A General Recipe for Likelihood-free Bayesian Optimization

Jiaming Song, Lantao Yu, Willie Neiswanger, Stefano Ermon
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:20384-20404, 2022.

Abstract

The acquisition function, a critical component in Bayesian optimization (BO), can often be written as the expectation of a utility function under a surrogate model. However, to ensure that acquisition functions are tractable to optimize, restrictions must be placed on the surrogate model and utility function. To extend BO to a broader class of models and utilities, we propose likelihood-free BO (LFBO), an approach based on likelihood-free inference. LFBO directly models the acquisition function without having to separately perform inference with a probabilistic surrogate model. We show that computing the acquisition function in LFBO can be reduced to optimizing a weighted classification problem, which extends an existing likelihood-free density ratio estimation method related to probability of improvement (PI). By choosing the utility function for expected improvement (EI), LFBO outperforms the aforementioned method, as well as various state-of-the-art black-box optimization methods on several real-world optimization problems. LFBO can also leverage composite structures of the objective function, which further improves its regret by several orders of magnitude.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-song22b, title = {A General Recipe for Likelihood-free {B}ayesian Optimization}, author = {Song, Jiaming and Yu, Lantao and Neiswanger, Willie and Ermon, Stefano}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {20384--20404}, 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/song22b/song22b.pdf}, url = {https://proceedings.mlr.press/v162/song22b.html}, abstract = {The acquisition function, a critical component in Bayesian optimization (BO), can often be written as the expectation of a utility function under a surrogate model. However, to ensure that acquisition functions are tractable to optimize, restrictions must be placed on the surrogate model and utility function. To extend BO to a broader class of models and utilities, we propose likelihood-free BO (LFBO), an approach based on likelihood-free inference. LFBO directly models the acquisition function without having to separately perform inference with a probabilistic surrogate model. We show that computing the acquisition function in LFBO can be reduced to optimizing a weighted classification problem, which extends an existing likelihood-free density ratio estimation method related to probability of improvement (PI). By choosing the utility function for expected improvement (EI), LFBO outperforms the aforementioned method, as well as various state-of-the-art black-box optimization methods on several real-world optimization problems. LFBO can also leverage composite structures of the objective function, which further improves its regret by several orders of magnitude.} }
Endnote
%0 Conference Paper %T A General Recipe for Likelihood-free Bayesian Optimization %A Jiaming Song %A Lantao Yu %A Willie Neiswanger %A Stefano Ermon %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-song22b %I PMLR %P 20384--20404 %U https://proceedings.mlr.press/v162/song22b.html %V 162 %X The acquisition function, a critical component in Bayesian optimization (BO), can often be written as the expectation of a utility function under a surrogate model. However, to ensure that acquisition functions are tractable to optimize, restrictions must be placed on the surrogate model and utility function. To extend BO to a broader class of models and utilities, we propose likelihood-free BO (LFBO), an approach based on likelihood-free inference. LFBO directly models the acquisition function without having to separately perform inference with a probabilistic surrogate model. We show that computing the acquisition function in LFBO can be reduced to optimizing a weighted classification problem, which extends an existing likelihood-free density ratio estimation method related to probability of improvement (PI). By choosing the utility function for expected improvement (EI), LFBO outperforms the aforementioned method, as well as various state-of-the-art black-box optimization methods on several real-world optimization problems. LFBO can also leverage composite structures of the objective function, which further improves its regret by several orders of magnitude.
APA
Song, J., Yu, L., Neiswanger, W. & Ermon, S.. (2022). A General Recipe for Likelihood-free Bayesian Optimization. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:20384-20404 Available from https://proceedings.mlr.press/v162/song22b.html.

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