Self-Supervised Primal-Dual Learning for Constrained Optimization

This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. is an empirical risk minimization under constraints, which challenging as training must balance optimality and feasibility conditions. Supervised learning methods often approach this challenge by model on a large collection pre-solved instances. takes different route proposes idea Primal-Dual Learning (PDL), self-supervised method does not require set instances or solver for inference. Instead, PDL mimics trajectory Augmented Lagrangian Method (ALM) jointly trains primal dual neural networks. Being primal-dual method, uses instance-specific penalties constraint terms in loss function used network. Experiments show that, nonlinear benchmarks, typically exhibits negligible violations minor gaps, remarkably close ALM optimization. also demonstrated improved similar performance violations, times compared existing approaches.