Fast Discrete Consensus Based on Gossip for Makespan Minimization in Networked Systems

In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip-like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O(n) in both theoretical and empirical comparisons

On Endogenous Random Consensus and Averaging Dynamics

Motivated by various random variations of Hegselmann-Krause model for opinion dynamics and gossip algorithm in an endogenously changing environment, we propose a general framework for the study of endogenously varying random averaging dynamics, i.e.\ an averaging dynamics whose evolution suffers from history dependent sources of randomness. We show that under general assumptions on the averaging dynamics, such dynamics is convergent almost surely. We also determine the limiting behavior of such dynamics and show such dynamics admit infinitely many time-varying Lyapunov functions

Exponentially Fast Parameter Estimation in Networks Using Distributed Dual Averaging

In this paper we present an optimization-based view of distributed parameter estimation and observational social learning in networks. Agents receive a sequence of random, independent and identically distributed (i.i.d.) signals, each of which individually may not be informative about the underlying true state, but the signals together are globally informative enough to make the true state identifiable. Using an optimization-based characterization of Bayesian learning as proximal stochastic gradient descent (with Kullback-Leibler divergence from a prior as a proximal function), we show how to efficiently use a distributed, online variant of Nesterov's dual averaging method to solve the estimation with purely local information. When the true state is globally identifiable, and the network is connected, we prove that agents eventually learn the true parameter using a randomized gossip scheme. We demonstrate that with high probability the convergence is exponentially fast with a rate dependent on the KL divergence of observations under the true state from observations under the second likeliest state. Furthermore, our work also highlights the possibility of learning under continuous adaptation of network which is a consequence of employing constant, unit stepsize for the algorithm.Comment: 6 pages, To appear in Conference on Decision and Control 201

Asynchrony and Acceleration in Gossip Algorithms

This paper considers the minimization of a sum of smooth and strongly convex functions dispatched over the nodes of a communication network. Previous works on the subject either focus on synchronous algorithms, which can be heavily slowed down by a few slow nodes (the straggler problem), or consider a model of asynchronous operation (Boyd et al., 2006) in which adjacent nodes communicate at the instants of Poisson point processes. We have two main contributions. 1) We propose CACDM (a Continuously Accelerated Coordinate Dual Method), and for the Poisson model of asynchronous operation, we prove CACDM to converge to optimality at an accelerated convergence rate in the sense of Nesterov et Stich, 2017. In contrast, previously proposed asynchronous algorithms have not been proven to achieve such accelerated rate. While CACDM is based on discrete updates, the proof of its convergence crucially depends on a continuous time analysis. 2) We introduce a new communication scheme based on Loss-Networks, that is programmable in a fully asynchronous and decentralized way, unlike the Poisson model of asynchronous operation that does not capture essential aspects of asynchrony such as non-instantaneous communications and computations. Under this Loss-Network model of asynchrony, we establish for CDM (a Coordinate Dual Method) a rate of convergence in terms of the eigengap of the Laplacian of the graph weighted by local effective delays. We believe this eigengap to be a fundamental bottleneck for convergence rates of asynchronous optimization. Finally, we verify empirically that CACDM enjoys an accelerated convergence rate in the Loss-Network model of asynchrony

Distributed estimation over a low-cost sensor network: a review of state-of-the-art

Proliferation of low-cost, lightweight, and power efficient sensors and advances in networked systems enable the employment of multiple sensors. Distributed estimation provides a scalable and fault-robust fusion framework with a peer-to-peer communication architecture. For this reason, there seems to be a real need for a critical review of existing and, more importantly, recent advances in the domain of distributed estimation over a low-cost sensor network. This paper presents a comprehensive review of the state-of-the-art solutions in this research area, exploring their characteristics, advantages, and challenging issues. Additionally, several open problems and future avenues of research are highlighted