Converging to Stability in Two-Sided Bandits: The Case of Unknown Preferences on Both Sides of a Matching Market

We study the problem of repeated two-sided matching with uncertain preferences (two-sided bandits), and no explicit communication between agents. Recent work has developed algorithms that converge to stable matchings when one side (the proposers or agents) must learn their preferences, but the preferences of the other side (the proposees or arms) are common knowledge, and the matching mechanism uses simultaneous proposals at each round. We develop new algorithms that provably converge to stable matchings for two more challenging settings: one where the arm preferences are no longer common knowledge, and a second, more general one where the arms are also uncertain about their preferences. In our algorithms, agents start with optimistic beliefs about arms' preferences and update these preferences over time. The key insight is in how to combine these beliefs about arm preferences with beliefs about the value of matching with an arm conditional on one's proposal being accepted when choosing whom to propose to.