DYNAMIC SELECTION OF P-NORM IN LINEAR ADAPTIVE FILTERING VIA ONLINE
KERNEL-BASED REINFORCEMENT LEARNING
Abstract
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 timevarying
probability density 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.
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