Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers
Year: 2025
Type: preprint
Abstract: We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $Π$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy $Π$net as a feasible-by-design optimization proxy for parametric constrained optimization problems and obtain modest-accuracy solutions faster than traditional solvers when solving a single problem, and significantly faster for a batch of problems. We surpass state-of-the-art learning approaches in terms of training time, solution quality, and robustness to hyperparameter tuning, while maintaining similar inference times. Finally, we tackle multi-vehicle motion planning with non-convex trajectory preferences and provide $Π$net as a GPU-ready package implemented in JAX with effective tuning heuristics.
Authors: Grontas, Panagiotis D., Terpin, Antonio, Balta, Efe, D'Andrea, Raffaello, Lygeros, John
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7108340259
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