Learning the Kalman Filter with Fine-Grained Sample Complexity

01/30/2023

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by   Xiangyuan Zhang, et al.

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We develop the first end-to-end sample complexity of model-free policy gradient (PG) methods in discrete-time infinite-horizon Kalman filtering. Specifically, we introduce the receding-horizon policy gradient (RHPG-KF) framework and demonstrate 𝒪̃(ϵ^-2) sample complexity for RHPG-KF in learning a stabilizing filter that is ϵ-close to the optimal Kalman filter. Notably, the proposed RHPG-KF framework does not require the system to be open-loop stable nor assume any prior knowledge of a stabilizing filter. Our results shed light on applying model-free PG methods to control a linear dynamical system where the state measurements could be corrupted by statistical noises and other (possibly adversarial) disturbances.