Reinforcement Learning for Decentralized Stable Matching

When it comes to finding a match/partner in the real world, it is usually an independent and autonomous task performed by people/entities. For a person, a match can be several things such as a romantic partner, business partner, school, roommate, etc. Our purpose in this paper is to train autonomous agents to find suitable matches for themselves using reinforcement learning. We consider the decentralized two-sided stable matching problem, where an agent is allowed to have at most one partner at a time from the opposite set. Each agent receives some utility for being in a match with a member of the opposite set. We formulate the problem spatially as a grid world environment and having autonomous agents acting independently makes our environment very uncertain and dynamic. We run experiments with various instances of both complete and incomplete weighted preference lists for agents. Agents learn their policies separately, using separate training modules. Our goal is to train agents to find partners such that the outcome is a stable matching if one exists and also a matching with set-equality, meaning the outcome is approximately equally likable by agents from both the sets.