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We address the problem of estimating the inputs of a dynamical system frommeasurements of the system's outputs. To this end, we introduce a novelestimation algorithm that explicitly trades off bias and variance to optimallyreduce the overall estimation error. This optimal trade-off is done efficientlyand adaptively in every time step. Experimentally, we show that our methodoften produces estimates with substantially lower error compared to thestate-of-the-art. Finally, we consider the more complex\emph{Learning-from-Observations} framework, where an agent should learn acontroller from the outputs of an expert's demonstration. We incorporate ourestimation algorithm as a building block inside this framework and show that itenables learning controllers successfully.

Adaptive Input Estimation in Linear Dynamical Systems with Applications to Learning-from-Observations