A Separation Principle for Control in the Age of Deep Learning
This work addresses the challenge of efficient state estimation in control systems for applications like robotics or autonomous vehicles, but it appears incremental as it builds on existing Information Bottleneck methods with deep learning extensions.
The paper tackles the problem of defining and inferring a state representation for control systems from complex, high-dimensional data like videos, aiming to retain only task-relevant information while discarding nuisance variability. It proposes using deep neural networks to minimize the Information Bottleneck Lagrangian, resulting in representations with millions of dimensions but reduced information content, and extends this to dynamic cases without needing Markovian assumptions.
We review the problem of defining and inferring a "state" for a control system based on complex, high-dimensional, highly uncertain measurement streams such as videos. Such a state, or representation, should contain all and only the information needed for control, and discount nuisance variability in the data. It should also have finite complexity, ideally modulated depending on available resources. This representation is what we want to store in memory in lieu of the data, as it "separates" the control task from the measurement process. For the trivial case with no dynamics, a representation can be inferred by minimizing the Information Bottleneck Lagrangian in a function class realized by deep neural networks. The resulting representation has much higher dimension than the data, already in the millions, but it is smaller in the sense of information content, retaining only what is needed for the task. This process also yields representations that are invariant to nuisance factors and having maximally independent components. We extend these ideas to the dynamic case, where the representation is the posterior density of the task variable given the measurements up to the current time, which is in general much simpler than the prediction density maintained by the classical Bayesian filter. Again this can be finitely-parametrized using a deep neural network, and already some applications are beginning to emerge. No explicit assumption of Markovianity is needed; instead, complexity trades off approximation of an optimal representation, including the degree of Markovianity.