Learn to Match with No Regret: Reinforcement Learning in Markov Matching Markets

TL;DR

This paper introduces a reinforcement learning framework for Markov matching markets, enabling a planner to optimize social welfare while agents seek stable matchings, with proven sublinear regret guarantees.

Contribution

It develops a novel RL algorithm combining optimistic value iteration with maximum weight matching for dynamic markets.

Findings

The algorithm achieves sublinear regret in the Markov matching setting.

It effectively balances exploration and stability in dynamic matching markets.

The framework applies to real-world scenarios like ridesharing platforms.

Abstract

We study a Markov matching market involving a planner and a set of strategic agents on the two sides of the market. At each step, the agents are presented with a dynamical context, where the contexts determine the utilities. The planner controls the transition of the contexts to maximize the cumulative social welfare, while the agents aim to find a myopic stable matching at each step. Such a setting captures a range of applications including ridesharing platforms. We formalize the problem by proposing a reinforcement learning framework that integrates optimistic value iteration with maximum weight matching. The proposed algorithm addresses the coupled challenges of sequential exploration, matching stability, and function approximation. We prove that the algorithm achieves sublinear regret.