Recent trends in combinatorial optimization augmented machine learning: A graph learning perspective.

Combinatorial optimization augmented machine learning (COAML) is a rapidly growing field that integrates machine learning and operations research methods to solve data-driven problems involving both uncertainty and combinatorial structures. These problems frequently arise in industrial settings where firms leverage large, noisy datasets to optimize operations. COAML embeds combinatorial optimization layers into neural networks and trains them using decision-aware learning techniques. It excels on contextual and dynamic stochastic optimization problems, as demonstrated by its winning performance in the 2022 EURO-NeurIPS dynamic vehicle routing challenge. After providing a field overview, we focus on recent learning algorithms for empirical cost minimization and structured reinforcement learning, along with new regularizations that exploit connections between local search and Monte Carlo methods. These algorithms improve performance, reduce computational costs, and lower data requirements, enabling new large-scale applications. They also provide convergence guarantees that enable new statistical learning generalization bounds. Graphs serve as a unifying theme throughout the presentation, highlighting their central role in the problems, architectures, layers, learning algorithms, and theoretical analysis frameworks we consider.