We address the problem of online multi-human multi-robot matching through the lens of a linear matching bandit framework, where a learner assigns robots with unknown features from a fixed pool to distinct sets of human agents over multiple rounds. To solve this problem, we propose LinMatch, an online learning algorithm that updates the confidence intervals of the unknown features and makes the optimistic matching under uncertainty. The contributions and novelty of this work are twofold. First, we recast the optimistic matching problem in each round as a linear program of maximum weighted matching, efficiently solvable by the celebrated Hungarian algorithm. Second, we provide novel bounds for matching with linear feature problems, showing that $Θ(\sqrt{T})$ is the optimal achievable regret with respect to the total number of rounds $T$. The proposed algorithm and bounds apply to a wide range of matching problems with applications beyond human-robot matching, such as housing allocation, recommendation systems, and more.
Causal inference is essential for data-driven decision-making, as it aims to uncover causal relationships from observational data. However, identifying causality remains challenging due to the potential for confounding and the distinction between correlation and causation. While recent advances in causal machine learning and matching algorithms have improved estimation accuracy, these methods often face trade-offs between interpretability and computational efficiency. This paper proposes a novel approach that combines a tree-based discretization technique, tailored for causal inference, with an integer linear programming-based matching algorithm. The discretization ensures approximately linear relationships for control datasets within strata, enabling effective matching, while the optimization framework optimizes for global balance. The resulting algorithm yields computational efficiency and less biased ATT estimates compared to state-of-the-art algorithms. Empirical evaluations demonstrate the proposed method's practical advantages over existing techniques in causal inference scenarios.