Enabling Long-term Fairness in Dynamic Resource Allocation

TL;DR

This paper explores long-term fairness in dynamic resource allocation, contrasting slot-fairness and horizon-fairness, and proposes an online policy ensuring vanishing regret under realistic adversarial restrictions.

Contribution

It introduces a new horizon-fairness concept, analyzes its social welfare implications, and develops an online policy that guarantees vanishing regret with adversarial restrictions.

Findings

Horizon-fairness incurs lower social welfare loss than slot-fairness.

Vanishing regret is impossible with an unrestricted adversary.

Proposed online policy achieves vanishing regret under realistic adversarial constraints.

Abstract

We study the fairness of dynamic resource allocation problem under the $\alpha$-fairness criterion. We recognize two different fairness objectives that naturally arise in this problem: the well-understood slot-fairness objective that aims to ensure fairness at every timeslot, and the less explored horizon-fairness objective that aims to ensure fairness across utilities accumulated over a time horizon. We argue that horizon-fairness comes at a lower price in terms of social welfare. We study horizon-fairness with the regret as a performance metric and show that vanishing regret cannot be achieved in presence of an unrestricted adversary. We propose restrictions on the adversary's capabilities corresponding to realistic scenarios and an online policy that indeed guarantees vanishing regret under these restrictions. We demonstrate the applicability of the proposed fairness framework to a representative resource management problem considering a virtualized caching system where different caches cooperate to serve content requests.