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Planning to Fairly Allocate: Probabilistic Fairness in the Restless Bandit Setting
arXiv - CS - Computers and Society Pub Date : 2021-06-14 , DOI: arxiv-2106.07677
Christine Herlihy, Aviva Prins, Aravind Srinivasan, John Dickerson

Restless and collapsing bandits are commonly used to model constrained resource allocation in settings featuring arms with action-dependent transition probabilities, such as allocating health interventions among patients [Whittle, 1988; Mate et al., 2020]. 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 [Mate et al., 2021]. Additionally, their optimality guarantees only apply when arms are indexable and threshold-optimal. We demonstrate that the incorporation of hard fairness constraints necessitates the coupling of arms, which undermines the tractability, and by extension, indexability of the problem. We then introduce ProbFair, a probabilistically fair stationary 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 obstructive sleep apnea (OSA) patients, as well as simulations on a broader class of synthetic transition matrices.

中文翻译:

计划公平分配:Restless Bandit 环境中的概率公平

不安和崩溃的强盗通常用于在具有依赖于动作的转换概率的武器的环境中对受限资源分配进行建模,例如在患者之间分配健康干预 [Whittle, 1988; Mate 等人,2020 年]。然而,针对这一规划问题的最先进的基于惠特尔指数的方法要么没有考虑武器之间的公平性,要么在没有保证的情况下激励公平性 [Mate et al., 2021]。此外,它们的最优性保证仅适用于手臂可索引且阈值最优的情况。我们证明了硬公平约束的结合需要臂的耦合,这破坏了问题的易处理性,进而破坏了问题的可索引性。然后我们介绍 ProbFair,一个概率公平的平稳策略,最大化总预期奖励并满足预算约束,同时确保在每个时间步被拉动的概率有一个严格的正下限。我们在实际应用中评估我们的算法,其中干预支持阻塞性睡眠呼吸暂停 (OSA) 患者的持续气道正压通气 (CPAP) 治疗依从性,以及对更广泛的合成转换矩阵的模拟。
更新日期:2021-06-16
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