Topology-aware distributed adaptation of Laplacian weights for in-network averaging

Laplacian weights are often used in distributed algorithms to fuse intermediate estimates of linked agents or nodes in a network. We propose a topology-aware (TA) distributed algorithm for on-line adaptation of the Laplacian weighting rule, when applied in an in-network averaging procedure. We demonstrate that the particular structure of the Laplacian weighting rule indeed allows for a distributed convergence rate optimization, based on the in-network computation of two eigenvectors of the Laplacian matrix and their corresponding eigenvalues. Although the proposed TA distributed algorithm cannot always reach the same (optimal) weights as its centralized equivalent, simulations demonstrate that it still provides a significant improvement on the convergence speed when compared to more general combination weights.