Sequential learning in a multi-agent resource constrained matching market has received significant interest in the past few years. We study decentralized learning in two-sided matching markets where the demand side (aka players or agents) competes for a `large' supply side (aka arms) with potentially time-varying preferences, to obtain a stable match. Despite a long line of work in the recent past, existing learning algorithms such as Explore-Then-Commit or Upper-Confidence-Bound remain inefficient for this problem. In particular, the per-agent regret achieved by these algorithms scales linearly with the number of arms, $K$. Motivated by the linear contextual bandit framework, we assume that for each agent an arm-mean can be represented by a linear function of a known feature vector and an unknown (agent-specific) parameter. Moreover, our setup captures the essence of a dynamic (non-stationary) matching market where the preferences over arms change over time. Our proposed algorithms achieve instance-dependent logarithmic regret, scaling independently of the number of arms, $K$.

翻译：近年来，多智能体资源受限匹配市场中的序贯学习问题受到广泛关注。本研究探讨双边匹配市场中的去中心化学习问题，其中需求侧（即参与者或智能体）为获得稳定匹配，需在具有潜在时变偏好的“大规模”供给侧（即臂）中进行竞争。尽管近期已有大量相关研究，但现有学习算法（如“探索-后提交”或“上置信界算法”）对此问题仍效率不足。具体而言，这些算法实现的单智能体遗憾与臂数量$K$呈线性比例关系。受线性情境赌博机框架启发，我们假设每个智能体的臂期望收益可由已知特征向量与未知（智能体特定）参数的线性函数表示。此外，我们的模型设置捕捉了动态（非平稳）匹配市场的本质特征，其中对臂的偏好会随时间变化。我们提出的算法实现了与实例相关的对数遗憾，其缩放独立于臂数量$K$。