论文标题
稳定线性系统的有限时间识别：最小二乘估计器的最佳性
Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimator
论文作者
论文摘要
我们对稳定的线性时间传播系统的普通最小二乘（OLS）估计器的估计误差（OLS）估计器的估计误差进行了新的有限时间分析。我们表征观察到的样品的数量（观察到的轨迹的长度）足以使OLS估计器为$（\ varepsilon，δ）$ - PAC，即产生小于$ \ varepsilon $的估计误差，概率至少为$ 1-δ$。我们表明，该数字与现有样品复杂性下限[1,2]与通用乘法因子（独立于（$ \ varepsilon，δ）$和系统的）。因此，本文确立了稳定系统OLS估计量的最佳性，结果在[1]中提出。与现有分析相比，我们对OLS估计器性能的分析更简单，更清晰，更容易解释。它依赖于协变量矩阵的新浓度结果。
We present a new finite-time analysis of the estimation error of the Ordinary Least Squares (OLS) estimator for stable linear time-invariant systems. We characterize the number of observed samples (the length of the observed trajectory) sufficient for the OLS estimator to be $(\varepsilon,δ)$-PAC, i.e., to yield an estimation error less than $\varepsilon$ with probability at least $1-δ$. We show that this number matches existing sample complexity lower bounds [1,2] up to universal multiplicative factors (independent of ($\varepsilon,δ)$ and of the system). This paper hence establishes the optimality of the OLS estimator for stable systems, a result conjectured in [1]. Our analysis of the performance of the OLS estimator is simpler, sharper, and easier to interpret than existing analyses. It relies on new concentration results for the covariates matrix.
