Online resource allocation (ORA) is a fundamental framework for sequential decision-making problems under budget constraints, with applications ranging from online advertising to revenue management. In this work, we study a broader setting that includes both budget constraints and general constraints, extending the classical budget-only model. This extension is essential for modeling critical economic requirements, such as Return-on-Investment (ROI) constraints. We develop an algorithm that achieves best-of-both-world guarantees within this generalized framework. In particular, against a dynamic benchmark, our algorithm achieves $\widetilde{\mathcal O}(\sqrt{T})$ regret in the \emph{stochastic} regime and $α$-regret of order $\widetilde{\mathcal O}(\sqrt{T})$ in the \emph{adversarial} regime, where $α$ depends on the feasibility margin of the corresponding offline problem. At the same time, our algorithm guarantees strict satisfaction of the budget constraints and $\widetilde{\mathcal O}(\sqrt{T})$ cumulative violation for the general ones. From a technical perspective, introducing general constraints alongside budgets precludes the use of standard budget-focus methods. While budget methods rely on a zero-consumption ``safe'' action to ensure feasibility, general constraints are much less ``aligned'' towards feasibility. We overcome these difficulties with a new analysis that exploits \emph{weak adaptivity} to get boundedness of the Lagrangian multipliers and best-of-both-world guarantees.

翻译：在线资源分配（ORA）是预算约束下序贯决策问题的基本框架，其应用涵盖在线广告到收益管理等领域。本文研究同时包含预算约束和一般约束的更广泛设置，扩展了经典的仅含预算模型。这种扩展对于建模关键经济要求（如投资回报率（ROI）约束）至关重要。我们开发了一种算法，在该广义框架下实现了"两全其美"的保证。具体而言，针对动态基准，我们的算法在*随机*情境下达到$\widetilde{\mathcal O}(\sqrt{T})$的遗憾值，在*对抗*情境下达到阶为$\widetilde{\mathcal O}(\sqrt{T})$的$α$-遗憾值，其中$α$取决于对应离线问题的可行性裕度。同时，我们的算法严格保证预算约束的满足，并对一般约束实现$\widetilde{\mathcal O}(\sqrt{T})$的累积违反量。从技术角度看，引入一般约束与预算约束并存使得标准聚焦预算的方法失效。虽然预算方法依赖零消耗"安全"动作来确保可行性，但一般约束与可行性的"对齐"程度远低于前者。我们通过利用*弱自适应性*的新分析克服了这些困难，从而获得拉格朗日乘子的有界性及"两全其美"的保证。