Course Correcting Koopman Representations

Mahan Fathi, Clement Gehring, Jonathan Pilault, David Kanaa, Pierre-Luc Bacon, Ross Goroshin

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Keywords: Koopman, Autoencoders, Dynamical Systems, Sequence Modeling, Inference-time Methods, Planning, Unsupervised Learning, Representation Learning, Robotics

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TL;DR: We use Periodic Reencoding as means for correcting the drift of Koopman representations at inference time.

Abstract: Koopman representations aim to learn features of nonlinear dynamical systems (NLDS) which lead to linear dynamics in the latent space. Theoretically, such features can be used to simplify many problems in modeling and control of NLDS. In this work we study autoencoder formulations of this problem, and different ways they can be used to model dynamics, specifically for future state prediction over long horizons. We discover several limitations of predicting future states in the latent space and propose an inference-time mechanism, which we refer to as Periodic Reencoding, for faithfully capturing long term dynamics. We justify this method both analytically and empirically via experiments in low and high dimensional NLDS.

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Primary Area: applications to robotics, autonomy, planning

Submission Number: 3629