We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity while allowing for efficient computation of an estimate of a system matrix. More specifically, we first establish lower bounds of the sample complexity for any active learning algorithm to attain the prescribed accuracy and confidence levels. Next, we derive a sample complexity upper bound of the proposed algorithm, which matches the lower bound for any algorithm up to universal factors. Our tight bounds are easy to interpret and explicitly show their dependence on the system parameters such as the state dimension.

翻译：我们提出一种针对线性系统辨识的最优中心噪声激励主动学习算法。值得注意的是，该算法基于普通最小二乘法和半定规划，在实现系统矩阵估计高效计算的同时，达到了最小样本复杂度。具体而言，我们首先为任何主动学习算法在达到预定精度与置信水平时所需样本复杂度建立了下界。其次，我们推导了所提出算法的样本复杂度上界，该上界与任何算法下界的差异仅受通用因子影响。这些紧致界不仅易于解释，还明确揭示了其与状态维度等系统参数的依赖关系。