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Approximate Dynamic Programming with Gaussian Processes

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84381

Deisenroth,  MP
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84135

Peters,  J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84156

Rasmussen,  CE
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Deisenroth, M., Peters, J., & Rasmussen, C. (2008). Approximate Dynamic Programming with Gaussian Processes. Proceedings of the 2008 American Control Conference (ACC 2008), 4480-4485.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-C8EF-B
Abstract
In general, it is difficult to determine an optimal closed-loop policy in nonlinear control problems with continuous-valued state and control domains. Hence, approximations are often inevitable. The standard method of discretizing states and controls suffers from the curse of dimensionality and strongly depends on the chosen temporal sampling rate. In this paper, we introduce Gaussian process dynamic programming (GPDP) and determine an approximate globally optimal closed-loop policy. In GPDP, value functions in the Bellman recursion of the dynamic programming algorithm are modeled using Gaussian processes. GPDP returns an optimal statefeedback for a finite set of states. Based on these outcomes, we learn a possibly discontinuous closed-loop policy on the entire state space by switching between two independently trained Gaussian processes. A binary classifier selects one Gaussian process to predict the optimal control signal. We show that GPDP is able to yield an almost optimal solution to an LQ problem using few sample points. Moreover, we successfully apply GPDP to the underpowered pendulum swing up, a complex nonlinear control problem.