Bayesian Optimization with Binary Auxiliary Information

Yehong Zhang, Zhongxiang Dai, Bryan Kian Hsiang Low
Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, PMLR 115:1222-1232, 2020.

Abstract

This paper presents novel mixed-type Bayesian optimization (BO) algorithms to accelerate the optimization of a target objective function by exploiting correlated auxiliary information of binary type that can be more cheaply obtained, such as in policy search for reinforcement learning and hyperparameter tuning of machine learning models with early stopping. To achieve this, we first propose a mixed-type multi-output Gaussian process (MOGP) to jointly model the continuous target function and binary auxiliary functions. Then, we propose information-based acquisition functions such as mixed-type entropy search (MT-ES) and mixed-type predictive ES (MT-PES) for mixed-type BO based on the MOGP predictive belief of the target and auxiliary functions. The exact acquisition functions of MT-ES and MT-PES cannot be computed in closed form and need to be approximated. We derive an efficient approximation of MT-PES via a novel mixed-type random features approximation of the MOGP model whose cross-correlation structure between the target and auxiliary functions can be exploited for improving the belief of the global target maximizer using the observations from evaluating these functions. We also propose new practical constraints to relate the global target maximizer to the binary auxiliary functions. We empirically evaluate the performance of MT-ES and MT-PES with synthetic and real-world experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v115-zhang20b, title = {Bayesian Optimization with Binary Auxiliary Information}, author = {Zhang, Yehong and Dai, Zhongxiang and Low, {Bryan Kian Hsiang}}, booktitle = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference}, pages = {1222--1232}, 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/zhang20b/zhang20b.pdf}, url = {https://proceedings.mlr.press/v115/zhang20b.html}, abstract = {This paper presents novel mixed-type Bayesian optimization (BO) algorithms to accelerate the optimization of a target objective function by exploiting correlated auxiliary information of binary type that can be more cheaply obtained, such as in policy search for reinforcement learning and hyperparameter tuning of machine learning models with early stopping. To achieve this, we first propose a mixed-type multi-output Gaussian process (MOGP) to jointly model the continuous target function and binary auxiliary functions. Then, we propose information-based acquisition functions such as mixed-type entropy search (MT-ES) and mixed-type predictive ES (MT-PES) for mixed-type BO based on the MOGP predictive belief of the target and auxiliary functions. The exact acquisition functions of MT-ES and MT-PES cannot be computed in closed form and need to be approximated. We derive an efficient approximation of MT-PES via a novel mixed-type random features approximation of the MOGP model whose cross-correlation structure between the target and auxiliary functions can be exploited for improving the belief of the global target maximizer using the observations from evaluating these functions. We also propose new practical constraints to relate the global target maximizer to the binary auxiliary functions. We empirically evaluate the performance of MT-ES and MT-PES with synthetic and real-world experiments. } }
Endnote
%0 Conference Paper %T Bayesian Optimization with Binary Auxiliary Information %A Yehong Zhang %A Zhongxiang Dai %A Bryan Kian Hsiang Low %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-zhang20b %I PMLR %P 1222--1232 %U https://proceedings.mlr.press/v115/zhang20b.html %V 115 %X This paper presents novel mixed-type Bayesian optimization (BO) algorithms to accelerate the optimization of a target objective function by exploiting correlated auxiliary information of binary type that can be more cheaply obtained, such as in policy search for reinforcement learning and hyperparameter tuning of machine learning models with early stopping. To achieve this, we first propose a mixed-type multi-output Gaussian process (MOGP) to jointly model the continuous target function and binary auxiliary functions. Then, we propose information-based acquisition functions such as mixed-type entropy search (MT-ES) and mixed-type predictive ES (MT-PES) for mixed-type BO based on the MOGP predictive belief of the target and auxiliary functions. The exact acquisition functions of MT-ES and MT-PES cannot be computed in closed form and need to be approximated. We derive an efficient approximation of MT-PES via a novel mixed-type random features approximation of the MOGP model whose cross-correlation structure between the target and auxiliary functions can be exploited for improving the belief of the global target maximizer using the observations from evaluating these functions. We also propose new practical constraints to relate the global target maximizer to the binary auxiliary functions. We empirically evaluate the performance of MT-ES and MT-PES with synthetic and real-world experiments.
APA
Zhang, Y., Dai, Z. & Low, B.K.H.. (2020). Bayesian Optimization with Binary Auxiliary Information. Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, in Proceedings of Machine Learning Research 115:1222-1232 Available from https://proceedings.mlr.press/v115/zhang20b.html.

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