6,404 research outputs found
Distributed Learning for Stochastic Generalized Nash Equilibrium Problems
This work examines a stochastic formulation of the generalized Nash
equilibrium problem (GNEP) where agents are subject to randomness in the
environment of unknown statistical distribution. We focus on fully-distributed
online learning by agents and employ penalized individual cost functions to
deal with coupled constraints. Three stochastic gradient strategies are
developed with constant step-sizes. We allow the agents to use heterogeneous
step-sizes and show that the penalty solution is able to approach the Nash
equilibrium in a stable manner within , for small step-size
value and sufficiently large penalty parameters. The operation
of the algorithm is illustrated by considering the network Cournot competition
problem
Sparse Distributed Learning Based on Diffusion Adaptation
This article proposes diffusion LMS strategies for distributed estimation
over adaptive networks that are able to exploit sparsity in the underlying
system model. The approach relies on convex regularization, common in
compressive sensing, to enhance the detection of sparsity via a diffusive
process over the network. The resulting algorithms endow networks with learning
abilities and allow them to learn the sparse structure from the incoming data
in real-time, and also to track variations in the sparsity of the model. We
provide convergence and mean-square performance analysis of the proposed method
and show under what conditions it outperforms the unregularized diffusion
version. We also show how to adaptively select the regularization parameter.
Simulation results illustrate the advantage of the proposed filters for sparse
data recovery.Comment: to appear in IEEE Trans. on Signal Processing, 201
Diffusion Adaptation Strategies for Distributed Estimation over Gaussian Markov Random Fields
The aim of this paper is to propose diffusion strategies for distributed
estimation over adaptive networks, assuming the presence of spatially
correlated measurements distributed according to a Gaussian Markov random field
(GMRF) model. The proposed methods incorporate prior information about the
statistical dependency among observations, while at the same time processing
data in real-time and in a fully decentralized manner. A detailed mean-square
analysis is carried out in order to prove stability and evaluate the
steady-state performance of the proposed strategies. Finally, we also
illustrate how the proposed techniques can be easily extended in order to
incorporate thresholding operators for sparsity recovery applications.
Numerical results show the potential advantages of using such techniques for
distributed learning in adaptive networks deployed over GMRF.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin
note: text overlap with arXiv:1206.309
Distributed Clustering and Learning Over Networks
Distributed processing over networks relies on in-network processing and
cooperation among neighboring agents. Cooperation is beneficial when agents
share a common objective. However, in many applications agents may belong to
different clusters that pursue different objectives. Then, indiscriminate
cooperation will lead to undesired results. In this work, we propose an
adaptive clustering and learning scheme that allows agents to learn which
neighbors they should cooperate with and which other neighbors they should
ignore. In doing so, the resulting algorithm enables the agents to identify
their clusters and to attain improved learning and estimation accuracy over
networks. We carry out a detailed mean-square analysis and assess the error
probabilities of Types I and II, i.e., false alarm and mis-detection, for the
clustering mechanism. Among other results, we establish that these
probabilities decay exponentially with the step-sizes so that the probability
of correct clustering can be made arbitrarily close to one.Comment: 47 pages, 6 figure
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