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Fairness plays a crucial role in various multi-agent systems (e.g.,communication networks, financial markets, etc.). Many multi-agent dynamicalinteractions can be cast as Markov Decision Processes (MDPs). While existingresearch has focused on studying fairness in known environments, theexploration of fairness in such systems for unknown environments remains open.In this paper, we propose a Reinforcement Learning (RL) approach to achievefairness in multi-agent finite-horizon episodic MDPs. Instead of maximizing thesum of individual agents' value functions, we introduce a fairness functionthat ensures equitable rewards across agents. Since the classical Bellman'sequation does not hold when the sum of individual value functions is notmaximized, we cannot use traditional approaches. Instead, in order to explore,we maintain a confidence bound of the unknown environment and then propose anonline convex optimization based approach to obtain a policy constrained tothis confidence region. We show that such an approach achieves sub-linearregret in terms of the number of episodes. Additionally, we provide a probablyapproximately correct (PAC) guarantee based on the obtained regret bound. Wealso propose an offline RL algorithm and bound the optimality gap with respectto the optimal fair solution. To mitigate computational complexity, weintroduce a policy-gradient type method for the fair objective. Simulationexperiments also demonstrate the efficacy of our approach.

Achieving Fairness in Multi-Agent Markov Decision Processes Using Reinforcement Learning