Dual Lagrangian Learning for Conic Optimization
Mathieu Tanneau Pascal Van Hentenryck
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.