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.

在线自适应控制有限时域周期性设置下风险敏感线性二次调节器的回避范围研究及拟合泛化条件的简化最小二乘贪婪算法