题目：Variance Reduced Median-of-Means Estimator for Byzantine-Robust Distributed Inference

主讲人：上海交通大学 刘卫东教授

主持人：西南财经大学统计学院 常晋源教授

时间：2020年4月21日（星期二）14:00-15:20

直播平台及会议ID：腾讯会议，426 910 840

报告摘要：

This paper develops an efficient distributed inference algorithm, which is robust against a moderate fraction of Byzantine nodes, namely arbitrary and possibly adversarial machines in a distributed learning system. In robust statistics, the median-of-means (MOM) has been a popular approach to hedge against Byzantine failures due to its ease of implementation and computational efficiency. However, the MOM estimator has the shortcoming in terms of statistical efficiency. The first main contribution of the paper is to propose a variance reduced median-of-means (VRMOM) estimator, which improves the statistical efficiency over the vanilla MOM estimator and is computationally as efficient as the MOM. Based on the proposed VRMOM estimator, we develop a general distributed inference algorithm that is robust against Byzantine failures. Theoretically, our distributed algorithm achieves a fast convergence rate with only a constant number of rounds of communications. We also provide the asymptotic normality result for the purpose of statistical inference. To the best of our knowledge, this is the first normality result in the setting of Byzantine-robust distributed learning. The simulation results are also presented to illustrate the effectiveness of our method.

主讲人简介：

刘卫东，上海交通大学数学科学学院，特聘教授，博士生导师。2003年本科毕业于浙江大学数学系，于2008年取得浙江大学博士学位，2008-2011年在香港科技大学和美国宾夕法尼亚大学沃顿商学院担任博士后研究员；2010年取得全国百篇优秀博士论文奖；新世界数学奖；2011年至今任上海市东方学者高校特聘教授；2013年取得国家优秀青年科学基金；2014年取得上海市曙光学者称号；2016年取得国家万人计划青年拔尖人才；2018年获国家杰出青年科学基金。在《Annals of Statistics》、《Journal of the American Statistical Association》、《Annals of Probability》等顶级期刊发表学术论文40余篇，主要研究方向为统计学理论和机器学习等。