online and lightweight kernel-based approximated policy iteration for dynamic p-norm linear adaptive filtering

TL;DR

This paper presents an online, kernel-based reinforcement learning approach for adaptive filtering that dynamically selects the optimal p-norm to handle outliers without prior knowledge of their distribution.

Contribution

It introduces a novel Bellman mapping on RKHSs and an approximate policy iteration framework using random Fourier features to efficiently adapt the p-norm in real-time.

Findings

Outperforms existing non-RL and KBRL methods in synthetic outlier scenarios.

Effectively adapts to outliers without prior distribution knowledge.

Reduces computational complexity with random Fourier features.

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.