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This paper studies linear stochastic approximation (SA) algorithms and their application to multiagent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA algorithms to a deterministic or random final vector. We also characterize the system convergence rate, when the system is convergent. Moreover, differing from non-negative gain functions in traditional SA algorithms, this paper considers also the case when the gain functions are allowed to take arbitrary real numbers. Using our general treatment, we provide necessary and sufficient conditions to reach consensus and group consensus for first-order discrete-time multiagent system over random signed networks and with state-dependent noise. Finally, we extend our results to the setting of multidimensional linear SA algorithms and characterize the behavior of the multidimensional Friedkin–Johnsen model over random interaction networks. [ABSTRACT FROM AUTHOR]

This paper discusses consensus problems for multiagent networks under directed communication graphs. The motions of agents are described by impulsive differential equations, and thus, consensus algorithms can be designed in terms of impulsive systems. Different from the standard consensus algorithms which rely on continuous-time or discrete-time models, the proposed algorithms based on impulsive systems take advantages of instantaneous information. It is shown that the proposed algorithms have a faster convergence speed than the standard consensus algorithms. Moreover, conditions under which all agents reach consensus with the desired performance are presented for the multiagent networks with external disturbances. Simulation results demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this article, distributed algorithms are proposed for training a group of neural networks with private data sets. Stochastic gradients are utilized in order to eliminate the requirement for true gradients. To obtain a universal model of the distributed neural networks trained using local data sets only, consensus tools are introduced to derive the model toward the optimum. Most of the existing works employ diminishing learning rates, which are often slow and impracticable for online learning, while constant learning rates are studied in some recent works, but the principle for choosing the rates is not well established. In this article, constant learning rates are adopted to empower the proposed algorithms with tracking ability. Under mild conditions, the convergence of the proposed algorithms is established by exploring the error dynamics of the connected agents, which provides an upper bound for selecting the constant learning rates. Performances of the proposed algorithms are analyzed with and without gradient noises, in the sense of mean square error (MSE). It is proved that the MSE converges with bounded errors determined by the gradient noises, and the MSE converges to zero if the gradient noises are absent. Simulation results are provided to validate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

An accelerated algorithm is proposed in this article for solving the linear quadratic optimal consensus problem of multiagent systems. To optimize the linear quadratic response and the final consensus state simultaneously, a nonseparable multiobjective optimization problem with coupled constraints on decision variables is formulated. The main difficulty in solving the optimization problem lies in the nonlinear coupling of objectives, which is overcome by separating the problem into two independent and solvable single-objective optimization subproblems using the alternating direction method of multipliers. The proximal gradient decent scheme is then introduced to approximate the precise optimal solutions of the subproblems so as to improve the computing efficiency. Convergence analysis is performed to estimate the convergence rate and derive the convergence condition, which is independent of any global information of the system and, therefore, is fully distributed. Furthermore, the solution of each subproblem is obtained in a distributed form, allowing the multiagent system to achieve optimal consensus. Numerical examples show the effectiveness of the accelerated algorithm. [ABSTRACT FROM AUTHOR]