ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projection

Abstract

Ensuring neural networks adhere to domain-specific constraints is crucial for addressing safety and ethical concerns while also enhancing inference accuracy. Despite the nonlinear nature of most real-world tasks, existing methods are predominantly limited to affine or convex constraints. We introduce ENFORCE, a neural network architecture that uses an adaptive projection module (AdaNP) to enforce nonlinear equality constraints in the predictions. We prove that our projection mapping is 1-Lipschitz, making it well-suited for stable training. We evaluate ENFORCE on an illustrative regression task and for learning solutions to high-dimensional optimization problems in an unsupervised setting. The predictions of our new architecture satisfy $N_C$ equality constraints that are nonlinear in both the inputs and outputs of the neural network, while maintaining scalability with a tractable computational complexity of $\mathcal{O}(N_C^3)$ at training and inference time.