This paper examines learning the optimal filtering policy, known as the Kalman gain, for a linear system with unknown noise covariance matrices using noisy output data. The learning problem is formulated as a stochastic policy optimization problem, aiming to minimize the output prediction error. This formulation provides a direct bridge between data-driven optimal control and, its dual, optimal filtering.

Network pruning is a commonly used measure to alleviate the storage and computational burden of deep neural networks. However, the fundamental limit of network pruning is still lacking. To close the gap, in this work we'll take a first-principles approach, i.e. we'll directly impose the sparsity constraint on the loss function and leverage the framework of statistical dimension in convex geometry, thus enabling us to characterize the sharp phase transition point, which can be regarded as the fundamental limit of the pruning ratio. Through this limit, we're able to identify two key factors that determine the pruning ratio limit, namely, weight magnitude and network sharpness .

Neural Information Processing Systems http://nips.cc/

This paper examines learning the optimal filtering policy, known as the Kalman gain, for a linear system with unknown noise covariance matrices using noisy output data. The learning problem is formulated as a stochastic policy optimization problem, aiming to minimize the output prediction error. This formulation provides a direct bridge between data-driven optimal control and, its dual, optimal filtering.

Numerical results are also provided to demonstrate our theory.