Learning-Augmented Approximation Algorithms for Maximum Cut and Related Problems

Many optimization problems are computationally hard, meaning that finding the absolute best solution is practically impossible. Approximation algorithms offer a way to find good-enough solutions in reasonable time, but these solutions are often limited by theoretical lower bounds. This paper tackles this issue by exploring the use of machine learning to augment approximation algorithms. The core challenge is to overcome the computational hurdles by using predictions even if those predictions contain errors or are incomplete.

The paper focuses on the MAX-CUT problem, a classic example of a hard problem. The researchers developed novel algorithms that incorporate noisy predictions about the optimal solution. These algorithms demonstrably outperform traditional methods, showcasing how machine-learning predictions can improve upon the worst-case computational bounds for hard optimization problems. The results extend beyond MAX-CUT to a broader class of problems, suggesting the wider applicability of this machine learning-assisted approach.