NDLI: Relative entropy and free energy dualities: Connections to Path Integral and KL control

Content Provider	IEEE Xplore Digital Library
Author	Theodorou, E.A. Todorov, E.
Copyright Year	2012
Description	Author affiliation: Department of Computer Science and Engineering, University of Washington, Seattle, USA (Theodorou, E.A.; Todorov, E.)
Abstract	This paper integrates recent work on Path Integral (PI) and Kullback Leibler (KL) divergence stochastic optimal control theory with earlier work on risk sensitivity and the fundamental dualities between free energy and relative entropy. We derive the path integral optimal control framework and its iterative version based on the aforemetioned dualities. The resulting formulation of iterative path integral control is valid for general feedback policies and in contrast to previous work, it does not rely on pre-specified policy parameterizations. The derivation is based on successive applications of Girsanov's theorem and the use of Radon-Nikodým derivative as applied to diffusion processes due to the change of measure in the stochastic dynamics. We compare the PI control derived based on Dynamic Programming with PI based on the duality between free energy and relative entropy. Moreover we extend our analysis on the applicability of the relationship between free energy and relative entropy to optimal control of markov jump diffusions processes. Furthermore, we present the links between KL stochastic optimal control and the aforementioned dualities and discuss its generalizability.
Starting Page	1466
Ending Page	1473
File Size	452688
Page Count	8
File Format	PDF
ISBN	9781467320658
ISSN	07431546
e-ISBN	9781467320665
e-ISBN	9781467320641
DOI	10.1109/CDC.2012.6426381
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-12-10
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Optimal control Entropy Diffusion processes Trajectory Cost function Markov processes Aerospace electronics
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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