18 research outputs found
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
Distributed Average Consensus under Quantized Communication via Event-Triggered Mass Summation
We study distributed average consensus problems in multi-agent systems with
directed communication links that are subject to quantized information flow.
The goal of distributed average consensus is for the nodes, each associated
with some initial value, to obtain the average (or some value close to the
average) of these initial values. In this paper, we present and analyze a
distributed averaging algorithm which operates exclusively with quantized
values (specifically, the information stored, processed and exchanged between
neighboring agents is subject to deterministic uniform quantization) and relies
on event-driven updates (e.g., to reduce energy consumption, communication
bandwidth, network congestion, and/or processor usage). We characterize the
properties of the proposed distributed averaging protocol on quantized values
and show that its execution, on any time-invariant and strongly connected
digraph, will allow all agents to reach, in finite time, a common consensus
value represented as the ratio of two integer that is equal to the exact
average. We conclude with examples that illustrate the operation, performance,
and potential advantages of the proposed algorithm
Robust and Communication-Efficient Collaborative Learning
We consider a decentralized learning problem, where a set of computing nodes
aim at solving a non-convex optimization problem collaboratively. It is
well-known that decentralized optimization schemes face two major system
bottlenecks: stragglers' delay and communication overhead. In this paper, we
tackle these bottlenecks by proposing a novel decentralized and gradient-based
optimization algorithm named as QuanTimed-DSGD. Our algorithm stands on two
main ideas: (i) we impose a deadline on the local gradient computations of each
node at each iteration of the algorithm, and (ii) the nodes exchange quantized
versions of their local models. The first idea robustifies to straggling nodes
and the second alleviates communication efficiency. The key technical
contribution of our work is to prove that with non-vanishing noises for
quantization and stochastic gradients, the proposed method exactly converges to
the global optimal for convex loss functions, and finds a first-order
stationary point in non-convex scenarios. Our numerical evaluations of the
QuanTimed-DSGD on training benchmark datasets, MNIST and CIFAR-10, demonstrate
speedups of up to 3x in run-time, compared to state-of-the-art decentralized
optimization methods