题    目:  Robust Learning: From Supervised and Unsupervised to Distributed Optimization

报告人:  张慧铭  副教授

单    位: 北京航天航空大学

时    间:  2025年10月17日13:00

地    点:  九章学堂南楼C302

摘   要: In supervised learning, we study a large family of robust statistical regressions by the proposed log-truncated M-estimator under the condition that the data have (1+ε)-th moment. We obtain the excess risk bound and the consistency of various convex regressions [such as robust quantile regression and robust GLMs] as well as non-convex regressions including robust deep neural network regressions. In unsupervised learning, we develop a robust and deep neural network (DNN) method to estimate the learning distribution based on the adversarial nets and median-of-mean (MoM) approach, and it is called the MoM-GAN method. Theoretically, we obtain a non-asymptotic error bound for the DNN-based Wasserstein-1 MoM-GANs estimator measured by integral probability metrics with the Holder function class. In distributed optimization, we consider a scenario where there is no centralized server and the agents can only exchange information with neighbors within a communication graph. A distributed method combining gradient clipping and distributed stochastic gradient projection is proposed. It is proven that when the gradient descent step size and the gradient clipping step-size meet certain conditions, the state of each agent converges to an optimal solution of the distributed optimization problem with probability 1.

简   介: 张慧铭是北航人工智能研究院的副教授(准聘)、硕士生导师。曾在澳门大学担任濠江学者博士后研究员(2020-2022)；曾就读于北京大学(2016-2020)获得统计学博士学位。研究方向：机器学习与AI理论(泛化误差、非渐近方法与调参理论)、稳健估计、高维概率统计、函数型数据、子抽样估计、莱维过程等。发表SCI论文28篇(包括AI与自动化领域顶刊JMLR, IEEE-TAC；统计顶刊JASA, Biometrika、精算顶刊IME；统计、数学与物理主流期刊Statistica Sinica、Journal of Multivariate Analysis、Communications in Mathematics and Statistics、Journal of Complexity、Physica Scripta等。担任过美国《数学评论》评论员，担任过概率统计、AI与机器学习领域顶刊（AOS,AOAP,JASA,JMLR,IEEE-TSP）的审稿人。