Triple-Optimistic Learning for Stochastic Contextual Bandits with General Constraints

Hengquan Guo, Lingkai Zu, Xin Liu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:21252-21276, 2025.

Abstract

We study contextual bandits with general constraints, where a learner observes contexts and aims to maximize cumulative rewards while satisfying a wide range of general constraints. We introduce the Optimistic$^3$ framework, a novel learning and decision-making approach that integrates optimistic design into parameter learning, primal decision, and dual violation adaptation (i.e., triple-optimism), combined with an efficient primal-dual architecture. Optimistic$^3$ achieves $\tilde{O}(\sqrt{T})$ regret and constraint violation for contextual bandits with general constraints. This framework not only outperforms the state-of-the-art results that achieve $\tilde{O}(T^{\frac{3}{4}})$ guarantees when Slater’s condition does not hold but also improves on previous results that achieve $\tilde{O}(\sqrt{T}/\delta)$ when Slater’s condition holds ($\delta$ denotes the Slater’s condition parameter), offering a $O(1/\delta)$ improvement. Note this improvement is significant because $\delta$ can be arbitrarily small when constraints are particularly challenging. Moreover, we show that Optimistic$^3$ can be extended to classical multi-armed bandits with both stochastic and adversarial constraints, recovering the best-of-both-worlds guarantee established in the state-of-the-art works, but with significantly less computational overhead.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-guo25v, title = {Triple-Optimistic Learning for Stochastic Contextual Bandits with General Constraints}, author = {Guo, Hengquan and Zu, Lingkai and Liu, Xin}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {21252--21276}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/guo25v/guo25v.pdf}, url = {https://proceedings.mlr.press/v267/guo25v.html}, abstract = {We study contextual bandits with general constraints, where a learner observes contexts and aims to maximize cumulative rewards while satisfying a wide range of general constraints. We introduce the Optimistic$^3$ framework, a novel learning and decision-making approach that integrates optimistic design into parameter learning, primal decision, and dual violation adaptation (i.e., triple-optimism), combined with an efficient primal-dual architecture. Optimistic$^3$ achieves $\tilde{O}(\sqrt{T})$ regret and constraint violation for contextual bandits with general constraints. This framework not only outperforms the state-of-the-art results that achieve $\tilde{O}(T^{\frac{3}{4}})$ guarantees when Slater’s condition does not hold but also improves on previous results that achieve $\tilde{O}(\sqrt{T}/\delta)$ when Slater’s condition holds ($\delta$ denotes the Slater’s condition parameter), offering a $O(1/\delta)$ improvement. Note this improvement is significant because $\delta$ can be arbitrarily small when constraints are particularly challenging. Moreover, we show that Optimistic$^3$ can be extended to classical multi-armed bandits with both stochastic and adversarial constraints, recovering the best-of-both-worlds guarantee established in the state-of-the-art works, but with significantly less computational overhead.} }
Endnote
%0 Conference Paper %T Triple-Optimistic Learning for Stochastic Contextual Bandits with General Constraints %A Hengquan Guo %A Lingkai Zu %A Xin Liu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-guo25v %I PMLR %P 21252--21276 %U https://proceedings.mlr.press/v267/guo25v.html %V 267 %X We study contextual bandits with general constraints, where a learner observes contexts and aims to maximize cumulative rewards while satisfying a wide range of general constraints. We introduce the Optimistic$^3$ framework, a novel learning and decision-making approach that integrates optimistic design into parameter learning, primal decision, and dual violation adaptation (i.e., triple-optimism), combined with an efficient primal-dual architecture. Optimistic$^3$ achieves $\tilde{O}(\sqrt{T})$ regret and constraint violation for contextual bandits with general constraints. This framework not only outperforms the state-of-the-art results that achieve $\tilde{O}(T^{\frac{3}{4}})$ guarantees when Slater’s condition does not hold but also improves on previous results that achieve $\tilde{O}(\sqrt{T}/\delta)$ when Slater’s condition holds ($\delta$ denotes the Slater’s condition parameter), offering a $O(1/\delta)$ improvement. Note this improvement is significant because $\delta$ can be arbitrarily small when constraints are particularly challenging. Moreover, we show that Optimistic$^3$ can be extended to classical multi-armed bandits with both stochastic and adversarial constraints, recovering the best-of-both-worlds guarantee established in the state-of-the-art works, but with significantly less computational overhead.
APA
Guo, H., Zu, L. & Liu, X.. (2025). Triple-Optimistic Learning for Stochastic Contextual Bandits with General Constraints. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:21252-21276 Available from https://proceedings.mlr.press/v267/guo25v.html.

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