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.

中文翻译：

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具有乘法不确定性的数据驱动随机 LQR 的样本复杂度

本文研究了随机线性二次调节器应用于具有乘法噪声的系统时的样本复杂度。我们假设噪声的协方差是未知的，并使用样本协方差对其进行估计，这会导致次优行为。本文的主要贡献是限制了该方法的次优性，并证明它以 1/N 下降，其中 N 表示样本量。该方法很容易推广到均值未知的情况以及作者先前工作中研究的分布稳健的情况。分析主要基于矩阵函数微扰分析的结果。