Reference
A. Athrey, O. Mazhar, M. Guo, B. De Schutter, and S. Shi, "Regret analysis of
learning-based linear quadratic Gaussian control with additive exploration,"
Proceedings of the 2024 European Control Conference,
Stockholm, Sweden, pp. 1795-1801, June 2024.
Abstract
In this paper, we analyze the regret incurred by a computationally efficient
exploration strategy, known as naive exploration, for controlling unknown
partially observable systems within the Linear Quadratic Gaussian (LQG)
framework. We introduce a two-phase control algorithm called LQG-NAIVE, which
involves an initial phase of injecting Gaussian input signals to obtain a
system model, followed by a second phase of an interplay between naive
exploration and control in an episodic fashion. We show that LQG-NAIVE achieves
a regret growth rate of Õ(T
1/2), i.e., O(T
1/2) up
to logarithmic factors after T time steps, and we validate its performance
through numerical simulations. Additionally, we propose LQG-IF2E, which extends
the exploration signal to a 'closed-loop' setting by incorporating the Fisher
Information Matrix (FIM). We provide compelling numerical evidence of the
competitive performance of LQG-IF2E compared to LQG-NAIVE.
Publisher page
Downloads
BibTeX
@inproceedings{AthMaz:24-016,
author = {Athrey, Archith and Mazhar, Othmane and Guo, Meichen and De
Schutter, Bart and Shi, Shengling},
title = {Regret Analysis of Learning-Based Linear Quadratic {G}aussian
Control with Additive Exploration},
booktitle = {Proceedings of the 2024 European Control Conference},
address = {Stockholm, Sweden},
pages = {1795--1801},
month = jun,
year = {2024}
}