234 research outputs found
Consensus with Ternary Messages
We provide a protocol for real-valued average consensus by networks of agents
which exchange only a single message from the ternary alphabet {-1,0,1} between
neighbors at each step. Our protocol works on time-varying undirected graphs
subject to a connectivity condition, has a worst-case convergence time which is
polynomial in the number of agents and the initial values, and requires no
global knowledge about the graph topologies on the part of each node to
implement except for knowing an upper bound on the degrees of its neighbors
Design and Analysis of Distributed Averaging with Quantized Communication
Consider a network whose nodes have some initial values, and it is desired to
design an algorithm that builds on neighbor to neighbor interactions with the
ultimate goal of convergence to the average of all initial node values or to
some value close to that average. Such an algorithm is called generically
"distributed averaging," and our goal in this paper is to study the performance
of a subclass of deterministic distributed averaging algorithms where the
information exchange between neighboring nodes (agents) is subject to uniform
quantization. With such quantization, convergence to the precise average cannot
be achieved in general, but the convergence would be to some value close to it,
called quantized consensus. Using Lyapunov stability analysis, we characterize
the convergence properties of the resulting nonlinear quantized system. We show
that in finite time and depending on initial conditions, the algorithm will
either cause all agents to reach a quantized consensus where the consensus
value is the largest quantized value not greater than the average of their
initial values, or will lead all variables to cycle in a small neighborhood
around the average. In the latter case, we identify tight bounds for the size
of the neighborhood and we further show that the error can be made arbitrarily
small by adjusting the algorithm's parameters in a distributed manner
Improved Convergence Rates for Distributed Resource Allocation
In this paper, we develop a class of decentralized algorithms for solving a
convex resource allocation problem in a network of agents, where the agent
objectives are decoupled while the resource constraints are coupled. The agents
communicate over a connected undirected graph, and they want to collaboratively
determine a solution to the overall network problem, while each agent only
communicates with its neighbors. We first study the connection between the
decentralized resource allocation problem and the decentralized consensus
optimization problem. Then, using a class of algorithms for solving consensus
optimization problems, we propose a novel class of decentralized schemes for
solving resource allocation problems in a distributed manner. Specifically, we
first propose an algorithm for solving the resource allocation problem with an
convergence rate guarantee when the agents' objective functions are
generally convex (could be nondifferentiable) and per agent local convex
constraints are allowed; We then propose a gradient-based algorithm for solving
the resource allocation problem when per agent local constraints are absent and
show that such scheme can achieve geometric rate when the objective functions
are strongly convex and have Lipschitz continuous gradients. We have also
provided scalability/network dependency analysis. Based on these two
algorithms, we have further proposed a gradient projection-based algorithm
which can handle smooth objective and simple constraints more efficiently.
Numerical experiments demonstrates the viability and performance of all the
proposed algorithms
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