4,491 research outputs found
Fast Multidimensional Asymptotic and Approximate Consensus
We study the problems of asymptotic and approximate consensus in which agents have to get their values arbitrarily close to each others\u27 inside the convex hull of initial values, either without or with an explicit decision by the agents. In particular, we are concerned with the case of multidimensional data, i.e., the agents\u27 values are d-dimensional vectors. We introduce two new algorithms for dynamic networks, subsuming classical failure models like asynchronous message passing systems with Byzantine agents. The algorithms are the first to have a contraction rate and time complexity independent of the dimension d. In particular, we improve the time complexity from the previously fastest approximate consensus algorithm in asynchronous message passing systems with Byzantine faults by Mendes et al. [Distrib. Comput. 28] from Omega(d log (d Delta)/epsilon) to O(log Delta/epsilon), where Delta is the initial and epsilon is the terminal diameter of the set of vectors of correct agents
Tight Bounds for Asymptotic and Approximate Consensus
We study the performance of asymptotic and approximate consensus algorithms
under harsh environmental conditions. The asymptotic consensus problem requires
a set of agents to repeatedly set their outputs such that the outputs converge
to a common value within the convex hull of initial values. This problem, and
the related approximate consensus problem, are fundamental building blocks in
distributed systems where exact consensus among agents is not required or
possible, e.g., man-made distributed control systems, and have applications in
the analysis of natural distributed systems, such as flocking and opinion
dynamics. We prove tight lower bounds on the contraction rates of asymptotic
consensus algorithms in dynamic networks, from which we deduce bounds on the
time complexity of approximate consensus algorithms. In particular, the
obtained bounds show optimality of asymptotic and approximate consensus
algorithms presented in [Charron-Bost et al., ICALP'16] for certain dynamic
networks, including the weakest dynamic network model in which asymptotic and
approximate consensus are solvable. As a corollary we also obtain
asymptotically tight bounds for asymptotic consensus in the classical
asynchronous model with crashes.
Central to our lower bound proofs is an extended notion of valency, the set
of reachable limits of an asymptotic consensus algorithm starting from a given
configuration. We further relate topological properties of valencies to the
solvability of exact consensus, shedding some light on the relation of these
three fundamental problems in dynamic networks
Gaussian Belief with dynamic data and in dynamic network
In this paper we analyse Belief Propagation over a Gaussian model in a
dynamic environment. Recently, this has been proposed as a method to average
local measurement values by a distributed protocol ("Consensus Propagation",
Moallemi & Van Roy, 2006), where the average is available for read-out at every
single node. In the case that the underlying network is constant but the values
to be averaged fluctuate ("dynamic data"), convergence and accuracy are
determined by the spectral properties of an associated Ruelle-Perron-Frobenius
operator. For Gaussian models on Erdos-Renyi graphs, numerical computation
points to a spectral gap remaining in the large-size limit, implying
exceptionally good scalability. In a model where the underlying network also
fluctuates ("dynamic network"), averaging is more effective than in the dynamic
data case. Altogether, this implies very good performance of these methods in
very large systems, and opens a new field of statistical physics of large (and
dynamic) information systems.Comment: 5 pages, 7 figure
-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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