Dual Lagrangian Learning for Conic Optimization

This paper presents Dual Lagrangian Learning (DLL), a principled learning methodology that combines conic duality theory with the representation power of ML models. DLL leverages conic duality to provide dual-feasible solutions, and therefore valid Lagrangian dual bounds, for parametric linear and nonlinear conic optimization problems. The paper introduces differentiable conic projection layers, a systematic dual completion procedure, and a self-supervised learning framework. The effectiveness of DLL is demonstrated on linear and nonlinear parametric optimization problems for which DLL provides valid dual bounds within 0.5% of optimality.