Hypervolume Knowledge Gradient: A Lookahead Approach for Multi-Objective Bayesian Optimization with Partial Information

Sam Daulton, Maximilian Balandat, Eytan Bakshy
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:7167-7204, 2023.

Abstract

Bayesian optimization is a popular method for sample efficient multi-objective optimization. However, existing Bayesian optimization techniques fail to effectively exploit common and often-neglected problem structure such as decoupled evaluations, where objectives can be queried independently from one another and each may consume different resources, or multi-fidelity evaluations, where lower fidelity-proxies of the objectives can be evaluated at lower cost. In this work, we propose a general one-step lookahead acquisition function based on the Knowledge Gradient that addresses the complex question of what to evaluate when and at which design points in a principled Bayesian decision-theoretic fashion. Hence, our approach naturally addresses decoupled, multi-fidelity, and standard multi-objective optimization settings in a unified Bayesian decision making framework. By construction, our method is the one-step Bayes-optimal policy for hypervolume maximization. Empirically, we demonstrate that our method improves sample efficiency in a wide variety of synthetic and real-world problems. Furthermore, we show that our method is general-purpose and yields competitive performance in standard (potentially noisy) multi-objective optimization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-daulton23a, title = {Hypervolume Knowledge Gradient: A Lookahead Approach for Multi-Objective {B}ayesian Optimization with Partial Information}, author = {Daulton, Sam and Balandat, Maximilian and Bakshy, Eytan}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {7167--7204}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/daulton23a/daulton23a.pdf}, url = {https://proceedings.mlr.press/v202/daulton23a.html}, abstract = {Bayesian optimization is a popular method for sample efficient multi-objective optimization. However, existing Bayesian optimization techniques fail to effectively exploit common and often-neglected problem structure such as decoupled evaluations, where objectives can be queried independently from one another and each may consume different resources, or multi-fidelity evaluations, where lower fidelity-proxies of the objectives can be evaluated at lower cost. In this work, we propose a general one-step lookahead acquisition function based on the Knowledge Gradient that addresses the complex question of what to evaluate when and at which design points in a principled Bayesian decision-theoretic fashion. Hence, our approach naturally addresses decoupled, multi-fidelity, and standard multi-objective optimization settings in a unified Bayesian decision making framework. By construction, our method is the one-step Bayes-optimal policy for hypervolume maximization. Empirically, we demonstrate that our method improves sample efficiency in a wide variety of synthetic and real-world problems. Furthermore, we show that our method is general-purpose and yields competitive performance in standard (potentially noisy) multi-objective optimization.} }
Endnote
%0 Conference Paper %T Hypervolume Knowledge Gradient: A Lookahead Approach for Multi-Objective Bayesian Optimization with Partial Information %A Sam Daulton %A Maximilian Balandat %A Eytan Bakshy %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-daulton23a %I PMLR %P 7167--7204 %U https://proceedings.mlr.press/v202/daulton23a.html %V 202 %X Bayesian optimization is a popular method for sample efficient multi-objective optimization. However, existing Bayesian optimization techniques fail to effectively exploit common and often-neglected problem structure such as decoupled evaluations, where objectives can be queried independently from one another and each may consume different resources, or multi-fidelity evaluations, where lower fidelity-proxies of the objectives can be evaluated at lower cost. In this work, we propose a general one-step lookahead acquisition function based on the Knowledge Gradient that addresses the complex question of what to evaluate when and at which design points in a principled Bayesian decision-theoretic fashion. Hence, our approach naturally addresses decoupled, multi-fidelity, and standard multi-objective optimization settings in a unified Bayesian decision making framework. By construction, our method is the one-step Bayes-optimal policy for hypervolume maximization. Empirically, we demonstrate that our method improves sample efficiency in a wide variety of synthetic and real-world problems. Furthermore, we show that our method is general-purpose and yields competitive performance in standard (potentially noisy) multi-objective optimization.
APA
Daulton, S., Balandat, M. & Bakshy, E.. (2023). Hypervolume Knowledge Gradient: A Lookahead Approach for Multi-Objective Bayesian Optimization with Partial Information. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:7167-7204 Available from https://proceedings.mlr.press/v202/daulton23a.html.

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