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

• URL: http://arxiv.org/abs/2106.07677v4
• Date: Wed, 19 Jul 2023 14:45:15 GMT
• Title: Planning to Fairly Allocate: Probabilistic Fairness in the Restless Bandit Setting
• Authors: Christine Herlihy, Aviva Prins, Aravind Srinivasan, and John P. Dickerson
• Abstract summary: We introduce ProbFair, a probabilistically fair policy that maximizes total expected reward and satisfies a budget constraint. We evaluate our algorithm on a real-world application, where interventions support continuous positive airway pressure (CPAP) therapy adherence among patients.
• Score: 30.120134596715154
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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