125 research outputs found
Decentralized Maximum Likelihood Estimation for Sensor Networks Composed of Nonlinearly Coupled Dynamical Systems
In this paper we propose a decentralized sensor network scheme capable to
reach a globally optimum maximum likelihood (ML) estimate through
self-synchronization of nonlinearly coupled dynamical systems. Each node of the
network is composed of a sensor and a first-order dynamical system initialized
with the local measurements. Nearby nodes interact with each other exchanging
their state value and the final estimate is associated to the state derivative
of each dynamical system. We derive the conditions on the coupling mechanism
guaranteeing that, if the network observes one common phenomenon, each node
converges to the globally optimal ML estimate. We prove that the synchronized
state is globally asymptotically stable if the coupling strength exceeds a
given threshold. Acting on a single parameter, the coupling strength, we show
how, in the case of nonlinear coupling, the network behavior can switch from a
global consensus system to a spatial clustering system. Finally, we show the
effect of the network topology on the scalability properties of the network and
we validate our theoretical findings with simulation results.Comment: Journal paper accepted on IEEE Transactions on Signal Processin
Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Asymmetric Channels
In this paper we propose and analyze a distributed algorithm for achieving
globally optimal decisions, either estimation or detection, through a
self-synchronization mechanism among linearly coupled integrators initialized
with local measurements. We model the interaction among the nodes as a directed
graph with weights (possibly) dependent on the radio channels and we pose
special attention to the effect of the propagation delay occurring in the
exchange of data among sensors, as a function of the network geometry. We
derive necessary and sufficient conditions for the proposed system to reach a
consensus on globally optimal decision statistics. One of the major results
proved in this work is that a consensus is reached with exponential convergence
speed for any bounded delay condition if and only if the directed graph is
quasi-strongly connected. We provide a closed form expression for the global
consensus, showing that the effect of delays is, in general, the introduction
of a bias in the final decision. Finally, we exploit our closed form expression
to devise a double-step consensus mechanism able to provide an unbiased
estimate with minimum extra complexity, without the need to know or estimate
the channel parameters.Comment: To be published on IEEE Transactions on Signal Processin
Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Nonreciprocal Channels
In this paper we propose and analyze a distributed algorithm for achieving
globally optimal decisions, either estimation or detection, through a
self-synchronization mechanism among linearly coupled integrators initialized
with local measurements. We model the interaction among the nodes as a directed
graph with weights dependent on the radio interface and we pose special
attention to the effect of the propagation delays occurring in the exchange of
data among sensors, as a function of the network geometry. We derive necessary
and sufficient conditions for the proposed system to reach a consensus on
globally optimal decision statistics. One of the major results proved in this
work is that a consensus is achieved for any bounded delay condition if and
only if the directed graph is quasi-strongly connected. We also provide a
closed form expression for the global consensus, showing that the effect of
delays is, in general, to introduce a bias in the final decision. The closed
form expression is also useful to modify the consensus mechanism in order to
get rid of the bias with minimum extra complexity.Comment: Conference paper. Journal version submitted to IEEE Transactions on
Signal Processing, January 10, 2007. Paper accepted for the publication on
the VIII IEEE Workshop on Signal Processing Advances in Wireless
Communications, (SPAWC 2007), January 22, 200
Distributed Dictionary Learning
The paper studies distributed Dictionary Learning (DL) problems where the
learning task is distributed over a multi-agent network with time-varying
(nonsymmetric) connectivity. This formulation is relevant, for instance, in
big-data scenarios where massive amounts of data are collected/stored in
different spatial locations and it is unfeasible to aggregate and/or process
all the data in a fusion center, due to resource limitations, communication
overhead or privacy considerations. We develop a general distributed
algorithmic framework for the (nonconvex) DL problem and establish its
asymptotic convergence. The new method hinges on Successive Convex
Approximation (SCA) techniques coupled with i) a gradient tracking mechanism
instrumental to locally estimate the missing global information; and ii) a
consensus step, as a mechanism to distribute the computations among the agents.
To the best of our knowledge, this is the first distributed algorithm with
provable convergence for the DL problem and, more in general, bi-convex
optimization problems over (time-varying) directed graphs
Parallel Selective Algorithms for Big Data Optimization
We propose a decomposition framework for the parallel optimization of the sum
of a differentiable (possibly nonconvex) function and a (block) separable
nonsmooth, convex one. The latter term is usually employed to enforce structure
in the solution, typically sparsity. Our framework is very flexible and
includes both fully parallel Jacobi schemes and Gauss- Seidel (i.e.,
sequential) ones, as well as virtually all possibilities "in between" with only
a subset of variables updated at each iteration. Our theoretical convergence
results improve on existing ones, and numerical results on LASSO, logistic
regression, and some nonconvex quadratic problems show that the new method
consistently outperforms existing algorithms.Comment: This work is an extended version of the conference paper that has
been presented at IEEE ICASSP'14. The first and the second author contributed
equally to the paper. This revised version contains new numerical results on
non convex quadratic problem
Distributed Nonconvex Multiagent Optimization Over Time-Varying Networks
We study nonconvex distributed optimization in multiagent networks where the
communications between nodes is modeled as a time-varying sequence of arbitrary
digraphs. We introduce a novel broadcast-based distributed algorithmic
framework for the (constrained) minimization of the sum of a smooth (possibly
nonconvex and nonseparable) function, i.e., the agents' sum-utility, plus a
convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually
employed to enforce some structure in the solution, typically sparsity. The
proposed method hinges on Successive Convex Approximation (SCA) techniques
coupled with i) a tracking mechanism instrumental to locally estimate the
gradients of agents' cost functions; and ii) a novel broadcast protocol to
disseminate information and distribute the computation among the agents.
Asymptotic convergence to stationary solutions is established. A key feature of
the proposed algorithm is that it neither requires the double-stochasticity of
the consensus matrices (but only column stochasticity) nor the knowledge of the
graph sequence to implement. To the best of our knowledge, the proposed
framework is the first broadcast-based distributed algorithm for convex and
nonconvex constrained optimization over arbitrary, time-varying digraphs.
Numerical results show that our algorithm outperforms current schemes on both
convex and nonconvex problems.Comment: Copyright 2001 SS&C. Published in the Proceedings of the 50th annual
Asilomar conference on signals, systems, and computers, Nov. 6-9, 2016, CA,
US
- …