Distributed stochastic optimization under imperfect information

Aswin Kannan, Angelia Nedic, Vinayak V. Shanbhag

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We consider a stochastic convex optimization problem that requires minimizing a sum of misspecified agent-specific expectation-valued convex functions over the intersection of a collection of agent-specific convex sets. This misspecification is manifested in a parametric sense and may be resolved through solving a distinct stochastic convex learning problem. Our interest lies in the development of distributed algorithms in which every agent makes decisions based on the knowledge of its objective and feasibility set while learning the decisions of other agents by communicating with its local neighbors over a time-varying connectivity graph. While a significant body of research currently exists in the context of such problems, we believe that the misspecified generalization of this problem is both important and has seen little study, if at all. Accordingly, our focus lies on the simultaneous resolution of both problems through a joint set of schemes that combine three distinct steps: (i) An alignment step in which every agent updates its current belief by averaging over the beliefs of its neighbors; (ii) A projected (stochastic) gradient step in which every agent further updates this averaged estimate; and (iii) A learning step in which agents update their belief of the misspecified parameter by utilizing a stochastic gradient step. Under an assumption of mere convexity on agent objectives and strong convexity of the learning problems, we show that the sequences generated by this collection of update rules converge almost surely to the solution of the correctly specified stochastic convex optimization problem and the stochastic learning problem, respectively.

Original languageEnglish (US)
Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages400-405
Number of pages6
ISBN (Electronic)9781479978861
DOIs
StatePublished - Feb 8 2015
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: Dec 15 2015Dec 18 2015

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)0743-1546

Other

Other54th IEEE Conference on Decision and Control, CDC 2015
CountryJapan
CityOsaka
Period12/15/1512/18/15

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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  • Cite this

    Kannan, A., Nedic, A., & Shanbhag, V. V. (2015). Distributed stochastic optimization under imperfect information. In 54rd IEEE Conference on Decision and Control,CDC 2015 (pp. 400-405). [7402233] (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7402233