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.
The theory we describe here emphasize that, in order to obtain efficient representations of the data, we should focus on a specific task, such as control, rather than predicting high-dimensional future data. @cite_10 assume that there is a low-dimensional vector of measurements'' separate from the actual measured data, which can be easily obtained, and on which the control loss depends linearly. In our parlance, predicting the future is a task sufficient for control, and therefore allows us to learn a sufficient representation for control. In particular, optimal control reduces to minimum-prediction error, and one can simply train a network to predict future measurements conditioned on the current policy a given control action taken at present. Using this technique for control shows state of the art performance on video games.
@cite_10
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We present an approach to sensorimotor control in immersive environments. Our approach utilizes a high-dimensional sensory stream and a lower-dimensional measurement stream. The cotemporal structure of these streams provides a rich supervisory signal, which enables training a sensorimotor control model by interacting with the environment. The model is trained using supervised learning techniques, but without extraneous supervision. It learns to act based on raw sensory input from a complex three-dimensional environment. The presented formulation enables learning without a fixed goal at training time, and pursuing dynamically changing goals at test time. We conduct extensive experiments in three-dimensional simulations based on the classical first-person game Doom. The results demonstrate that the presented approach outperforms sophisticated prior formulations, particularly on challenging tasks. The results also show that trained models successfully generalize across environments and goals. A model trained using the presented approach won the Full Deathmatch track of the Visual Doom AI Competition, which was held in previously unseen environments.