数学科学学院学术报告[2024]120号

(高水平大学建设系列报告1000号)

报告题目: An Efficient Halpern Accelerating Algorithm for Optimal Transport Problems

报告人：Yancheng Yuan 助理教授（香港理工大学）

报告时间：2024年11月22日（周五）上午10:30-11:30

讲座地点：深圳大学粤海校区校友广场308

报告内容：This talk introduces an efficient HOT algorithm for solving the optimal transport (OT) problems with finite supports. We particularly focus on an efficient implementation of the HOT algorithm for the case where the supports are in $\mathbb{R}^2$ with ground distances calculated by $L_2^2$-norm. Specifically, we design a Halpern accelerating algorithm to solve the equivalent reduced model of the discrete OT problem. Moreover, we derive a novel procedure to solve the involved linear systems in the HOT algorithm in linear time complexity. Consequently, we can obtain an $\varepsilon$-approximate solution to the optimal transport problem with $M$ supports in $O(M^{1.5}/\varepsilon)$ flops, which significantly improves the best-known computational complexity. We further propose an efficient procedure to recover an optimal transport plan for the original OT problem based on a solution to the reduced model, thereby overcoming the limitations of the reduced OT model in applications that require the transport map. We implement the HOT algorithm in PyTorch and extensive numerical results show the superior performance of the HOT algorithm compared to existing state-of-the-art algorithms for solving the OT problems.

报告人简历： Yancheng Yuan is an Assistant Professor at the Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University. He also serves as an Assistant Director at Research Center for Intelligent Operations Research. His research focuses on continuous optimization, the mathematical foundation of data science, and data-driven applications. His research has been published in leading academic journals and conferences, including Journal of Machine Learning Research, SIAM Journal on Optimization, IEEE Transactions on Neural Networks and Learning Systems, NeurIPS, ICML, WWW, SIGIR, ACL. His papers have been featured in Best Paper Award Finalist of ACM WWW 2021 and ACM SIGIR 2024.

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邀请人：吴育洽

                                              数学科学学院

                                        2024年11月18日