Computer Science > Machine Learning
[Submitted on 11 Feb 2024 (v1), last revised 28 May 2024 (this version, v2)]
Title:Decoupling Learning and Decision-Making: Breaking the $\mathcal{O}(\sqrt{T})$ Barrier in Online Resource Allocation with First-Order Methods
View PDF HTML (experimental)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 a regret no better than $\mathcal{O}(\sqrt{T})$, which is suboptimal compared to the $\mathcal{O}(\log T)$ bound 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-method-based online algorithms to achieve beyond $\mathcal{O}(\sqrt{T})$ regret. To address the challenge, we introduce a new algorithmic framework that decouples learning from decision-making. For the first time, we show that first-order methods can attain regret $\mathcal{O}(T^{1/3})$ with this new framework.
Submission history
From: Wenzhi Gao [view email][v1] Sun, 11 Feb 2024 05:35:50 UTC (2,120 KB)
[v2] Tue, 28 May 2024 20:43:21 UTC (2,300 KB)
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