Stochastic ADMM Frameworks for Resolving Structured Stochastic Convex Programs

Event Sponsor: 
Mathmatics and Computer Science Division Seminar
Start Date: 
May 8 2018 - 10:30am
Building/Room: 
Building 240/Room 4301
Location: 
Argonne National Laboratory
Speaker(s): 
Yue Xie
Speaker(s) Title: 
Pennsylvania State University
Host: 
Jeffrey Larson

We consider the program: min{E[f(x,xi)] + E[g(y,xi)] | Ax + By = b}, which finds application in regularized expected risk minimization and distributed regression. To exploit problem structure and allow for distributed computation, we propose a stochastic inexact ADMM (SI-ADMM) where subproblems are solved inexactly via stochastic approximation. A.s. convergence and geometric convergence rate of mean-squared error can be obtained for SI-ADMM.

Meanwhile, the related program min{E[f(x,xi)] + g(y) | Ax + By = b} where g(y) is deterministic but non-smooth is also studied. We propose variable sample-size stochastic ADMM (VSS-ADMM) and its accelerated variant (AVSS-ADMM). It is shown that the gap of convergence rate is closed between these stochastic frameworks and their deterministic counterparts. Furthermore, VSS-ADMM may recover the canonical oracle complexity.

Preliminary numerical experiments demonstrate some favorable properties of SI-ADMM and we observe that AVSS-ADMM is comparable to the state-of-art algorithm in addressing graph-guided fused Lasso.

Miscellaneous Information: 

This seminar will be streamed, see details at https://anlpress.cels.anl.gov/mcs-streaming-seminars.

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