Dynamic selection of p-norm in linear adaptive filtering via online kernel-based reinforcement learning
This work addresses outlier robustness in adaptive filtering for signal processing applications, but it is incremental as it builds on existing kernel-based reinforcement learning methods.
The study tackled the problem of dynamically selecting the optimal p-norm to combat outliers in linear adaptive filtering without prior knowledge of outlier distributions, resulting in a framework that consistently selects the optimal p-norm and outperforms several non-RL and KBRL schemes in numerical tests on synthetic data.
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.