  This study addresses the problem of selecting dynamically, at each time
instance, the ``optimal'' p-norm to combat outliers in linear adaptive
filtering without any knowledge on the potentially time-varying probability
distribution function of the outliers. To this end, an online and data-driven
framework is designed via kernel-based reinforcement learning (KBRL). Novel
Bellman mappings on reproducing kernel Hilbert spaces (RKHSs) are introduced
that need no knowledge on transition probabilities of Markov decision
processes, and are nonexpansive with respect to the underlying Hilbertian norm.
An approximate policy-iteration framework is finally offered via the
introduction of a finite-dimensional affine superset of the fixed-point set of
the proposed Bellman mappings. The well-known ``curse of dimensionality'' in
RKHSs is addressed by building a basis of vectors via an approximate linear
dependency criterion. Numerical tests on synthetic data demonstrate that the
proposed framework selects always the ``optimal'' p-norm for the outlier
scenario at hand, outperforming at the same time several non-RL and KBRL
schemes.
