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

TL;DR

This paper introduces a novel bandit learning algorithm, MMTS, for stable two-sided matching markets with quotas and complementary preferences, demonstrating theoretical guarantees and empirical effectiveness.

Contribution

The paper formulates a new matching problem with complex constraints as a bandit learning task and proposes the MMTS algorithm with proven stability and regret bounds.

Findings

MMTS achieves stability in complex matching markets.

Theoretical regret bound of old (rac{Q}{ ext{K_{max}T}}).

Simulation results confirm effectiveness across settings.

Abstract

In this paper, we propose a new recommendation algorithm for addressing the problem of two-sided online 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 new double matching technique to provide a stable matching outcome. Our theoretical analysis demonstrates the effectiveness of MMTS as it can achieve stability and has a total $\widetilde{\mathcal{O}}(Q{\sqrt{K_{\max}T}})$-Bayesian regret with high probability, 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 also demonstrate MMTS's effectiveness in various settings. We provide code used in our experiments \url{https://github.com/Likelyt/Double-Matching}.