Dynamic Matching Bandit For Two-Sided Online Markets

TL;DR

This paper introduces a dynamic matching bandit algorithm for two-sided online markets with evolving preferences based on contextual information, providing theoretical guarantees and practical robustness in various settings.

Contribution

It proposes a novel dynamic matching framework with an online preference estimation method and proves logarithmic regret bounds, advancing beyond static preference models.

Findings

Algorithm achieves high-probability agent-optimal stable matchings.

Logarithmic regret upper bound of O(log(T)).

Robust performance across diverse preference and context scenarios.

Abstract

Two-sided online matching platforms are employed in various markets. However, agents' preferences in the current market are usually implicit and unknown, thus needing to be learned from data. With the growing availability of dynamic side information involved in the decision process, modern online matching methodology demands the capability to track shifting preferences for agents based on contextual information. This motivates us to propose a novel framework for this dynamic online matching problem with contextual information, which allows for dynamic preferences in matching decisions. Existing works focus on online matching with static preferences, but this is insufficient: the two-sided preference changes as soon as one side's contextual information updates, resulting in non-static matching. In this paper, we propose a dynamic matching bandit algorithm to adapt to this problem. The key component of the proposed dynamic matching algorithm is an online estimation of the preference ranking with a statistical guarantee. Theoretically, we show that the proposed dynamic matching algorithm delivers an agent-optimal stable matching result with high probability. In particular, we prove a logarithmic regret upper bound $\mathcal{O}(\log(T))$ and construct a corresponding instance-dependent matching regret lower bound. In the experiments, we demonstrate that dynamic matching algorithm is robust to various preference schemes, dimensions of contexts, reward noise levels, and context variation levels, and its application to a job-seeking market further demonstrates the practical usage of the proposed method.