论文标题
遗憾的是学习线性二次高斯系统的下限
Regret Lower Bounds for Learning Linear Quadratic Gaussian Systems
论文作者
论文摘要
TWE建立后悔的下限，以适应以二次成本控制未知的线性高斯系统。我们结合了实验设计，估计理论和某些信息矩阵的扰动界的想法，从而在时光范围内$ t $ to sude ture suffers taude sude sude suffer。我们的界限准确地捕获了控制理论参数的作用，我们能够证明难以控制的系统也很难控制。当实例化对状态反馈系统时，我们恢复了早期工作的维度依赖性，但通过系统理论常数（例如系统成本和Gramians）进行了改进的缩放。此外，我们将结果扩展到一类部分观察到的系统，并证明具有较差可观察力结构的系统也很难学习。
TWe establish regret lower bounds for adaptively controlling an unknown linear Gaussian system with quadratic costs. We combine ideas from experiment design, estimation theory and a perturbation bound of certain information matrices to derive regret lower bounds exhibiting scaling on the order of magnitude $\sqrt{T}$ in the time horizon $T$. Our bounds accurately capture the role of control-theoretic parameters and we are able to show that systems that are hard to control are also hard to learn to control; when instantiated to state feedback systems we recover the dimensional dependency of earlier work but with improved scaling with system-theoretic constants such as system costs and Gramians. Furthermore, we extend our results to a class of partially observed systems and demonstrate that systems with poor observability structure also are hard to learn to control.
