FSNet让神经网络求解约束优化时既快又保证可行
FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees
- 在训练中嵌入可微的可行性修正步骤
- 速度远超传统方法，且解严格满足约束
- 适合需要实时、可靠解的工程场景
高效求解约束优化问题对众多现实应用至关重要，但传统求解器在实时使用中往往计算开销过大。基于机器学习的方法虽能快速提供近似解，却难以严格满足约束，导致实际中出现不可行解。为此，我们提出可行性寻求神经网络（FSNet），将可行性寻求步骤直接融入求解过程，确保约束满足。该步骤通过求解一个可微的无约束优化问题来最小化约束违反，支持端到端训练，并提供可行性与收敛性保证。我们在多种优化问题上进行实验，涵盖光滑/非光滑及凸/非凸问题，结果表明FSNet能在显著更快速度下提供与传统求解器相当（或在某些情况下更优）的可行解。
原文摘要 · Abstract (English)
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 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.
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