A High-order Tuner for Accelerated Learning and Control

TL;DR

This paper investigates a high-order tuner that enhances convergence speed and stability in iterative algorithms for estimation, learning, and control, even under noisy conditions, broadening its applicability in real-time decision-making.

Contribution

It demonstrates that the high-order tuner maintains bounded estimates with noisy gradients and achieves exponential convergence to a noise-dependent set, extending its robustness and efficiency.

Findings

Bounded parameter estimates under noisy gradients.

Exponential convergence to a noise-dependent set.

Applicable to a wide range of estimation and control problems.

Abstract

Gradient-descent based iterative algorithms pervade a variety of problems in estimation, prediction, learning, control, and optimization. Recently iterative algorithms based on higher-order information have been explored in an attempt to lead to accelerated learning. In this paper, we explore a specific a high-order tuner that has been shown to result in stability with time-varying regressors in linearly parametrized systems, and accelerated convergence with constant regressors. We show that this tuner continues to provide bounded parameter estimates even if the gradients are corrupted by noise. Additionally, we also show that the parameter estimates converge exponentially to a compact set whose size is dependent on noise statistics. As the HT algorithms can be applied to a wide range of problems in estimation, filtering, control, and machine learning, the result obtained in this paper represents an important extension to the topic of real-time and fast decision making.