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arXiv · 1211.6013

Online Stochastic Optimization with Multiple Objectives

Mehrdad Mahdavi·Tianbao Yang·Rong Jin
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Abstract

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.

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Mehrdad Mahdavi, Tianbao Yang, Rong Jin. 2012-11-26. Online Stochastic Optimization with Multiple Objectives. https://arxiv.org/abs/1211.6013

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