Synergy between machine learning and optimization

Optimization algorithms (OAs) and machine learning (ML) have both seen significant advancements in recent years. OAs are good at exploiting known structures and finding solutions in large decision spaces, while ML excels at detecting patterns. Rather than competing, there is a natural synergy in integrating these two approaches. This integration can take place in several ways, including using OA to provide input to ML, using ML to provide input to OA, using ML to accelerate OA, and using OA to solve subroutines in ML. The integration of OA and ML makes sense in situations where traditional methods are too slow, heuristic solutions can be improved, good solutions need to be identified, fast approximations are needed, and when the algorithmic pipeline involves both pattern detection and exploration. The integration of OA and ML has been studied in various domains, such as using ML to guide branch-and-bound algorithms, using ML to improve routing problems with Graph Neural Networks, and using mathematical programming as a subroutine in reinforcement learning.