  We present a novel diffusion scheme for online kernel-based learning over
networks. So far, a major drawback of any online learning algorithm, operating
in a reproducing kernel Hilbert space (RKHS), is the need for updating a
growing number of parameters as time iterations evolve. Besides complexity,
this leads to an increased need of communication resources, in a distributed
setting. In contrast, the proposed method approximates the solution as a
fixed-size vector (of larger dimension than the input space) using Random
Fourier Features. This paves the way to use standard linear combine-then-adapt
techniques. To the best of our knowledge, this is the first time that a
complete protocol for distributed online learning in RKHS is presented.
Conditions for asymptotic convergence and boundness of the networkwise regret
are also provided. The simulated tests illustrate the performance of the
proposed scheme.
