Long-Term Resource Allocation Fairness in Average Markov Decision Process (AMDP) Environment

Ganesh Ghalme; Vineet Nair; Vishakha Patil; Yilun Zhou

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arXiv · 2102.07120

Long-Term Resource Allocation Fairness in Average Markov Decision Process (AMDP) Environment

Ganesh Ghalme·Vineet Nair·Vishakha Patil·Yilun Zhou

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Abstract

Fairness has emerged as an important concern in automated decision-making in recent years, especially when these decisions affect human welfare. In this work, we study fairness in temporally extended decision-making settings, specifically those formulated as Markov Decision Processes (MDPs). Our proposed notion of fairness ensures that each state's long-term visitation frequency is at least a specified fraction. This quota-based notion of fairness is natural in many resource-allocation settings where the dynamics of a single resource being allocated is governed by an MDP and the distribution of the shared resource is captured by its state-visitation frequency. In an average-reward MDP (AMDP) setting, we formulate the problem as a bilinear saddle point program and, for a generative model, solve it using a Stochastic Mirror Descent (SMD) based algorithm. The proposed solution guarantees a simultaneous approximation on the expected average-reward and fairness requirement. We give sample complexity bounds for the proposed algorithm and validate our theoretical results with experiments on simulated data.

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Ganesh Ghalme, Vineet Nair, Vishakha Patil, Yilun Zhou. 2021-02-14. Long-Term Resource Allocation Fairness in Average Markov Decision Process (AMDP) Environment. https://arxiv.org/abs/2102.07120

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