Online Fair Allocation of Reusable Resources

Qingsong Liu

Abstract:

Motivated by the emerging paradigm of resource allocation that integrates classical objectives, such as cost minimization, with societal objectives, such as carbon awareness, this paper proposes a general framework for the online fair allocation of reusable resources. Within this framework, an online decision-maker seeks to allocate a finite resource with capacity $C$ to a sequence of requests arriving with unknown distributions of types, utilities, and resource usage durations. To accommodate diverse objectives, the framework supports multiple actions and utility types, and the goal is to achieve max-min fairness among utilities, i.e., maximize the minimum time-averaged utility across all utility types. Our performance metric is an $(\alpha,\beta)$-competitive guarantee of the form: $ \text{ALG} \geq \alpha \cdot \text{OPT}^* - O({T^{\beta-1}}),\; \alpha, \beta \in (0, 1]$, where $\text{OPT}^*$ and ALG are the time-averaged optimum and objective value achieved by the decision maker, respectively.
We propose a novel algorithm that achieves a competitive guarantee of $(1-O( \sqrt{\nicefrac{\log C}{C}}),\nicefrac{2}{3})$ under the bandit feedback. As resource capacity increases, the multiplicative competitive ratio term $1-O( \sqrt{\nicefrac{\log C}{C}})$ asymptotically approaches optimality. Notably, when the resource capacity exceeds a certain threshold, our algorithm achieves an improved competitive guarantee of $(1,\nicefrac{2}{3})$. Our algorithm employs an optimistic penalty-weight mechanism coupled with a dual exploration-discarding strategy to balance resource feasibility, exploration, and fairness among utilities.