# Sequential Fair Resource Allocation under a Markov Decision Process Framework

arXiv: https://arxiv.org/abs/2301.03758 · HTML: https://mlsanity.com/paper/2301.03758/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 54 references that are in the map.
- First posted on arXiv 10 Jan 2023.

## Builds on (most cited first, 12 of 12)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Individual Fairness in Hindsight](https://mlsanity.com/paper/1812.04069/) (2018)
- [Online Fair Division: analysing a Food Bank problem](https://mlsanity.com/paper/1502.07571/) (2015)
- [Fair Dynamic Rationing](https://mlsanity.com/paper/2102.01240/) (2021)
- [Fairness and Utilization in Allocating Resources with Uncertain Demand](https://mlsanity.com/paper/1906.09050/) (2019)
- [Sequential Fair Allocation: Achieving the Optimal Envy-Efficiency Tradeoff Curve](https://mlsanity.com/paper/2105.05308/) (2021)
- [Fairness-Efficiency Tradeoffs in Dynamic Fair Division](https://mlsanity.com/paper/1907.11672/) (2019)
- [Sequential Fair Allocation of Limited Resources under Stochastic Demands](https://mlsanity.com/paper/2011.14382/) (2020)
- [Initialization-free Distributed Algorithms for Optimal Resource Allocation with Feasibility Constraints and its Application to Economic Dispatch of Power Systems](https://mlsanity.com/paper/1510.08579/) (2015)
- [Online Resource Allocation with Customer Choice](https://mlsanity.com/paper/1511.01837/) (2015)
- [Mechanism Design for Online Resource Allocation: A Unified Approach](https://mlsanity.com/paper/2004.09640/) (2020)

## Built on by (most cited first, 3 of 3)

- [Online Fair Allocation of Perishable Resources](https://mlsanity.com/paper/2406.02402/) (2024)
- [Fair Resource Allocation in Weakly Coupled Markov Decision Processes](https://mlsanity.com/paper/2411.09804/) (2024)
- [Fair Policy Optimization in Major-Minor Weakly Coupled Markov Decision Processes](https://mlsanity.com/paper/2609.36174/) (2026)

## Abstract (arXiv)

We study the sequential decision-making problem of allocating a limited resource to agents that reveal their stochastic demands on arrival over a finite horizon. Our goal is to design fair allocation algorithms that exhaust the available resource budget. This is challenging in sequential settings where information on future demands is not available at the time of decision-making. We formulate the problem as a discrete time Markov decision process (MDP). We propose a new algorithm, SAFFE, that makes fair allocations with respect to the entire demands revealed over the horizon by accounting for expected future demands at each arrival time. The algorithm introduces regularization which enables the prioritization of current revealed demands over future potential demands depending on the uncertainty in agents' future demands. Using the MDP formulation, we show that SAFFE optimizes allocations based on an upper bound on the Nash Social Welfare fairness objective, and we bound its gap to optimality with the use of concentration bounds on total future demands. Using synthetic and real data, we compare the performance of SAFFE against existing approaches and a reinforcement learning policy trained on the MDP. We show that SAFFE leads to more fair and efficient allocations and achieves close-to-optimal performance in settings with dense arrivals.