Bandit Learning in Matching Markets with Interviews

TL;DR

This paper introduces a bandit learning framework for two-sided matching markets with interviews, allowing firms and agents to learn preferences over time despite initial uncertainty, and proposes algorithms with strong regret guarantees.

Contribution

It extends existing matching market models by incorporating firm-side uncertainty and strategic deferral, enabling decentralized learning with improved regret bounds.

Findings

Algorithms achieve time-independent regret in various settings.

Decentralized performance approaches centralized benchmarks under mild conditions.

Significant improvement over previous $O(\log T)$ regret bounds.

Abstract

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.