Combinatorial Optimization Augmented Machine Learning

TL;DR

This paper reviews the emerging field of combinatorial optimization augmented machine learning (COAML), highlighting its frameworks, methodologies, applications, and future research directions at the intersection of optimization and machine learning.

Contribution

It provides a comprehensive overview, unifying framework, taxonomy, and survey of algorithmic approaches and applications in COAML, serving as a tutorial and research roadmap.

Findings

Developed a unifying framework for COAML pipelines

Classified problem settings based on uncertainty and decision structure

Surveyed applications across multiple domains and methodologies

Abstract

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.