Title: Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers
Primary area: optimization
Keywords: hard constrained neural networks, network architecture, implicit layers, operator splitting, optimization

Abstract: We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $\Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy $\Pi$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 by orders of magnitude 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 $\Pi$net as a GPU-ready package implemented in JAX.