Regret Analysis of Learning-Based Linear Quadratic Gaussian Control with Additive Exploration

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(T1/2), i.e., O(T1/2) 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}
   }


Go to the publications overview page.

This page is maintained by Bart De Schutter. Last update: March 16, 2026.