  Risk-sensitive linear quadratic regulator is one of the most fundamental
problems in risk-sensitive optimal control. In this paper, we study online
adaptive control of risk-sensitive linear quadratic regulator in the finite
horizon episodic setting. We propose a simple least-squares greedy algorithm
and show that it achieves $\widetilde{\mathcal{O}}(\log N)$ regret under a
specific identifiability assumption, where $N$ is the total number of episodes.
If the identifiability assumption is not satisfied, we propose incorporating
exploration noise into the least-squares-based algorithm, resulting in an
algorithm with $\widetilde{\mathcal{O}}(\sqrt{N})$ regret. To our best
knowledge, this is the first set of regret bounds for episodic risk-sensitive
linear quadratic regulator. Our proof relies on perturbation analysis of
less-standard Riccati equations for risk-sensitive linear quadratic control,
and a delicate analysis of the loss in the risk-sensitive performance criterion
due to applying the suboptimal controller in the online learning process.
