Planning to Fairly Allocate: Probabilistic Fairness in the Restless Bandit Setting
This addresses fairness in resource allocation for applications like healthcare interventions, offering a novel guarantee but is incremental in extending bandit methods.
The paper tackled the problem of ensuring fairness in restless bandit resource allocation, where existing methods lack guarantees, by introducing ProbFair, a policy that maximizes expected reward under budget constraints while providing a probabilistic fairness guarantee with a positive lower bound on selection probability.
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.