Counterfactual Credit Guided Bayesian Optimization

Qiyu Wei, Haowei Wang, Richard Allmendinger, Mauricio A Álvarez
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:73-81, 2026.

Abstract

Bayesian optimization has emerged as a prominent methodology for optimizing expensive black-box functions by leveraging Gaussian process surrogates, which focus on capturing the global characteristics of the objective function. However, in numerous practical scenarios, the primary objective is not to construct an exhaustive global surrogate, but rather to quickly pinpoint the global optimum. Due to the aleatoric nature of the sequential optimization problem and its dependence on the quality of the surrogate model and the initial design, it is restrictive to assume that all observed samples contribute equally to the discovery of the optimum in this context. In this paper, we introduce Counterfactual Credit Guided Bayesian Optimization (CCGBO), a novel framework that explicitly quantifies the contribution of individual historical observations through counterfactual credit. By incorporating counterfactual credit into the acquisition function, our approach can selectively allocate resources in areas where optimal solutions are most likely to occur. We prove that CCGBO retains sublinear regret. Empirical evaluations on various synthetic and real-world benchmarks demonstrate that CCGBO consistently reduces simple regret and accelerates convergence to the global optimum.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-wei26a, title = { Counterfactual Credit Guided Bayesian Optimization }, author = {Wei, Qiyu and Wang, Haowei and Allmendinger, Richard and {\'A}lvarez, Mauricio A}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {73--81}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/wei26a/wei26a.pdf}, url = {https://proceedings.mlr.press/v300/wei26a.html}, abstract = { Bayesian optimization has emerged as a prominent methodology for optimizing expensive black-box functions by leveraging Gaussian process surrogates, which focus on capturing the global characteristics of the objective function. However, in numerous practical scenarios, the primary objective is not to construct an exhaustive global surrogate, but rather to quickly pinpoint the global optimum. Due to the aleatoric nature of the sequential optimization problem and its dependence on the quality of the surrogate model and the initial design, it is restrictive to assume that all observed samples contribute equally to the discovery of the optimum in this context. In this paper, we introduce Counterfactual Credit Guided Bayesian Optimization (CCGBO), a novel framework that explicitly quantifies the contribution of individual historical observations through counterfactual credit. By incorporating counterfactual credit into the acquisition function, our approach can selectively allocate resources in areas where optimal solutions are most likely to occur. We prove that CCGBO retains sublinear regret. Empirical evaluations on various synthetic and real-world benchmarks demonstrate that CCGBO consistently reduces simple regret and accelerates convergence to the global optimum. } }
Endnote
%0 Conference Paper %T Counterfactual Credit Guided Bayesian Optimization %A Qiyu Wei %A Haowei Wang %A Richard Allmendinger %A Mauricio A Álvarez %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-wei26a %I PMLR %P 73--81 %U https://proceedings.mlr.press/v300/wei26a.html %V 300 %X Bayesian optimization has emerged as a prominent methodology for optimizing expensive black-box functions by leveraging Gaussian process surrogates, which focus on capturing the global characteristics of the objective function. However, in numerous practical scenarios, the primary objective is not to construct an exhaustive global surrogate, but rather to quickly pinpoint the global optimum. Due to the aleatoric nature of the sequential optimization problem and its dependence on the quality of the surrogate model and the initial design, it is restrictive to assume that all observed samples contribute equally to the discovery of the optimum in this context. In this paper, we introduce Counterfactual Credit Guided Bayesian Optimization (CCGBO), a novel framework that explicitly quantifies the contribution of individual historical observations through counterfactual credit. By incorporating counterfactual credit into the acquisition function, our approach can selectively allocate resources in areas where optimal solutions are most likely to occur. We prove that CCGBO retains sublinear regret. Empirical evaluations on various synthetic and real-world benchmarks demonstrate that CCGBO consistently reduces simple regret and accelerates convergence to the global optimum.
APA
Wei, Q., Wang, H., Allmendinger, R. & Álvarez, M.A.. (2026). Counterfactual Credit Guided Bayesian Optimization . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:73-81 Available from https://proceedings.mlr.press/v300/wei26a.html.

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