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We study the problem of repeated two-sided matching with uncertainpreferences (two-sided bandits), and no explicit communication between agents.Recent work has developed algorithms that converge to stable matchings when oneside (the proposers or agents) must learn their preferences, but thepreferences of the other side (the proposees or arms) are common knowledge, andthe matching mechanism uses simultaneous proposals at each round. We developnew algorithms that converge to stable matchings for two more challengingsettings: one where the arm preferences are no longer common knowledge, and asecond, more general one where the arms are also uncertain about their ownpreferences. In our algorithms, agents start with optimistic beliefs aboutarms' preferences, updating these preferences over time, and combining beliefsabout preferences with beliefs about the value of matching when choosing whomto propose to.

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