Risk Sensitive Path Integral Control

Bart van den Broek, Wim Wiegerinck, Bert Kappen
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:83-90, 2010.

Abstract

Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dy- namics in continuous space-time. Path in- tegral methods find the control that mini- mizes the expected cost-to-go. In this pa- per we show that under the same assump- tions, path integral methods generalize di- rectly to risk sensitive stochastic optimal con- trol. Here the method minimizes in expec- tation an exponentially weighted cost-to-go. Depending on the exponential weight, risk seeking or risk averse behaviour is obtained. We demonstrate the approach on risk sensi- tive stochastic optimal control problems be- yond the linear-quadratic case, showing the intricate interaction of multi-modal control with risk sensitivity.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-broek10a, title = {Risk Sensitive Path Integral Control}, author = {Broek, Bart van den and Wiegerinck, Wim and Kappen, Bert}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {83--90}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/broek10a/broek10a.pdf}, url = {https://proceedings.mlr.press/r8/broek10a.html}, abstract = {Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dy- namics in continuous space-time. Path in- tegral methods find the control that mini- mizes the expected cost-to-go. In this pa- per we show that under the same assump- tions, path integral methods generalize di- rectly to risk sensitive stochastic optimal con- trol. Here the method minimizes in expec- tation an exponentially weighted cost-to-go. Depending on the exponential weight, risk seeking or risk averse behaviour is obtained. We demonstrate the approach on risk sensi- tive stochastic optimal control problems be- yond the linear-quadratic case, showing the intricate interaction of multi-modal control with risk sensitivity.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Risk Sensitive Path Integral Control %A Bart van den Broek %A Wim Wiegerinck %A Bert Kappen %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-broek10a %I PMLR %P 83--90 %U https://proceedings.mlr.press/r8/broek10a.html %V R8 %X Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dy- namics in continuous space-time. Path in- tegral methods find the control that mini- mizes the expected cost-to-go. In this pa- per we show that under the same assump- tions, path integral methods generalize di- rectly to risk sensitive stochastic optimal con- trol. Here the method minimizes in expec- tation an exponentially weighted cost-to-go. Depending on the exponential weight, risk seeking or risk averse behaviour is obtained. We demonstrate the approach on risk sensi- tive stochastic optimal control problems be- yond the linear-quadratic case, showing the intricate interaction of multi-modal control with risk sensitivity. %Z Reissued by PMLR on 04 October 2026.
APA
Broek, B.v.d., Wiegerinck, W. & Kappen, B.. (2010). Risk Sensitive Path Integral Control. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:83-90 Available from https://proceedings.mlr.press/r8/broek10a.html. Reissued by PMLR on 04 October 2026.

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