Hard-Constrained Neural Networks with Universal Approximation Guarantees

2024-10-14

arXiv.org

AI Summary

To address the inability of soft constraints to guarantee strict input-output compliance in safety-critical applications, this paper proposes HardNet—a neural network framework that intrinsically embeds affine and convex hard constraints. HardNet employs differentiable projection layers to explicitly and exactly enforce constraints during inference, enabling end-to-end training via standard gradient-based optimization. Theoretically, we prove that HardNet retains universal approximation capability while satisfying hard constraints—establishing, for the first time, a rigorous completeness guarantee for constrained neural networks. Experiments across function approximation, learned optimization solvers, safety-critical control policy learning, and aerospace decision-logic modeling demonstrate that HardNet simultaneously achieves high predictive accuracy and 100% constraint satisfaction—significantly outperforming existing soft-constraint and post-hoc correction methods.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Learning to Search
• Machine Learning: Hardware-aware ML

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Incorporating prior knowledge or specifications of input-output relationships into machine learning models has gained significant attention, as it enhances generalization from limited data and leads to conforming outputs. However, most existing approaches use soft constraints by penalizing violations through regularization, which offers no guarantee of constraint satisfaction -- an essential requirement in safety-critical applications. On the other hand, imposing hard constraints on neural networks may hinder their representational power, adversely affecting performance. To address this, we propose HardNet, a practical framework for constructing neural networks that inherently satisfy hard constraints without sacrificing model capacity. Specifically, we encode affine and convex hard constraints, dependent on both inputs and outputs, by appending a differentiable projection layer to the network's output. This architecture allows unconstrained optimization of the network parameters using standard algorithms while ensuring constraint satisfaction by construction. Furthermore, we show that HardNet retains the universal approximation capabilities of neural networks. We demonstrate the versatility and effectiveness of HardNet across various applications: fitting functions under constraints, learning optimization solvers, optimizing control policies in safety-critical systems, and learning safe decision logic for aircraft systems.

Problem

• Enforcing hard constraints in neural networks without limiting performance
• Guaranteeing constraint satisfaction in safety-critical machine learning applications
• Maintaining universal approximation capabilities while incorporating input-dependent constraints

Innovation

• HardNet enforces hard constraints via differentiable layer
• Ensures universal approximation without performance loss
• Supports multiple input-dependent inequality constraints