Combinatorial Optimization Augmented Machine Learning

Combinatorial optimization augmented machine learning (COAML) has recently emerged as a powerful paradigm for integrating predictive models with combinatorial decision-making. By embedding combinatorial optimization oracles into learning pipelines, COAML enables the construction of policies that are both data-driven and feasibility-preserving, bridging the traditions of machine learning, operations research, and stochastic optimization. This paper provides a comprehensive overview of the state of the art in COAML. We introduce a unifying framework for COAML pipelines, describe their methodological building blocks, and formalize their connection to empirical cost minimization. We then develop a taxonomy of problem settings based on the form of uncertainty and decision structure. Using this taxonomy, we review algorithmic approaches for static and dynamic problems, survey applications across domains such as scheduling, vehicle routing, stochastic programming, and reinforcement learning, and synthesize methodological contributions in terms of empirical cost minimization, imitation learning, and reinforcement learning. Finally, we identify key research frontiers. This survey aims to serve both as a tutorial introduction to the field and as a roadmap for future research at the interface of combinatorial optimization and machine learning.

Global Rewards in Multi-Agent Deep Reinforcement Learning for Autonomous Mobility on Demand Systems

We study vehicle dispatching in autonomous mobility on demand (AMoD) systems, where a central operator assigns vehicles to customer requests or rejects these with the aim of maximizing its total profit. Recent approaches use multi-agent deep reinforcement learning (MADRL) to realize scalable yet performant algorithms, but train agents based on local rewards, which distorts the reward signal with respect to the system-wide profit, leading to lower performance. We therefore propose a novel global-rewards-based MADRL algorithm for vehicle dispatching in AMoD systems, which resolves so far existing goal conflicts between the trained agents and the operator by assigning rewards to agents leveraging a counterfactual baseline. Our algorithm shows statistically significant improvements across various settings on real-world data compared to state-of-the-art MADRL algorithms with local rewards. We further provide a structural analysis which shows that the utilization of global rewards can improve implicit vehicle balancing and demand forecasting abilities. Our code is available at https://github.com/tumBAIS/GR-MADRL-AMoD.