We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide finite sample error bounds of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems, such as upper bounds on noise levels and model difference, is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.

翻译：我们考虑在拥有来自真实系统数据的同时，还能访问由具有相似（但不完全相同）动态特性的辅助系统生成数据的情况下，学习线性系统动态特性的问题。我们采用加权最小二乘法，并根据样本数量、两个系统的各项参数以及辅助数据所分配的权重，给出学习模型的有限样本误差界。研究表明，辅助数据有助于降低由噪声引起的固有系统辨识误差，但代价是引入一部分由两个系统模型间差异导致的误差。我们进一步给出了一个数据依赖的误差界，该误差界在可获得系统先验知识（如噪声水平和模型差异的上界）时可计算。该误差界也可用于确定在模型训练阶段应分配给辅助数据的权重。