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

TL;DR

This paper introduces an adaptive input estimation algorithm for linear dynamical systems that optimally balances bias and variance, improving estimation accuracy and enabling effective learning of controllers from demonstrations.

Contribution

The paper presents a novel adaptive estimation method that explicitly trades off bias and variance in real-time, enhancing input estimation in dynamical systems and supporting learning-from-observations.

Findings

The proposed method reduces estimation error compared to state-of-the-art techniques.

It effectively balances bias and variance adaptively at each time step.

The approach enables successful learning of controllers from expert demonstrations.

Abstract

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.