Distributed Approximate Methods of Multipliers for Convex Composite Optimization
We are happy to present Xuyang Wu, Postdoctoral researcher at Digital Futures. Xuyang Wu received a B.S. degree in Applied Mathematics in Northwestern Polytechnical University, China, in 2015, and the PhD degree in Communication and Information System at the University of Chinese Academy of Sciences, China, in 2020.
Date and time: 18 February 2021, 12 pm – 1 pm
Speaker: Xuyang Wu
Title: Distributed Approximate Methods of Multipliers for Convex Composite Optimization
Meeting ID: 674 3268 2790
Watch the recorded presentation:
Abstract: In many engineering scenarios, a network of agents needs to cooperatively find a common decision that minimizes the sum of local objective functions. A large body of distributed optimization algorithms has been proposed to solve this problem. However, relatively few of them are able to address general convex and nonsmooth local objective functions. This talk considers such a problem on an arbitrarily connected network, where each local objective function is composite, i.e., the sum of a smooth component function and a nonsmooth one.
To address the problem, a general Approximate Method of Multipliers (AMM) is developed, which attempts to approximate the Method of Multipliers by virtue of a surrogate function with numerous options. We then design the surrogate function in various ways, leading to different realizations of AMM that enable distributed implementations over the network. We demonstrate that AMM generalizes over ten state-of-the-art distributed optimization algorithms, and certain specific designs of its surrogate function introduce a variety of brand-new algorithms to the literature. Furthermore, we show that AMM is able to achieve an O(1/k) rate of convergence to optimality, and the convergence rate becomes linear when the problem is locally restricted strongly convex and smooth. Such convergence rates provide stronger convergence results to many prior methods that can be viewed as specializations of AMM. Link to the corresponding paper: A Unifying Approximate Method of Multipliers for Distributed Composite Optimization: https://arxiv.org/abs/2009.12732.
Bio: Xuyang Wu is a Postdoctoral researcher at Digital Futures, co-supervised by Prof. Mikael Johansson at KTH (DCS, EECS) and Prof. Sindri Magnusson at SU (DSV). He received the B.S. degree in Applied Mathematics in Northwestern Polytechnical University, China, in 2015, and the PhD degree in Communication and Information System at the University of Chinese Academy of Sciences, China, in 2020. He works on distributed optimization during his PhD and has 6 journal papers submitted to or published on IEEE Transactions on Automatic Control, SIAM Journal on Control and Optimization, etc, as well as 4 conference papers published on IEEE Conference on Decision and Control. He also wins IEEE ICCA finalist award in 2019. His current research interests include distributed optimization and federated learning. More information can be found on his homepage.