11,123 research outputs found
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
A Coordinate Descent Primal-Dual Algorithm and Application to Distributed Asynchronous Optimization
Based on the idea of randomized coordinate descent of -averaged
operators, a randomized primal-dual optimization algorithm is introduced, where
a random subset of coordinates is updated at each iteration. The algorithm
builds upon a variant of a recent (deterministic) algorithm proposed by V\~u
and Condat that includes the well known ADMM as a particular case. The obtained
algorithm is used to solve asynchronously a distributed optimization problem. A
network of agents, each having a separate cost function containing a
differentiable term, seek to find a consensus on the minimum of the aggregate
objective. The method yields an algorithm where at each iteration, a random
subset of agents wake up, update their local estimates, exchange some data with
their neighbors, and go idle. Numerical results demonstrate the attractive
performance of the method. The general approach can be naturally adapted to
other situations where coordinate descent convex optimization algorithms are
used with a random choice of the coordinates.Comment: 10 page
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
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