A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations

Biswajit Paria, Kirthevasan Kandasamy, Barnabás Póczos
Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, PMLR 115:766-776, 2020.

Abstract

Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the evaluation of the functions in question are expensive. Traditional methods for multi-objective optimization, both Bayesian and otherwise, are aimed at recovering the Pareto front of these objectives. However, in certain cases a practitioner might desire to identify Pareto optimal points only in a subset of the Pareto front due to external considerations. In this work, we propose a strategy based on random scalarizations of the objectives that addresses this problem. Our approach is able to flexibly sample from desired regions of the Pareto front and, computationally, is considerably cheaper than most approaches for MOO. We also study a notion of regret in the multi-objective setting and show that our strategy achieves sublinear regret. We experiment with both synthetic and real-life problems, and demonstrate superior performance of our proposed algorithm in terms of the flexibility and regret.

Cite this Paper

BibTeX
@InProceedings{pmlr-v115-paria20a, title = {A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations}, author = {Paria, Biswajit and Kandasamy, Kirthevasan and P{\'{o}}czos, Barnab{\'{a}}s}, booktitle = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference}, pages = {766--776}, year = {2020}, editor = {Adams, Ryan P. and Gogate, Vibhav}, volume = {115}, series = {Proceedings of Machine Learning Research}, month = {22--25 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v115/paria20a/paria20a.pdf}, url = {https://proceedings.mlr.press/v115/paria20a.html}, abstract = {Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the evaluation of the functions in question are expensive. Traditional methods for multi-objective optimization, both Bayesian and otherwise, are aimed at recovering the Pareto front of these objectives. However, in certain cases a practitioner might desire to identify Pareto optimal points only in a subset of the Pareto front due to external considerations. In this work, we propose a strategy based on random scalarizations of the objectives that addresses this problem. Our approach is able to flexibly sample from desired regions of the Pareto front and, computationally, is considerably cheaper than most approaches for MOO. We also study a notion of regret in the multi-objective setting and show that our strategy achieves sublinear regret. We experiment with both synthetic and real-life problems, and demonstrate superior performance of our proposed algorithm in terms of the flexibility and regret.} }
Endnote
%0 Conference Paper %T A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations %A Biswajit Paria %A Kirthevasan Kandasamy %A Barnabás Póczos %B Proceedings of The 35th Uncertainty in Artificial Intelligence Conference %C Proceedings of Machine Learning Research %D 2020 %E Ryan P. Adams %E Vibhav Gogate %F pmlr-v115-paria20a %I PMLR %P 766--776 %U https://proceedings.mlr.press/v115/paria20a.html %V 115 %X Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the evaluation of the functions in question are expensive. Traditional methods for multi-objective optimization, both Bayesian and otherwise, are aimed at recovering the Pareto front of these objectives. However, in certain cases a practitioner might desire to identify Pareto optimal points only in a subset of the Pareto front due to external considerations. In this work, we propose a strategy based on random scalarizations of the objectives that addresses this problem. Our approach is able to flexibly sample from desired regions of the Pareto front and, computationally, is considerably cheaper than most approaches for MOO. We also study a notion of regret in the multi-objective setting and show that our strategy achieves sublinear regret. We experiment with both synthetic and real-life problems, and demonstrate superior performance of our proposed algorithm in terms of the flexibility and regret.
APA
Paria, B., Kandasamy, K. & Póczos, B.. (2020). A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations. Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, in Proceedings of Machine Learning Research 115:766-776 Available from https://proceedings.mlr.press/v115/paria20a.html.

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