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  Approximate Dynamic Programming with Gaussian Processes

Deisenroth, M., Peters, J., & Rasmussen, C. (2008). Approximate Dynamic Programming with Gaussian Processes. In 2008 American Control Conference (pp. 4480-4485). Piscataway, NJ, USA: IEEE Service Center.

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 Creators:
Deisenroth, MP, Author           
Peters, J1, 2, Author           
Rasmussen, CE, Author           
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 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.

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 Dates: 2008-06
 Publication Status: Published in print
 Pages: -
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 Rev. Type: -
 Identifiers: BibTex Citekey: 4975
DOI: 10.1109/ACC.2008.4587201
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Title: 2008 American Control Conference (ACC 2008)
Place of Event: Seattle, WA, USA
Start-/End Date: 2008-06-11 - 2008-06-13

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Title: 2008 American Control Conference
Source Genre: Proceedings
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Publ. Info: Piscataway, NJ, USA : IEEE Service Center
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 4480 - 4485 Identifier: ISBN: 978-1-4244-2079-7