ﻻ يوجد ملخص باللغة العربية
We study a process of emph{averaging} in a distributed system with emph{noisy communication}. Each of the agents in the system starts with some value and the goal of each agent is to compute the average of all the initial values. In each round, one pair of agents is drawn uniformly at random from the whole population, communicates with each other and each of these two agents updates their local value based on their own value and the received message. The communication is noisy and whenever an agent sends any value $v$, the receiving agent receives $v+N$, where $N$ is a zero-mean Gaussian random variable. The two quality measures of interest are (i) the total sum of squares $TSS(t)$, which measures the sum of square distances from the average load to the emph{initial average} and (ii) $bar{phi}(t)$, measures the sum of square distances from the average load to the emph{running average} (average at time $t$). It is known that the simple averaging protocol---in which an agent sends its current value and sets its new value to the average of the received value and its current value---converges eventually to a state where $bar{phi}(t)$ is small. It has been observed that $TSS(t)$, due to the noise, eventually diverges and previous research---mostly in control theory---has focused on showing eventual convergence w.r.t. the running average. We obtain the first probabilistic bounds on the convergence time of $bar{phi}(t)$ and precise bounds on the drift of $TSS(t)$ that show that albeit $TSS(t)$ eventually diverges, for a wide and interesting range of parameters, $TSS(t)$ stays small for a number of rounds that is polynomial in the number of agents. Our results extend to the synchronous setting and settings where the agents are restricted to discrete values and perform rounding.
Improving transaction throughput is an important challenge for Bitcoin. However, shortening the block generation interval or increasing the block size to improve throughput makes it sharing blocks within the network slower and increases the number of
We study first-order optimization algorithms for computing the barycenter of Gaussian distributions with respect to the optimal transport metric. Although the objective is geodesically non-convex, Riemannian GD empirically converges rapidly, in fact
We study the stochastic bilinear minimax optimization problem, presenting an analysis of the Stochastic ExtraGradient (SEG) method with constant step size, and presenting variations of the method that yield favorable convergence. We first note that t
In population protocols, the underlying distributed network consists of $n$ nodes (or agents), denoted by $V$, and a scheduler that continuously selects uniformly random pairs of nodes to interact. When two nodes interact, their states are updated by
We study the convergence problem in fully asynchronous, uni-dimensional robot networks that are prone to Byzantine (i.e. malicious) failures. In these settings, oblivious anonymous robots with arbitrary initial positions are required to eventually co