Decoupling Learning and Decision-Making: Breaking the $\mathcalO(\sqrtT)$ Barrier in Online Resource Allocation with First-Order Methods

Wenzhi Gao, Chunlin Sun, Chenyu Xue, Yinyu Ye
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:14859-14883, 2024.

Abstract

Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of first-order methods, they typically achieve regret no better than $\mathcal{O}(\sqrt{T})$, which is suboptimal compared to the $\mathcal{O}(\log T)$ result guaranteed by the state-of-the-art linear programming (LP)-based online algorithms. This paper establishes several important facts about online linear programming, which unveils the challenge for first-order online algorithms to achieve beyond $\mathcal{O}(\sqrt{T})$ regret. To address this challenge, we introduce a new algorithmic framework which decouples learning from decision-making. For the first time, we show that first-order methods can achieve regret $\mathcal{O}(T^{1/3})$ with this new framework.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-gao24n, title = {Decoupling Learning and Decision-Making: Breaking the $\mathcal{O}(\sqrt{T})$ Barrier in Online Resource Allocation with First-Order Methods}, author = {Gao, Wenzhi and Sun, Chunlin and Xue, Chenyu and Ye, Yinyu}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {14859--14883}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/gao24n/gao24n.pdf}, url = {https://proceedings.mlr.press/v235/gao24n.html}, abstract = {Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of first-order methods, they typically achieve regret no better than $\mathcal{O}(\sqrt{T})$, which is suboptimal compared to the $\mathcal{O}(\log T)$ result guaranteed by the state-of-the-art linear programming (LP)-based online algorithms. This paper establishes several important facts about online linear programming, which unveils the challenge for first-order online algorithms to achieve beyond $\mathcal{O}(\sqrt{T})$ regret. To address this challenge, we introduce a new algorithmic framework which decouples learning from decision-making. For the first time, we show that first-order methods can achieve regret $\mathcal{O}(T^{1/3})$ with this new framework.} }
Endnote
%0 Conference Paper %T Decoupling Learning and Decision-Making: Breaking the $\mathcalO(\sqrtT)$ Barrier in Online Resource Allocation with First-Order Methods %A Wenzhi Gao %A Chunlin Sun %A Chenyu Xue %A Yinyu Ye %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-gao24n %I PMLR %P 14859--14883 %U https://proceedings.mlr.press/v235/gao24n.html %V 235 %X Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of first-order methods, they typically achieve regret no better than $\mathcal{O}(\sqrt{T})$, which is suboptimal compared to the $\mathcal{O}(\log T)$ result guaranteed by the state-of-the-art linear programming (LP)-based online algorithms. This paper establishes several important facts about online linear programming, which unveils the challenge for first-order online algorithms to achieve beyond $\mathcal{O}(\sqrt{T})$ regret. To address this challenge, we introduce a new algorithmic framework which decouples learning from decision-making. For the first time, we show that first-order methods can achieve regret $\mathcal{O}(T^{1/3})$ with this new framework.
APA
Gao, W., Sun, C., Xue, C. & Ye, Y.. (2024). Decoupling Learning and Decision-Making: Breaking the $\mathcalO(\sqrtT)$ Barrier in Online Resource Allocation with First-Order Methods. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:14859-14883 Available from https://proceedings.mlr.press/v235/gao24n.html.

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