Regularized iterative stochastic approximation methods for stochastic variational inequality problems

Jayash Koshal, Angelia Nedich, Uday V. Shanbhag

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

We consider a Cartesian stochastic variational inequality problem with a monotone map. Monotone stochastic variational inequalities arise naturally, for instance, as the equilibrium conditions of monotone stochastic Nash games over continuous strategy sets or multiuser stochastic optimization problems. We introduce two classes of stochastic approximation methods, each of which requires exactly one projection step at every iteration, and provide convergence analysis for each of them. Of these, the first is a stochastic iterative Tikhonov regularization method which necessitates the update of the regularization parameter after every iteration. The second method is a stochastic iterative proximal-point method, where the centering term is updated after every iteration. The Cartesian structure lends itself to constructing distributed multi-agent extensions and conditions are provided for recovering global convergence in limited coordination variants where agents are allowed to choose their steplength sequences, regularization and centering parameters independently, while meeting a suitable coordination requirement. We apply the proposed class of techniques and their limited coordination versions to a stochastic networked rate allocation problem.

Original languageEnglish (US)
Article number6286992
Pages (from-to)594-609
Number of pages16
JournalIEEE Transactions on Automatic Control
Volume58
Issue number3
DOIs
StatePublished - 2013
Externally publishedYes

Keywords

  • Distributed algorithms
  • proximal-point methods
  • stochastic approximation
  • stochastic optimization
  • Tikhonov regularization
  • variational inequality

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications

Cite this

Regularized iterative stochastic approximation methods for stochastic variational inequality problems. / Koshal, Jayash; Nedich, Angelia; Shanbhag, Uday V.

In: IEEE Transactions on Automatic Control, Vol. 58, No. 3, 6286992, 2013, p. 594-609.

Research output: Contribution to journalArticle

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