Optimistic Safety for Online Convex Optimization with Unknown Linear Constraints

Spencer Hutchinson, Tianyi Chen, Mahnoosh Alizadeh
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:2809-2817, 2025.

Abstract

We study the problem of online convex optimization (OCO) under unknown linear constraints that are either static, or stochastically time-varying. For this problem, we introduce an algorithm that we term Optimistically Safe OCO (OSOCO) and show that it enjoys $\tilde{O}(\sqrt{T})$ regret and no constraint violation. In the case of static linear constraints, this improves on the previous best known $\tilde{O}(T^{2/3})$ regret under the same assumptions. In the case of stochastic time-varying constraints, our work supplements existing results that show $O(\sqrt{T})$ regret and $O(\sqrt{T})$ cumulative violation under more general convex constraints and a different set of assumptions. In addition to our theoretical guarantees, we also give numerical results that further validate the effectiveness of our approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-hutchinson25a, title = {Optimistic Safety for Online Convex Optimization with Unknown Linear Constraints}, author = {Hutchinson, Spencer and Chen, Tianyi and Alizadeh, Mahnoosh}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {2809--2817}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/hutchinson25a/hutchinson25a.pdf}, url = {https://proceedings.mlr.press/v258/hutchinson25a.html}, abstract = {We study the problem of online convex optimization (OCO) under unknown linear constraints that are either static, or stochastically time-varying. For this problem, we introduce an algorithm that we term Optimistically Safe OCO (OSOCO) and show that it enjoys $\tilde{O}(\sqrt{T})$ regret and no constraint violation. In the case of static linear constraints, this improves on the previous best known $\tilde{O}(T^{2/3})$ regret under the same assumptions. In the case of stochastic time-varying constraints, our work supplements existing results that show $O(\sqrt{T})$ regret and $O(\sqrt{T})$ cumulative violation under more general convex constraints and a different set of assumptions. In addition to our theoretical guarantees, we also give numerical results that further validate the effectiveness of our approach.} }
Endnote
%0 Conference Paper %T Optimistic Safety for Online Convex Optimization with Unknown Linear Constraints %A Spencer Hutchinson %A Tianyi Chen %A Mahnoosh Alizadeh %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-hutchinson25a %I PMLR %P 2809--2817 %U https://proceedings.mlr.press/v258/hutchinson25a.html %V 258 %X We study the problem of online convex optimization (OCO) under unknown linear constraints that are either static, or stochastically time-varying. For this problem, we introduce an algorithm that we term Optimistically Safe OCO (OSOCO) and show that it enjoys $\tilde{O}(\sqrt{T})$ regret and no constraint violation. In the case of static linear constraints, this improves on the previous best known $\tilde{O}(T^{2/3})$ regret under the same assumptions. In the case of stochastic time-varying constraints, our work supplements existing results that show $O(\sqrt{T})$ regret and $O(\sqrt{T})$ cumulative violation under more general convex constraints and a different set of assumptions. In addition to our theoretical guarantees, we also give numerical results that further validate the effectiveness of our approach.
APA
Hutchinson, S., Chen, T. & Alizadeh, M.. (2025). Optimistic Safety for Online Convex Optimization with Unknown Linear Constraints. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:2809-2817 Available from https://proceedings.mlr.press/v258/hutchinson25a.html.

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