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

Distributed Coupled Multi-Agent Stochastic Optimization

This work develops effective distributed strategies for the solution of constrained multi-agent stochastic optimization problems with coupled parameters across the agents. In this formulation, each agent is influenced by only a subset of the entries of a global parameter vector or model, and is subject to convex constraints that are only known locally. Problems of this type arise in several applications, most notably in disease propagation models, minimum-cost flow problems, distributed control formulations, and distributed power system monitoring. This work focuses on stochastic settings, where a stochastic risk function is associated with each agent and the objective is to seek the minimizer of the aggregate sum of all risks subject to a set of constraints. Agents are not aware of the statistical distribution of the data and, therefore, can only rely on stochastic approximations in their learning strategies. We derive an effective distributed learning strategy that is able to track drifts in the underlying parameter model. A detailed performance and stability analysis is carried out showing that the resulting coupled diffusion strategy converges at a linear rate to an $O(\mu)-$neighborhood of the true penalized optimizer

Controller design for synchronization of an array of delayed neural networks using a controllable

This is the post-print version of the Article - Copyright @ 2011 ElsevierIn this paper, a controllable probabilistic particle swarm optimization (CPPSO) algorithm is introduced based on Bernoulli stochastic variables and a competitive penalized method. The CPPSO algorithm is proposed to solve optimization problems and is then applied to design the memoryless feedback controller, which is used in the synchronization of an array of delayed neural networks (DNNs). The learning strategies occur in a random way governed by Bernoulli stochastic variables. The expectations of Bernoulli stochastic variables are automatically updated by the search environment. The proposed method not only keeps the diversity of the swarm, but also maintains the rapid convergence of the CPPSO algorithm according to the competitive penalized mechanism. In addition, the convergence rate is improved because the inertia weight of each particle is automatically computed according to the feedback of fitness value. The efficiency of the proposed CPPSO algorithm is demonstrated by comparing it with some well-known PSO algorithms on benchmark test functions with and without rotations. In the end, the proposed CPPSO algorithm is used to design the controller for the synchronization of an array of continuous-time delayed neural networks.This research was partially supported by the National Natural Science Foundation of PR China (Grant No 60874113), the Research Fund for the Doctoral Program of Higher Education (Grant No 200802550007), the Key Creative Project of Shanghai Education Community (Grant No 09ZZ66), the Key Foundation Project of Shanghai(Grant No 09JC1400700), the Engineering and Physical Sciences Research Council EPSRC of the U.K. under Grant No. GR/S27658/01, an International Joint Project sponsored by the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Evolutionary robotics and neuroscience

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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

Individual and global adaptation in networks

The structure of complex biological and socio-economic networks affects the selective pressures or behavioural incentives of components in that network, and reflexively, the evolution/behaviour of individuals in those networks changes the structure of such networks over time. Such ‘adaptive networks’ underlie how gene-regulation networks evolve, how ecological networks self-organise, and how networks of strategic agents co-create social organisations. Although such domains are different in the details, they can each be characterised as networks of self-interested agents where agents alter network connections in the direction that increases their individual utility. Recent work shows that such dynamics are equivalent to associative learning, well-understood in the context of neural networks. Associative learning in neural substrates is the result of mandated learning rules (e.g. Hebbian learning), but in networks of autonomous agents ‘associative induction’ occurs as a result of local individual incentives to alter connections. Using results from a number of recent studies, here we review the theoretical principles that can be transferred between disciplines as a result of this isomorphism, and the implications for the organisation of genetic, social and ecological networks