ONLINE AND LIGHTWEIGHT KERNEL-BASED APPROXIMATE POLICY ITERATION FOR
DYNAMIC P-NORM LINEAR ADAPTIVE FILTERING
Abstract
This paper introduces a solution to the problem of selecting
dynamically (online) the “optimal’‘ p-norm to combat outliers in linear
adaptive filtering without any knowledge on the probability density
function of the outliers. The proposed online and data-driven framework
is built on kernel-based reinforcement learning (KBRL). To this end,
novel Bellman mappings on reproducing kernel Hilbert spaces (RKHSs) are
introduced. These mappings do not require any knowledge on transition
probabilities of Markov decision processes, and are nonexpansive with
respect to the underlying Hilbertian norm. The fixed-point sets of the
proposed Bellman mappings are utilized to build an approximate
policy-iteration (API) framework for the problem at hand. To address the
“curse of dimensionality” in RKHSs, random Fourier features are
utilized to bound the computational complexity of the API. Numerical
tests on synthetic data for several outlier scenarios demonstrate the
superior performance of the proposed API framework over several non-RL
and KBRL schemes.
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