We address the problem of estimating the inputs of a dynamical system from measurements of the system's outputs. To this end, we introduce a novel estimation algorithm that explicitly trades off bias and variance to optimally reduce the overall estimation error. This optimal trade-off is done efficiently and adaptively in every time step. Experimentally, we show that our method often produces estimates with substantially lower error compared to the state-of-the-art. Finally, we consider the more complex Learning-from-Observations framework, where an agent should learn a controller from the outputs of an expert's demonstration. We incorporate our estimation algorithm as a building block inside this framework and show that it enables learning controllers successfully.

@inproceedings{curi2019adaptive,
	author = {Curi, Sebastian and Levy, Kfir Y and Krause, Andreas},
	booktitle = {2019 IEEE 58th Conference on Decision and Control (CDC)},
	organization = {IEEE},
	pages = {4115--4120},
	title = {Adaptive Input Estimation in Linear Dynamical Systems with Applications to Learning-from-Observations},
	year = {2019}}