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.

翻译：组合优化增强机器学习（COAML）作为一种将预测模型与组合决策相结合的新兴范式，近年来展现出强大的应用潜力。通过将组合优化求解器嵌入学习流程，COAML能够构建兼具数据驱动特性与可行性保障的决策策略，从而在机器学习、运筹学与随机优化的传统领域间架起桥梁。本文对COAML领域的前沿进展进行了系统性综述。我们首先提出了统一的COAML流程框架，阐述了其方法论构建模块，并形式化地论证了其与经验风险最小化的理论关联。随后基于不确定性形式与决策结构建立了问题设置的分类体系，并以此为主线综述了静态与动态问题的算法进展，梳理了在调度、车辆路径规划、随机规划及强化学习等领域的应用案例，从经验风险最小化、模仿学习与强化学习三个维度整合了方法论贡献。最后，本文指出了该领域的关键研究前沿。本综述旨在为相关领域研究者提供入门导引，并为组合优化与机器学习的交叉研究方向提供发展路线图。