Distributed Diffusion-based LMS for Node-Specific Parameter Estimation over Adaptive Networks

A distributed adaptive algorithm is proposed to solve a node-specific parameter estimation problem where nodes are interested in estimating parameters of local interest and parameters of global interest to the whole network. To address the different node-specific parameter estimation problems, this novel algorithm relies on a diffusion-based implementation of different Least Mean Squares (LMS) algorithms, each associated with the estimation of a specific set of local or global parameters. Although all the different LMS algorithms are coupled, the diffusion-based implementation of each LMS algorithm is exclusively undertaken by the nodes of the network interested in a specific set of local or global parameters. To illustrate the effectiveness of the proposed technique we provide simulation results in the context of cooperative spectrum sensing in cognitive radio networks.Comment: 5 pages, 2 figures, Published in Proc. IEEE ICASSP, Florence, Italy, May 201

On the Learning Behavior of Adaptive Networks - Part I: Transient Analysis

This work carries out a detailed transient analysis of the learning behavior of multi-agent networks, and reveals interesting results about the learning abilities of distributed strategies. Among other results, the analysis reveals how combination policies influence the learning process of networked agents, and how these policies can steer the convergence point towards any of many possible Pareto optimal solutions. The results also establish that the learning process of an adaptive network undergoes three (rather than two) well-defined stages of evolution with distinctive convergence rates during the first two stages, while attaining a finite mean-square-error (MSE) level in the last stage. The analysis reveals what aspects of the network topology influence performance directly and suggests design procedures that can optimize performance by adjusting the relevant topology parameters. Interestingly, it is further shown that, in the adaptation regime, each agent in a sparsely connected network is able to achieve the same performance level as that of a centralized stochastic-gradient strategy even for left-stochastic combination strategies. These results lead to a deeper understanding and useful insights on the convergence behavior of coupled distributed learners. The results also lead to effective design mechanisms to help diffuse information more thoroughly over networks.Comment: to appear in IEEE Transactions on Information Theory, 201

Half a billion simulations: evolutionary algorithms and distributed computing for calibrating the SimpopLocal geographical model

Multi-agent geographical models integrate very large numbers of spatial interactions. In order to validate those models large amount of computing is necessary for their simulation and calibration. Here a new data processing chain including an automated calibration procedure is experimented on a computational grid using evolutionary algorithms. This is applied for the first time to a geographical model designed to simulate the evolution of an early urban settlement system. The method enables us to reduce the computing time and provides robust results. Using this method, we identify several parameter settings that minimise three objective functions that quantify how closely the model results match a reference pattern. As the values of each parameter in different settings are very close, this estimation considerably reduces the initial possible domain of variation of the parameters. The model is thus a useful tool for further multiple applications on empirical historical situations

Distributed Pareto Optimization via Diffusion Strategies

We consider solving multi-objective optimization problems in a distributed manner by a network of cooperating and learning agents. The problem is equivalent to optimizing a global cost that is the sum of individual components. The optimizers of the individual components do not necessarily coincide and the network therefore needs to seek Pareto optimal solutions. We develop a distributed solution that relies on a general class of adaptive diffusion strategies. We show how the diffusion process can be represented as the cascade composition of three operators: two combination operators and a gradient descent operator. Using the Banach fixed-point theorem, we establish the existence of a unique fixed point for the composite cascade. We then study how close each agent converges towards this fixed point, and also examine how close the Pareto solution is to the fixed point. We perform a detailed mean-square error analysis and establish that all agents are able to converge to the same Pareto optimal solution within a sufficiently small mean-square-error (MSE) bound even for constant step-sizes. We illustrate one application of the theory to collaborative decision making in finance by a network of agents.Comment: 35 pages, 9 figures, submitted for publicatio

Distributed Diffusion-Based LMS for Node-Specific Adaptive Parameter Estimation

A distributed adaptive algorithm is proposed to solve a node-specific parameter estimation problem where nodes are interested in estimating parameters of local interest, parameters of common interest to a subset of nodes and parameters of global interest to the whole network. To address the different node-specific parameter estimation problems, this novel algorithm relies on a diffusion-based implementation of different Least Mean Squares (LMS) algorithms, each associated with the estimation of a specific set of local, common or global parameters. Coupled with the estimation of the different sets of parameters, the implementation of each LMS algorithm is only undertaken by the nodes of the network interested in a specific set of local, common or global parameters. The study of convergence in the mean sense reveals that the proposed algorithm is asymptotically unbiased. Moreover, a spatial-temporal energy conservation relation is provided to evaluate the steady-state performance at each node in the mean-square sense. Finally, the theoretical results and the effectiveness of the proposed technique are validated through computer simulations in the context of cooperative spectrum sensing in Cognitive Radio networks.Comment: 13 pages, 6 figure

Diffusion Adaptation Strategies for Distributed Optimization and Learning over Networks

We propose an adaptive diffusion mechanism to optimize a global cost function in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components. Diffusion adaptation allows the nodes to cooperate and diffuse information in real-time; it also helps alleviate the effects of stochastic gradient noise and measurement noise through a continuous learning process. We analyze the mean-square-error performance of the algorithm in some detail, including its transient and steady-state behavior. We also apply the diffusion algorithm to two problems: distributed estimation with sparse parameters and distributed localization. Compared to well-studied incremental methods, diffusion methods do not require the use of a cyclic path over the nodes and are robust to node and link failure. Diffusion methods also endow networks with adaptation abilities that enable the individual nodes to continue learning even when the cost function changes with time. Examples involving such dynamic cost functions with moving targets are common in the context of biological networks.Comment: 34 pages, 6 figures, to appear in IEEE Transactions on Signal Processing, 201

Ecosystem-Oriented Distributed Evolutionary Computing

We create a novel optimisation technique inspired by natural ecosystems, where the optimisation works at two levels: a first optimisation, migration of genes which are distributed in a peer-to-peer network, operating continuously in time; this process feeds a second optimisation based on evolutionary computing that operates locally on single peers and is aimed at finding solutions to satisfy locally relevant constraints. We consider from the domain of computer science distributed evolutionary computing, with the relevant theory from the domain of theoretical biology, including the fields of evolutionary and ecological theory, the topological structure of ecosystems, and evolutionary processes within distributed environments. We then define ecosystem- oriented distributed evolutionary computing, imbibed with the properties of self-organisation, scalability and sustainability from natural ecosystems, including a novel form of distributed evolu- tionary computing. Finally, we conclude with a discussion of the apparent compromises resulting from the hybrid model created, such as the network topology.Comment: 8 pages, 5 figures. arXiv admin note: text overlap with arXiv:1112.0204, arXiv:0712.4159, arXiv:0712.4153, arXiv:0712.4102, arXiv:0910.067