Regret Analysis of Learning-Based Linear Quadratic Gaussian Control with Additive Exploration
Archith Athrey (Student TU Delft)
Othmane Mazhar (Université Paris Cité Grands)
Meichen Guo (TU Delft - Mechanical Engineering)
Bart De Schutter (TU Delft - Mechanical Engineering)
Shengling Shi (TU Delft - Mechanical Engineering)
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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), i.e., O(√T) 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.