Intersectional Fairness in Reinforcement Learning with Large State and Constraint Spaces

In traditional reinforcement learning (RL), the learner aims to solve a single objective optimization problem: find the policy that maximizes expected reward. However, in many real-world settings, it is important to optimize over multiple objectives simultaneously. For example, when we are interested in fairness, states might have feature annotations corresponding to multiple (intersecting) demographic groups to whom reward accrues, and our goal might be to maximize the reward of the group receiving the minimal reward. In this work, we consider a multi-objective optimization problem in which each objective is defined by a state-based reweighting of a single scalar reward function. This generalizes the problem of maximizing the reward of the minimum reward group. We provide oracle-efficient algorithms to solve these multi-objective RL problems even when the number of objectives is very large -for tabular MDPs, as well as for large MDPs when the group functions have additional structure. The contribution of this paper is that we are able to solve this class of multi-objective RL problems with a possibly exponentially large class of constraints over intersecting groups in both tabular and large state space MDPs in an oracle-efficient manner. Finally, we experimentally validate our theoretical results and demonstrate applications on a preferential attachment graph MDP.