Accelerated Multi-Agent Optimization Method over Stochastic Networks

We propose a distributed method to solve a multi-agent optimization problem with strongly convex cost function and equality coupling constraints. The method is based on Nesterov's accelerated gradient approach and works over stochastically time-varying communication networks. We consider the standard assumptions of Nesterov's method and show that the sequence of the expected dual values converge toward the optimal value with the rate of $\mathcal{O}(1/k^2)$. Furthermore, we provide a simulation study of solving an optimal power flow problem with a well-known benchmark case.Comment: to appear at the 59th Conference on Decision and Contro

Asynchronous Distributed Optimization over Lossy Networks via Relaxed ADMM: Stability and Linear Convergence

In this work we focus on the problem of minimizing the sum of convex cost functions in a distributed fashion over a peer-to-peer network. In particular, we are interested in the case in which communications between nodes are prone to failures and the agents are not synchronized among themselves. We address the problem proposing a modified version of the relaxed ADMM, which corresponds to the Peaceman-Rachford splitting method applied to the dual. By exploiting results from operator theory, we are able to prove the almost sure convergence of the proposed algorithm under general assumptions on the distribution of communication loss and node activation events. By further assuming the cost functions to be strongly convex, we prove the linear convergence of the algorithm in mean to a neighborhood of the optimal solution, and provide an upper bound to the convergence rate. Finally, we present numerical results testing the proposed method in different scenarios.Comment: To appear in IEEE Transactions on Automatic Contro

Distributed Constrained Recursive Nonlinear Least-Squares Estimation: Algorithms and Asymptotics

This paper focuses on the problem of recursive nonlinear least squares parameter estimation in multi-agent networks, in which the individual agents observe sequentially over time an independent and identically distributed (i.i.d.) time-series consisting of a nonlinear function of the true but unknown parameter corrupted by noise. A distributed recursive estimator of the \emph{consensus} + \emph{innovations} type, namely $\mathcal{CIWNLS}$, is proposed, in which the agents update their parameter estimates at each observation sampling epoch in a collaborative way by simultaneously processing the latest locally sensed information~(\emph{innovations}) and the parameter estimates from other agents~(\emph{consensus}) in the local neighborhood conforming to a pre-specified inter-agent communication topology. Under rather weak conditions on the connectivity of the inter-agent communication and a \emph{global observability} criterion, it is shown that at every network agent, the proposed algorithm leads to consistent parameter estimates. Furthermore, under standard smoothness assumptions on the local observation functions, the distributed estimator is shown to yield order-optimal convergence rates, i.e., as far as the order of pathwise convergence is concerned, the local parameter estimates at each agent are as good as the optimal centralized nonlinear least squares estimator which would require access to all the observations across all the agents at all times. In order to benchmark the performance of the proposed distributed $\mathcal{CIWNLS}$ estimator with that of the centralized nonlinear least squares estimator, the asymptotic normality of the estimate sequence is established and the asymptotic covariance of the distributed estimator is evaluated. Finally, simulation results are presented which illustrate and verify the analytical findings.Comment: 28 pages. Initial Submission: Feb. 2016, Revised: July 2016, Accepted: September 2016, To appear in IEEE Transactions on Signal and Information Processing over Networks: Special Issue on Inference and Learning over Network

Asynchronous Distributed Optimization Via Randomized Dual Proximal Gradient

In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one. The second term is typically used to encode constraints or to regularize the solution. We propose a class of distributed optimization algorithms based on proximal gradient methods applied to the dual problem. We show that, by choosing suitable primal variable copies, the dual problem is itself separable when written in terms of conjugate functions, and the dual variables can be stacked into non-overlapping blocks associated to the computing nodes. We first show that a weighted proximal gradient on the dual function leads to a synchronous distributed algorithm with local dual proximal gradient updates at each node. Then, as main paper contribution, we develop asynchronous versions of the algorithm in which the node updates are triggered by local timers without any global iteration counter. The algorithms are shown to be proper randomized block-coordinate proximal gradient updates on the dual function