Predictive Entropy Search for Bayesian Optimization with Unknown Constraints

By José Miguel Hernández-Lobato, Michael A. Gelbart, Matthew W. Hoffman, Ryan P. Adams, Zoubin Ghahramani. 2015

172 citations recorded by the source corpus.

Unknown constraints arise in many types of expensive black-box optimization problems. Several methods have been proposed recently for performing Bayesian optimization with constraints, based on the expected improvement (EI) heuristic. However, EI can lead to pathologies when used with constraints. For example, in the case of decoupled constraints--i.e., when one can independently evaluate the objective or the constraints--EI can encounter a pathology that prevents exploration. Additionally, computing EI requires a current best solution, which may not exist if none of the data collected so far satisfy the constraints. By contrast, informationbased approaches do not suffer from these failure modes. In this paper, we present a new information-based method called Predictive Entropy Search with Constraints (PESC). We analyze the performance of PESC and show that it compares favorably to EI-based approaches on synthetic and benchmark problems, as well as several real-world examples. We demonstrate that PESC is an effective algorithm that provides a promising direction towards a unified solution for constrained Bayesian optimization.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

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Citations in the corpus

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, background): “Hern ´ andez-Lobato et al. [68] recently proposed a variation of the predictive entropy search acquisition function to deal with the decoupled case, where the function and constraints can be evaluated independently.”
Learning to Learn for Global Optimization of Black Box Functions (2016, methodology): “We will make use of two types of RNN: long-short-term memory networks (LSTMs) by Hochreiter and Schmidhuber [1997] and differentiable neural computers (DNCs) by Graves et al.”
ProBO: a Framework for Using Probabilistic Programming in Bayesian Optimization (2019, methodology): “Special cases of sample-based (Monte Carlo) estimates of certain acquisition functions have been described in prior work (Snoek et al., 2012; Wilson et al., 2018; Hern´andez-Lobato et al., 2015).”
Bayesian Optimization for Adaptive Experimental Design: A Review (2020, unknown): “weighted predictive entropy search [86].”
BoTorch: Programmable Bayesian Optimization in PyTorch (2019, background): “Spearmint also supports parallel optimization via fantasies, and constrained optimization with the expected improvement and predictive entropy search acquisition functions [30, 38].”
Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020 (2021, background): “Additionally, while we only focused on unconstrained single-objective optimization performance, many relevant problems have additional blackbox constraints that need to be satisfied or are more naturally phrased as multi-objective optimization problems (Gardner et al., 2014; Hernández-Lobato et al.,”
ProBO: Versatile Bayesian Optimization Using Any Probabilistic Programming Language (2019, methodology): “These algorithms are related to Monte Carlo acquisition function estimates for GP models [44, 15, 16], which have been developed for speciﬁc acquisition functions.”
A Stratified Analysis of Bayesian Optimization Methods (2016, unknown): “The use of such artificial test functions is well established within the Bayesian optimization community and plays an important role in current research (Snoek et al., 2015; Hernández-Lobato et al., 2015; González et al., 2015).”
A Tutorial on Bayesian Optimization (2018, methodology): “PES has also been studied for this setting (Hern´andez-Lobato et al., 2015).”
Recent Advances in Bayesian Optimization (2022, methodology): “[71] extended PES to unknown constrained problems by introducing the conditional predictive distributions, with the assumption of the independent GP priors of the objective and constraints.”
Constrained Bayesian Optimization with Noisy Experiments (2017, methodology): “PESC has been compared to Spearmint EI on these same problems before, but in settings more similar to hyper-parameter optimization than our noisy experiments setting.”