Planning to Fairly Allocate: Probabilistic Fairness in the Restless Bandit Setting

TL;DR

This paper introduces ProbFair, a novel policy for restless bandits that maximizes reward, respects budget constraints, and guarantees a positive probability of arm selection, ensuring fairness in resource allocation.

Contribution

The paper proposes ProbFair, a probabilistically fair policy for restless bandits that guarantees fairness without sacrificing utility, addressing limitations of existing Whittle-index approaches.

Findings

ProbFair maintains high reward while ensuring fairness.

ProbFair provides a positive lower bound on arm selection probability.

ProbFair performs well on real-world and synthetic data.

Abstract

Restless and collapsing bandits are often used to model budget-constrained resource allocation in settings where arms have action-dependent transition probabilities, such as the allocation of health interventions among patients. However, state-of-the-art Whittle-index-based approaches to this planning problem either do not consider fairness among arms, or incentivize fairness without guaranteeing it. We thus introduce ProbFair, a probabilistically fair policy that maximizes total expected reward and satisfies the budget constraint while ensuring a strictly positive lower bound on the probability of being pulled at each timestep. We evaluate our algorithm on a real-world application, where interventions support continuous positive airway pressure (CPAP) therapy adherence among patients, as well as on a broader class of synthetic transition matrices. We find that ProbFair preserves utility while providing fairness guarantees.