Unsupervised Learning for Combinatorial Optimization with Principled Objective Relaxation

Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems. Our framework follows the standard relaxation-plus-rounding approach and adopts neural networks to parameterize the relaxed solutions so that simple back-propagation can train them end-to-end. Our key contribution is the observation that if the relaxed objective satisfies entry-wise concavity, a low optimization loss guarantees the quality of the obtained integral solutions. This observation significantly generalizes the applicability of the previous framework inspired by Erdos' probabilistic method (Karalias & Loukas, 2020).