Enforcing convex constraints in Graph Neural Networks
This addresses the problem of ensuring constraint satisfaction in GNN outputs for applications like optimization, offering a novel framework but with incremental improvements in method integration.
The paper tackles the challenge of enforcing input-dependent convex constraints in Graph Neural Networks (GNNs) for graph-structured data with variable output sizes, introducing ProjNet, which combines sparse vector clipping with the Component-Averaged Dykstra (CAD) algorithm and a surrogate gradient for efficient training, and validates it on four constrained optimization problems including linear programming and radio transmit power optimization.
Many machine learning applications require outputs that satisfy complex, dynamic constraints. This task is particularly challenging in Graph Neural Network models due to the variable output sizes of graph-structured data. In this paper, we introduce ProjNet, a Graph Neural Network framework which satisfies input-dependant constraints. ProjNet combines a sparse vector clipping method with the Component-Averaged Dykstra (CAD) algorithm, an iterative scheme for solving the best-approximation problem. We establish a convergence result for CAD and develop a GPU-accelerated implementation capable of handling large-scale inputs efficiently. To enable end-to-end training, we introduce a surrogate gradient for CAD that is both computationally efficient and better suited for optimization than the exact gradient. We validate ProjNet on four classes of constrained optimisation problems: linear programming, two classes of non-convex quadratic programs, and radio transmit power optimization, demonstrating its effectiveness across diverse problem settings.