Bandit Learning in Matching Markets with Interviews
This work addresses the challenge of preference uncertainty in matching markets for participants like firms and agents, offering a novel algorithmic framework that is incremental in extending bandit learning to include firm-side uncertainty and strategic deferral.
The paper tackles the problem of learning preferences in two-sided matching markets with limited interviews, modeling interviews as low-cost hints, and achieves time-independent regret, a significant improvement over previous O(log T) bounds, with decentralized performance matching centralized up to polynomial factors in structured markets.
Two-sided matching markets rely on preferences from both sides, yet it is often impractical to evaluate preferences. Participants, therefore, conduct a limited number of interviews, which provide early, noisy impressions and shape final decisions. We study bandit learning in matching markets with interviews, modeling interviews as \textit{low-cost hints} that reveal partial preference information to both sides. Our framework departs from existing work by allowing firm-side uncertainty: firms, like agents, may be unsure of their own preferences and can make early hiring mistakes by hiring less preferred agents. To handle this, we extend the firm's action space to allow \emph{strategic deferral} (choosing not to hire in a round), enabling recovery from suboptimal hires and supporting decentralized learning without coordination. We design novel algorithms for (i) a centralized setting with an omniscient interview allocator and (ii) decentralized settings with two types of firm-side feedback. Across all settings, our algorithms achieve time-independent regret, a substantial improvement over the $O(\log T)$ regret bounds known for learning stable matchings without interviews. Also, under mild structured markets, decentralized performance matches the centralized counterpart up to polynomial factors in the number of agents and firms.