Title: Decentralized consensus optimization on networks with delayed and stochastic gradients
时间: 2019年5月16日星期四 15：00
Abstract: Decentralized consensus optimization has extensive applications in many emerging big data, machine learning, and sensor network problems. In decentralized computing, nodes in a network privately hold parts of the objective function and need to collaboratively solve for the consensual optimal solution of the total objective, while they can only communicate with their immediate neighbors during updates. In real-world networks, it is often difficult and sometimes impossible to synchronize these nodes, and as a result they have to use stale and stochastic gradient information which may steer their iterates away from the optimal solution. In this talk, we focus on a decentralized consensus algorithm by taking the delays of gradients into consideration. We show that, as long as the random delays are bounded in expectation and a proper diminishing step size policy is employed, the iterates generated by this algorithm still converge to a consensual optimal solution. Convergence rates of both objective and consensus are derived. Numerical results on some synthetic optimization problems and on real seismic tomography will also be presented.
Dr. Xiaojing Ye is currently a tenure-track assistant professor at the Department of Mathematics and Statistics in Georgia State University, Atlanta, USA. Prior to joining Georgia State University in 2013, Dr. Ye was a visiting assistant professor at the School of Mathematics in Georgia Institute of Technology, USA. Dr. Ye received his doctoral degree in mathematics from the University of Florida, USA in 2011, the master’s degree in statistics from the University of Florida in 2009, and the bachelor’s degree in mathematics from Peking University in 2006. Dr. Ye’s research focuses on applied and computational mathematics, particularly PDE-based image analysis, numerical optimization, analysis and computations of stochastic differential equations, machine learning.