1,317 research outputs found
Extending Gossip Algorithms to Distributed Estimation of U-Statistics
Efficient and robust algorithms for decentralized estimation in networks are
essential to many distributed systems. Whereas distributed estimation of sample
mean statistics has been the subject of a good deal of attention, computation
of -statistics, relying on more expensive averaging over pairs of
observations, is a less investigated area. Yet, such data functionals are
essential to describe global properties of a statistical population, with
important examples including Area Under the Curve, empirical variance, Gini
mean difference and within-cluster point scatter. This paper proposes new
synchronous and asynchronous randomized gossip algorithms which simultaneously
propagate data across the network and maintain local estimates of the
-statistic of interest. We establish convergence rate bounds of and
for the synchronous and asynchronous cases respectively, where
is the number of iterations, with explicit data and network dependent
terms. Beyond favorable comparisons in terms of rate analysis, numerical
experiments provide empirical evidence the proposed algorithms surpasses the
previously introduced approach.Comment: to be presented at NIPS 201
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
Fully decentralized computation of aggregates over data streams
In several emerging applications, data is collected in massive streams at several distributed points of observation. A basic and challenging task is to allow every node to monitor a neighbourhood of interest by issuing continuous aggregate queries on the streams observed in its vicinity. This class of algorithms is fully decentralized and diffusive in nature: collecting all data at few central nodes of the network is unfeasible in networks of low capability devices or in the presence of massive data sets. The main difficulty in designing diffusive algorithms is to cope with duplicate detections. These arise both from the observation of the same event at several nodes of the network and/or receipt of the same aggregated information along multiple paths of diffusion. In this paper, we consider fully decentralized algorithms that answer locally continuous aggregate queries on the number of distinct events, total number of events and the second frequency moment in the scenario outlined above. The proposed algorithms use in the worst case or on realistic distributions sublinear space at every node. We also propose strategies that minimize the communication needed to update the aggregates when new events are observed. We experimentally evaluate for the efficiency and accuracy of our algorithms on realistic simulated scenarios
Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions
In decentralized networks (of sensors, connected objects, etc.), there is an
important need for efficient algorithms to optimize a global cost function, for
instance to learn a global model from the local data collected by each
computing unit. In this paper, we address the problem of decentralized
minimization of pairwise functions of the data points, where these points are
distributed over the nodes of a graph defining the communication topology of
the network. This general problem finds applications in ranking, distance
metric learning and graph inference, among others. We propose new gossip
algorithms based on dual averaging which aims at solving such problems both in
synchronous and asynchronous settings. The proposed framework is flexible
enough to deal with constrained and regularized variants of the optimization
problem. Our theoretical analysis reveals that the proposed algorithms preserve
the convergence rate of centralized dual averaging up to an additive bias term.
We present numerical simulations on Area Under the ROC Curve (AUC) maximization
and metric learning problems which illustrate the practical interest of our
approach
Optimal Statistical Rates for Decentralised Non-Parametric Regression with Linear Speed-Up
We analyse the learning performance of Distributed Gradient Descent in the
context of multi-agent decentralised non-parametric regression with the square
loss function when i.i.d. samples are assigned to agents. We show that if
agents hold sufficiently many samples with respect to the network size, then
Distributed Gradient Descent achieves optimal statistical rates with a number
of iterations that scales, up to a threshold, with the inverse of the spectral
gap of the gossip matrix divided by the number of samples owned by each agent
raised to a problem-dependent power. The presence of the threshold comes from
statistics. It encodes the existence of a "big data" regime where the number of
required iterations does not depend on the network topology. In this regime,
Distributed Gradient Descent achieves optimal statistical rates with the same
order of iterations as gradient descent run with all the samples in the
network. Provided the communication delay is sufficiently small, the
distributed protocol yields a linear speed-up in runtime compared to the
single-machine protocol. This is in contrast to decentralised optimisation
algorithms that do not exploit statistics and only yield a linear speed-up in
graphs where the spectral gap is bounded away from zero. Our results exploit
the statistical concentration of quantities held by agents and shed new light
on the interplay between statistics and communication in decentralised methods.
Bounds are given in the standard non-parametric setting with source/capacity
assumptions
Statistical structures for internet-scale data management
Efficient query processing in traditional database management systems relies on statistics on base data. For centralized systems, there is a rich body of research results on such statistics, from simple aggregates to more elaborate synopses such as sketches and histograms. For Internet-scale distributed systems, on the other hand, statistics management still poses major challenges. With the work in this paper we aim to endow peer-to-peer data management over structured overlays with the power associated with such statistical information, with emphasis on meeting the scalability challenge. To this end, we first contribute efficient, accurate, and decentralized algorithms that can compute key aggregates such as Count, CountDistinct, Sum, and Average. We show how to construct several types of histograms, such as simple Equi-Width, Average-Shifted Equi-Width, and Equi-Depth histograms. We present a full-fledged open-source implementation of these tools for distributed statistical synopses, and report on a comprehensive experimental performance evaluation, evaluating our contributions in terms of efficiency, accuracy, and scalability
-Learning: A Collaborative Distributed Strategy for Multi-Agent Reinforcement Learning Through Consensus + Innovations
The paper considers a class of multi-agent Markov decision processes (MDPs),
in which the network agents respond differently (as manifested by the
instantaneous one-stage random costs) to a global controlled state and the
control actions of a remote controller. The paper investigates a distributed
reinforcement learning setup with no prior information on the global state
transition and local agent cost statistics. Specifically, with the agents'
objective consisting of minimizing a network-averaged infinite horizon
discounted cost, the paper proposes a distributed version of -learning,
-learning, in which the network agents collaborate by means of
local processing and mutual information exchange over a sparse (possibly
stochastic) communication network to achieve the network goal. Under the
assumption that each agent is only aware of its local online cost data and the
inter-agent communication network is \emph{weakly} connected, the proposed
distributed scheme is almost surely (a.s.) shown to yield asymptotically the
desired value function and the optimal stationary control policy at each
network agent. The analytical techniques developed in the paper to address the
mixed time-scale stochastic dynamics of the \emph{consensus + innovations}
form, which arise as a result of the proposed interactive distributed scheme,
are of independent interest.Comment: Submitted to the IEEE Transactions on Signal Processing, 33 page
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