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In this paper, we analyze the regret incurred by a computationally efficientexploration strategy, known as naive exploration, for controlling unknownpartially observable systems within the Linear Quadratic Gaussian (LQG)framework. We introduce a two-phase control algorithm called LQG-NAIVE, whichinvolves an initial phase of injecting Gaussian input signals to obtain asystem model, followed by a second phase of an interplay between naiveexploration and control in an episodic fashion. We show that LQG-NAIVE achievesa regret growth rate of $\tilde{\mathcal{O}}(\sqrt{T})$, i.e.,$\mathcal{O}(\sqrt{T})$ up to logarithmic factors after $T$ time steps, and wevalidate its performance through numerical simulations. Additionally, wepropose LQG-IF2E, which extends the exploration signal to a `closed-loop'setting by incorporating the Fisher Information Matrix (FIM). We providecompelling numerical evidence of the competitive performance of LQG-IF2Ecompared to LQG-NAIVE.

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