutual information (MI). Unlike existing studies, our MI is defined so that uncertainty with respect to feasibility can be incorporated. We derive a lower bound of the MI that guarantees non-negativity, while a constrained counterpart of conventional MES can be negative. We further provide theoretical analysis that assures the low-variability of our estimator which has never been investigated for any existing information-theoretic BO. Moreover, using the conditional MI, we extend CMES-IBO to the parallel setting while maintaining the desirable properties. We demonstrate the effectiveness of CMES-IBO by several benchmark functions and real-world problems.
BibTeX
@InProceedings{pmlr-v162-takeno22a,
title = {Sequential and Parallel Constrained Max-value Entropy Search via Information Lower Bound},
author = {Takeno, Shion and Tamura, Tomoyuki and Shitara, Kazuki and Karasuyama, Masayuki},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {20960--20986},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/takeno22a/takeno22a.pdf},
url = {https://proceedings.mlr.press/v162/takeno22a.html},
abstract = {Max-value entropy search (MES) is one of the state-of-the-art approaches in Bayesian optimization (BO). In this paper, we propose a novel variant of MES for constrained problems, called Constrained MES via Information lower BOund (CMES-IBO), that is based on a Monte Carlo (MC) estimator of a lower bound of a mutual information (MI). Unlike existing studies, our MI is defined so that uncertainty with respect to feasibility can be incorporated. We derive a lower bound of the MI that guarantees non-negativity, while a constrained counterpart of conventional MES can be negative. We further provide theoretical analysis that assures the low-variability of our estimator which has never been investigated for any existing information-theoretic BO. Moreover, using the conditional MI, we extend CMES-IBO to the parallel setting while maintaining the desirable properties. We demonstrate the effectiveness of CMES-IBO by several benchmark functions and real-world problems.}
}