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In this paper, we propose a new recommendation algorithm for addressing theproblem of two-sided online matching markets with complementary preferences andquota constraints, where agents' preferences are unknown a priori and must belearned from data. The presence of mixed quota and complementary preferencesconstraints can lead to instability in the matching process, making thisproblem challenging to solve. To overcome this challenge, we formulate theproblem as a bandit learning framework and propose the Multi-agent Multi-typeThompson Sampling (MMTS) algorithm. The algorithm combines the strengths ofThompson Sampling for exploration with a new double matching technique toprovide a stable matching outcome. Our theoretical analysis demonstrates theeffectiveness of MMTS as it can achieve stability and has a total$\widetilde{\mathcal{O}}(Q{\sqrt{K_{\max}T}})$-Bayesian regret with highprobability, which exhibits linearity with respect to the total firm's quota$Q$, the square root of the maximum size of available type workers$\sqrt{K_{\max}}$ and time horizon $T$. In addition, simulation studies alsodemonstrate MMTS's effectiveness in various settings. We provide code used inour experiments \url{https://github.com/Likelyt/Double-Matching}.

Two-sided Competing Matching Recommendation Markets With Quota and Complementary Preferences Constraints