TCS Journal 2026 Journal Article
Bandit learning in matching markets with relative feedback
- Fang Kong
- Xiaoxi Zhang
- Xiao Huang
- Lijun Zhang
- Shuai Li
The two-sided matching market problem has been extensively studied in the literature. How to find a stable matching is a key focus in the field. A significant body of recent work considers scenarios where one side of the market (players) has uncertain preferences and learns them through the absolute rewards obtained during repeated interactions with the other side (arms). A common assumption in these works is that arms deterministically resolve conflicts when faced with multiple players. However, in practical applications, the arms’ selection process may also be stochastic due to fluctuations in players’ performances. Under such circumstances, it becomes challenging for players to observe absolute rewards that quantify the arms’ satisfaction. Instead, the relative feedback about which applicant wins in a competition is often more realistic. In this paper, we investigate the pure exploration problem for bandit learning in matching markets where players need to additionally learn the uncertain preferences of arms based on more practical relative feedback. We show that given confidence level δ ∈ (0, 1), the market can reach the player-optimal stable matching in at most O ( max { N, K } log ( 1 / δ ) / Δ 2 + N K log ( 1 / δ ) / ϵ 2 ) rounds with probability at least 1 − δ, where N, K correspond to market size, ϵ represents arms’ relative preference gap, and Δ corresponds to the players’ preference gap. We also conduct experiments to verify the performances of the proposed algorithms.