论文标题
数据驱动随机LQR的样品复杂性具有乘法不确定性
Sample Complexity of Data-Driven Stochastic LQR with Multiplicative Uncertainty
论文作者
论文摘要
本文研究了当应用于具有乘法噪声的系统时，随机线性二次调节器的样品复杂性。我们假设噪声的协方差是未知的，并使用样品协方差估算了噪声，这导致了次优行为。然后，本文的主要贡献是结合该方法的次优性，并证明它以1/N的降低，其中n表示样品的量。该方法很容易概括为平均值未知的情况以及在作者先前工作中研究的分布稳健案例。该分析主要基于矩阵函数扰动分析的结果。
This paper studies the sample complexity of the stochastic Linear Quadratic Regulator when applied to systems with multiplicative noise. We assume that the covariance of the noise is unknown and estimate it using the sample covariance, which results in suboptimal behaviour. The main contribution of this paper is then to bound the suboptimality of the methodology and prove that it decreases with 1/N, where N denotes the amount of samples. The methodology easily generalizes to the case where the mean is unknown and to the distributionally robust case studied in a previous work of the authors. The analysis is mostly based on results from matrix function perturbation analysis.
