题目: Optimal Transport and Bilevel Optimization
黄敏辉 （加州大学戴维斯分校 UC Davis）
3月27日：腾讯会议：157 564 733
3月29日：腾讯会议：357 525 911
上课时间：2022年 3月27日：上午09：00-11：00；
2022年 3月29日：上午10：00-12：00；
课程介绍：We study the equitable and optimal transport (EOT) problem, which has many applications such as fair division problems and optimal transport with multiple agents etc. In the discrete distributions case, the EOT problem can be formulated as a linear program (LP). Since this LP is prohibitively large for general LP solvers, Scetbon \etal \cite{scetbon2021equitable} suggests to perturb the problem by adding an entropy regularization. They proposed a projected alternating maximization algorithm (PAM) to solve the dual of the entropy regularized EOT. In this paper, we provide the first convergence analysis of PAM. A novel rounding procedure is proposed to help construct the primal solution for the original EOT problem. We also propose a variant of PAM by incorporating the extrapolation technique that can numerically improve the performance of PAM. Results in this work may shed lights on block coordinate (gradient) descent methods for general optimization problems.
授课人简介：黄敏辉是加州大学戴维斯分校 (UC Davis) 电子与计算机工程系的在读博士生。其本科毕业于中国科学技术大学物理学学院。他的研究兴趣包括非凸优化，博弈论，最优传输，双层优化等。他曾在机器学习顶级会议ICML以及信号处理顶级期刊 IEEE TSP发表论文，并多次担任优化期刊(Neural Computing, Journal of Scientific Compuing)和会议(ICML)审稿人。
