  One central theme in machine learning is function estimation from sparse and
noisy data. An example is supervised learning where the elements of the
training set are couples, each containing an input location and an output
response. In the last decades, a substantial amount of work has been devoted to
design estimators for the unknown function and to study their convergence to
the optimal predictor, also characterizing the learning rate. These results
typically rely on stationary assumptions where input locations are drawn from a
probability distribution that does not change in time. In this work, we
consider kernel-based ridge regression and derive convergence conditions under
non stationary distributions, addressing also cases where stochastic adaption
may happen infinitely often. This includes the important
exploration-exploitation problems where e.g. a set of agents/robots has to
monitor an environment to reconstruct a sensorial field and their movements
rules are continuously updated on the basis of the acquired knowledge on the
field and/or the surrounding environment.
