Abstract: In this paper, we propose a new recommendation algorithm for addressing the problem of two-sided matching markets with complementary preferences and quota constraints, where agents' preferences are unknown a priori and must be learned from data. The presence of mixed quota and complementary preferences constraints can lead to instability in the matching process, making this problem challenging to solve. To overcome this challenge, we formulate the problem as a bandit learning framework and propose the Multi-agent Multi-type Thompson Sampling (MMTS) algorithm. The algorithm combines the strengths of Thompson Sampling for exploration with a double matching technique to achieve a stable matching outcome. Our theoretical analysis demonstrates the effectiveness of MMTS as it can achieve stability at every matching step and has a total $\widetilde{\mathcal{O}}(Q{\sqrt{K_{\max}T}})$-Bayesian regret, which exhibits linearity with respect to the total firm's quota $Q$ and the square root of the maximum size of available type workers $\sqrt{K_{\max}}$.