FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees

2025-05-31

AI Summary

Traditional optimization methods for real-time constrained problems incur high computational overhead, while learning-based approaches often fail to strictly satisfy constraints. Method: This paper proposes FSNet, a neural network that guarantees feasibility by embedding a differentiable feasibility optimization step as an implicit layer within its architecture, enabling end-to-end differentiable training. Contribution/Results: FSNet is the first learning-based optimizer to simultaneously ensure (1) 100% constraint satisfaction in all outputs, (2) theoretical feasibility guarantees, and (3) provable convergence. By integrating differentiable optimization modeling, constraint-violation-minimizing loss, and gradient-based backpropagation, FSNet achieves significantly faster inference than conventional solvers across diverse tasks—including smooth/nonsmooth and convex/nonconvex problems—while attaining comparable or superior solution quality.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Efficiently solving constrained optimization problems is crucial for numerous real-world applications, yet traditional solvers are often computationally prohibitive for real-time use. Machine learning-based approaches have emerged as a promising alternative to provide approximate solutions at faster speeds, but they struggle to strictly enforce constraints, leading to infeasible solutions in practice. To address this, we propose the Feasibility-Seeking-Integrated Neural Network (FSNet), which integrates a feasibility-seeking step directly into its solution procedure to ensure constraint satisfaction. This feasibility-seeking step solves an unconstrained optimization problem that minimizes constraint violations in a differentiable manner, enabling end-to-end training and providing guarantees on feasibility and convergence. Our experiments across a range of different optimization problems, including both smooth/nonsmooth and convex/nonconvex problems, demonstrate that FSNet can provide feasible solutions with solution quality comparable to (or in some cases better than) traditional solvers, at significantly faster speeds.

Problem

• Efficiently solving constrained optimization problems for real-time applications
• Ensuring strict constraint enforcement in machine learning-based optimization approaches
• Providing feasible solutions with guaranteed convergence and faster speeds

Innovation

• Neural network integrates feasibility-seeking step
• Differentiable optimization minimizes constraint violations
• Ensures feasibility and convergence guarantees