题目：Machine Learning for Real-Time Constrained Optimization
报告人：陈名华
地点：2号学院楼222
时间：2024年3月1日10:00
报告人简介
陈名华毕业于清华大学电子工程系，获工学学士和硕士学位。他获得了加州大学伯克利分校电气工程与计算机科学系的博士学位。香港城市大学数据科学学院教授。他于2007年获得加州大学伯克利分校Eli评审团奖（授予在系统、通信、控制或信号处理领域取得杰出成就的研究生或应届校友），并于2013年获得香港中文大学青年研究员奖。他还获得了多个最佳论文奖，包括2009年IEEE ICME最佳论文奖、2009年IEEE Transactions on Multimedia Prize论文奖、2012年ACM多媒体最佳论文奖和2021年IEEE INFOCOM最佳海报奖、2023年ACM电子能源最佳论文奖以及2024年Gradient AI研究奖。联合发明的编码原语已被纳入微软Windows和Azure云存储，服务于数亿用户。他最近的研究兴趣包括在线优化和算法、电力系统运行中的机器学习、智能交通、分布式优化和延迟关键网络，以及在算法/系统设计中利用数据驱动预测的优势。他是ACM杰出科学家和IEEE Fellow。
报告摘要
Optimization problems subject to hard constraints are common in time-critical applications such as autonomous driving and high-frequency trading. However, existing iterative solvers often face difficulties in solving these problems in real-time. In this talk, we advocate a machine learning approach -- to employ NN's approximation capability to learn the input-solution mapping of a problem and then pass new input through the NN to obtain a quality solution, orders of magnitude faster than iterative solvers. To date, the approach has achieved promising empirical performance and exciting theoretical development for an essential optimal power flow problem in grid operation. A fundamental issue, however, is to ensure NN solution feasibility with respect to the hard constraints, which is non-trivial due to inherent NN prediction errors. To this end, we present two approaches, predict-and-reconstruct and homeomorphic projection, to ensure NN solution strictly satisfies the equality and inequality constraints, respectively. In particular, homeomorphic projection is a low-complexity scheme to guarantee NN solution feasibility for optimization over any set homeomorphic to a unit ball, covering all compact convex sets and certain classes of nonconvex sets. The idea is to (i) learn a minimum distortion homeomorphic mapping between the constraint set and a unit ball using an invertible NN (INN), and then (ii) perform a simple bisection operation concerning the unit ball so that the INN-mapped final solution is feasible with respect to the constraint set with minor distortion-induced optimality loss. We prove the feasibility guarantee and bound the optimality loss under mild conditions. Simulation results, including those for non-convex AC-OPF problems in power grid operation, show that homeomorphic projection outperforms existing methods in solution feasibility and run-time complexity, while achieving similar optimality loss. We will also discuss open problems and future directions.