Seminars in Applied Mathematics
Abstract:We consider the problem of finite-sum non-smooth convex optimization with general linear constraints, where the objective function summands are only accessible through their proximal operators. To solve it, we propose an Anderson accelerated Douglas-Rachford splitting (A2DR) algorithm, which combines the scalability of Douglas-Rachford splitting and the fast convergence of Anderson acceleration. We show that A2DR either globally converges or provides a certificate of infeasibility/unboundedness under very mild conditions. We describe an open-source implementation (https://github.com/cvxgrp/a2dr) and demonstrate its outstanding performance on a wide range of examples. The talk is mainly based on the joint work [SIAM Journal on Scientific Computing, 42.6 (2020): A3560–A3583] with Anqi Fu and Stephen Boyd.
题目：Landscape analysis of non-convex optimizations in phase retrieval
时间： 2020-07-17, 10:00-11:00 AM
摘要：Non-convex optimization is a ubiquitous tool in scientific and engineering research. For many important problems, simple non-convex optimization algorithms often provide good solutions efficiently and effectively, despite possible local minima. One way to explain the success of these algorithms is through the global landscape analysis. In this talk, we present some results along with this direction for phase retrieval. The main results are, for several of non-convex optimizations in phase retrieval, a local minimum is also global and all other critical points have a negative directional curvature. The results not only will explain why simple non-convex algorithms usually find a global minimizer for phase retrieval, but also will be useful for developing new efficient algorithms with a theoretical guarantee by applying algorithms that are guaranteed to find a local minimum.
时间： 2020-7-10, 9:00-10:00 AM
会议 ID： 304 179 559
报告人简介： 孟德宇，西安交通大学教授，博导，任西安交大大数据算法与分析技术国家工程实验室机器学习教研室负责人。主要研究兴趣为机器学习、计算机视觉与人工智能的基础研究问题。共发表论文100余篇，其中IEEE Trans.长文36篇， CCF A类会议论文37篇。
题目： The power of depth in deep Q-Learning
时间： 2020-7-10, 10:00-11:00 AM
会议 ID： 304 179 559
Abstract: With the help of massive data and rich computational resource, deep Q-learning has been widely used in operations research and management science and receives great success in numerous applications including, recommender system, games and robotic manipulation. Compared with avid research activities in practice, there lack solid theoretical verifications and interpretability for the success of deep Q-learning, making it be a little bit mystery. The aim of this talk is to discuss the power of depth in deep Q-learning. In the framework of statistical learning theory, we rigorously prove that deep Q-learning outperforms the traditional one by showing its good generalization error bound. Our results shows that the main reason of the success of deep Q-learning is due to the excellent performance of deep neural networks (deep nets) in capturing special properties of rewards such as the spatially sparse and piecewise constant rather than due to their large capacities. In particular, we provide answers to questions why and when deep Q-learning performs better than the traditional one and how about the generalization capability of deep Q-learning.