An Adaptive Projected Subgradient Approach to Learning in Diffusion Networks

We present an algorithm that minimizes asymptotically a sequence of nonnegative convex functions over diffusion networks. In the proposed algorithm, at each iteration the nodes in the network have only partial information of the cost function, but they are able to achieve consensus on a possible minimizer asymptotically. To account for possible node failures, position changes, and/or reachability problems (because of moving obstacles, jammers, etc.), the algorithm can cope with changing network topologies and cost functions, a desirable feature in online algorithms where information arrives sequentially. Many projection-based algorithms can be straightforwardly extended to (probabilistic) diffusion networks with the proposed scheme. The system identification problem in distributed networks is given as one example of a possible application.