发表机构
Politecnico di Milano（米兰理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对预算可补充的在线资源分配问题，提出基于对偶的算法，在随机与对抗环境下分别达到最优遗憾界，并严格满足预算约束。
AI 中文摘要
在线资源分配（ORA）是预算约束下序贯决策问题的基础框架。经典在线资源分配模型通常假设资源是单调的，即选择行动只会减少可用预算。本文研究了一种更具一般性的可补充预算场景，在该场景中，行动随时间推移既可能消耗资源，也可能补充资源。这一扩展对于刻画库存系统、能源市场等可主动恢复容量的场景是必要的。我们提出了一种基于对偶的算法，当补充因子为$β= 0$时，该算法可实现标准在线资源分配的“两全其美”保证，而当补充因子为$β> 0$时，其性能还可进一步提升。具体而言，该算法在随机环境下达到$\widetilde{\mathcal O}(\sqrt{T})$遗憾界，在对抗环境下达到$\widetilde{\mathcal O}(\sqrt{T})$ $α$-遗憾界，其中$α$取决于每轮预算以及空行动的补充因子。此外，该算法可确保严格满足预算约束。
英文摘要
Online Resource Allocation (ORA) is a fundamental framework for sequential decision-making problems under budget constraints. Classical ORA models typically assume that resources are monotonic, meaning that selecting actions can only decrease the available budget. In this work, we study a more general setting with replenishable budgets, in which actions may either consume or replenish resources over time. This extension is necessary to capture scenarios such as inventory systems or energy markets in which capacity can be actively recovered. We develop a dual-based algorithm that recovers best-of-both-worlds guarantees for standard ORA when the replenishment factor $β= 0$, and improves them when $β> 0$. In particular, our algorithm attains $\widetilde{\mathcal O}(\sqrt{T})$ regret in the stochastic setting and $\widetilde{\mathcal O}(\sqrt{T})$ $α$-regret in the adversarial setting, where $α$ depends on the per-round budget and on the replenishment factor of the void action. Moreover, the algorithm ensures strict satisfaction of the budget constraints.
