7,010 research outputs found
Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms with Directed Gossip Communication
We study distributed optimization in networked systems, where nodes cooperate
to find the optimal quantity of common interest, x=x^\star. The objective
function of the corresponding optimization problem is the sum of private (known
only by a node,) convex, nodes' objectives and each node imposes a private
convex constraint on the allowed values of x. We solve this problem for generic
connected network topologies with asymmetric random link failures with a novel
distributed, decentralized algorithm. We refer to this algorithm as AL-G
(augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented
Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast
gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual
function. Dual variables are updated by the standard method of multipliers, at
a slow time scale. To update the primal variables, we propose a novel,
Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses
unidirectional gossip communication, only between immediate neighbors in the
network and is resilient to random link failures. For networks with reliable
communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian
broadcast gossiping) algorithm reduces communication, computation and data
storage cost. We prove convergence for all proposed algorithms and demonstrate
by simulations the effectiveness on two applications: l_1-regularized logistic
regression for classification and cooperative spectrum sensing for cognitive
radio networks.Comment: 28 pages, journal; revise
Adaptation and learning over networks for nonlinear system modeling
In this chapter, we analyze nonlinear filtering problems in distributed
environments, e.g., sensor networks or peer-to-peer protocols. In these
scenarios, the agents in the environment receive measurements in a streaming
fashion, and they are required to estimate a common (nonlinear) model by
alternating local computations and communications with their neighbors. We
focus on the important distinction between single-task problems, where the
underlying model is common to all agents, and multitask problems, where each
agent might converge to a different model due to, e.g., spatial dependencies or
other factors. Currently, most of the literature on distributed learning in the
nonlinear case has focused on the single-task case, which may be a strong
limitation in real-world scenarios. After introducing the problem and reviewing
the existing approaches, we describe a simple kernel-based algorithm tailored
for the multitask case. We evaluate the proposal on a simulated benchmark task,
and we conclude by detailing currently open problems and lines of research.Comment: To be published as a chapter in `Adaptive Learning Methods for
Nonlinear System Modeling', Elsevier Publishing, Eds. D. Comminiello and J.C.
Principe (2018
Multi-hop Diffusion LMS for Energy-constrained Distributed Estimation
We propose a multi-hop diffusion strategy for a sensor network to perform
distributed least mean-squares (LMS) estimation under local and network-wide
energy constraints. At each iteration of the strategy, each node can combine
intermediate parameter estimates from nodes other than its physical neighbors
via a multi-hop relay path. We propose a rule to select combination weights for
the multi-hop neighbors, which can balance between the transient and the
steady-state network mean-square deviations (MSDs). We study two classes of
networks: simple networks with a unique transmission path from one node to
another, and arbitrary networks utilizing diffusion consultations over at most
two hops. We propose a method to optimize each node's information neighborhood
subject to local energy budgets and a network-wide energy budget for each
diffusion iteration. This optimization requires the network topology, and the
noise and data variance profiles of each node, and is performed offline before
the diffusion process. In addition, we develop a fully distributed and adaptive
algorithm that approximately optimizes the information neighborhood of each
node with only local energy budget constraints in the case where diffusion
consultations are performed over at most a predefined number of hops. Numerical
results suggest that our proposed multi-hop diffusion strategy achieves the
same steady-state MSD as the existing one-hop adapt-then-combine diffusion
algorithm but with a lower energy budget.Comment: 14 pages, 12 figures. Submitted for publicatio
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