  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
\emph{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.
