用神经网络快速求解复杂双层优化问题，提升控制设计效率。
Learning to Solve Constrained Bilevel Control Co-Design Problems
- 通过可微优化技术训练神经网络逼近双层优化解
- 在合成问题和控制协同设计中验证了高效性与准确性
- 适合需要快速求解复杂优化的工程系统设计场景
学习优化（L2O）是机器学习的一个分支，旨在训练模型以快速求解参数化优化问题。其核心目标是学习一个能快速近似求解约束优化问题的函数。现有方法主要针对单层问题，而双层问题的约束本身由优化子问题定义，应用场景广泛但求解困难，尤其在时间紧迫时更难处理。本文提出一种新框架，利用现代可微优化技术，学习求解一大类复杂的双层优化问题。该框架在一系列合成双层问题及具有挑战性的控制系统协同设计问题上得到验证，展示了神经网络作为参数化双层优化高效近似器的潜力。
原文摘要 · Abstract (English)
Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems, as a function of their defining parameters. Prior L2O methods focus almost entirely on single-level programs, in contrast to the bilevel programs, whose constraints are themselves expressed in terms of optimization subproblems. Bilevel programs have numerous important use cases but are notoriously difficult to solve, particularly under stringent time demands. This paper proposes a framework for learning to solve a broad class of challenging bilevel optimization problems, by leveraging modern techniques for differentiation through optimization problems. The framework is illustrated on an array of synthetic bilevel programs, as well as challenging control system co-design problems, showing how neural networks can be trained as efficient approximators of parametric bilevel optimization.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。