ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projection
This addresses the limitation of existing methods that are restricted to affine or convex constraints, providing a scalable solution for high-dimensional optimization problems, though it appears incremental as it builds on projection-based methods.
The paper tackled the problem of enforcing nonlinear equality constraints in neural network predictions, which is crucial for safety and ethical concerns, and introduced ENFORCE, an architecture that uses an adaptive projection module to achieve this with a computational complexity of O(N_C^3) at training and inference time.
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.