Distributed asynchronous constrained stochastic optimization

Kunal Srivastava, Angelia Nedić

Research output: Contribution to journalArticle

201 Scopus citations

Abstract

In this paper, we study two problems which often occur in various applications arising in wireless sensor networks. These are the problem of reaching an agreement on the value of local variables in a network of computational agents and the problem of cooperative solution to a convex optimization problem, where the objective function is the aggregate sum of local convex objective functions. We incorporate the presence of a random communication graph between the agents in our model as a more realistic abstraction of the gossip and broadcast communication protocols of a wireless network. An added ingredient is the presence of local constraint sets to which the local variables of each agent is constrained. Our model allows for the objective functions to be nondifferentiable and accommodates the presence of noisy communication links and subgradient errors. For the consensus problem we provide a diminishing step size algorithm which guarantees asymptotic convergence. The distributed optimization algorithm uses two diminishing step size sequences to account for communication noise and subgradient errors. We establish conditions on these step sizes under which we can achieve the dual task of reaching consensus and convergence to the optimal set with probability one. In both cases we consider the constant step size behavior of the algorithm and establish asymptotic error bounds.

Original languageEnglish (US)
Article number5719290
Pages (from-to)772-790
Number of pages19
JournalIEEE Journal on Selected Topics in Signal Processing
Volume5
Issue number4
DOIs
StatePublished - Aug 1 2011
Externally publishedYes

Keywords

  • Asynchronous model
  • distributed optimization
  • multiagent system
  • noisy communications
  • stochastic optimization

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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