2012/11/26 by Mehrdad Mahdavi, Mahdavi, Mehrdad, Tianbao Yang +3
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #cs.LG #math.OC
paper · pdf · doi:10.48550/arxiv.1211.6013
NIPS Workshop on Optimization for Machine Learning
arxiv created 2013/07/14 · arxiv updated 2013/07/16
In this paper we propose a general framework to characterize and solve the stochastic optimization problems with multiple objectives underlying many real world learning applications. We first propose a projection based algorithm which attains an O(T-1/3) convergence rate. Then, by leveraging on the theory of Lagrangian in constrained optimization, we devise a novel primal-dual stochastic approximation algorithm which attains the optimal convergence rate of O(T-1/2) for general Lipschitz continuous objectives.