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Stochastic Convex Optimization with Multiple Objectives
Mehrdad Mahdavi · Tianbao Yang · Rong Jin

Thu Dec 05 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor #None
In this paper, we are interested in the development of efficient algorithms for convex optimization problems in the simultaneous presence of multiple objectives and stochasticity in the first-order information. We cast the stochastic multiple objective optimization problem into a constrained optimization problem by choosing one function as the objective and try to bound other objectives by appropriate thresholds. We first examine a two stages exploration-exploitation based algorithm which first approximates the stochastic objectives by sampling and then solves a constrained stochastic optimization problem by projected gradient method. This method attains a suboptimal convergence rate even under strong assumption on the objectives. Our second approach is an efficient primal-dual stochastic algorithm. It leverages on the theory of Lagrangian method in constrained optimization and attains the optimal convergence rate of $[O(1/ \sqrt{T})]$ in high probability for general Lipschitz continuous objectives.

Author Information

Mehrdad Mahdavi (Michigan State University (MSU))
Tianbao Yang (NEC Labs America)
Rong Jin (Michigan State University (MSU))

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