Distributed Gaussian Learning over Time-varying Directed Graphs
This addresses distributed learning in dynamic networks for applications like sensor networks, but it is incremental as it builds on existing distributed estimation methods.
The paper tackles distributed parameter estimation with Gaussian noise by proposing a non-Bayesian learning algorithm with explicit updates on Gaussian belief parameters, achieving an O(1/k) convergence rate dependent on network topology and proving almost sure convergence to the optimal solution for time-varying directed graphs.
We present a distributed (non-Bayesian) learning algorithm for the problem of parameter estimation with Gaussian noise. The algorithm is expressed as explicit updates on the parameters of the Gaussian beliefs (i.e. means and precision). We show a convergence rate of $O(1/k)$ with the constant term depending on the number of agents and the topology of the network. Moreover, we show almost sure convergence to the optimal solution of the estimation problem for the general case of time-varying directed graphs.