Online Resource Allocation with Replenishable Budgets

2026-09-28

AI Summary

This study addresses the limitation of traditional online resource allocation (ORA), which relies on the assumption of monotonically decreasing budgets and thus struggles with replenishable resources such as inventory and energy. To overcome this, we extend ORA to non-monotonic budget settings for the first time, proposing a dual-optimization-based algorithmic framework that incorporates a "best-of-both-worlds" mechanism to handle both stochastic and adversarial environments while strictly enforcing budget constraints. Theoretically, we prove that the proposed algorithm achieves an optimal regret bound of $\widetilde{O}(\sqrt{T})$ in both environments under strict budget feasibility, significantly outperforming classical methods. This work provides a unified and efficient solution for online decision-making involving replenishable resources.

Abstract

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 $\beta = 0$, and improves them when $\beta>0$. In particular, our algorithm attains $\widetilde{\mathcal O}(\sqrt{T})$ regret in the stochastic setting and $\widetilde{\mathcal O}(\sqrt{T})$ $\alpha$-regret in the adversarial setting, where $\alpha$ 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.

Problem

• Online Resource Allocation
• Replenishable Budgets
• Sequential Decision-Making
• Budget Constraints

Innovation

• Online Resource Allocation
• Replenishable Budgets
• Dual-based Algorithm
• Regret Bounds
• Budget Constraints