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Reference TypeJournal Article
Author(s)Theodorou, E. , Righetti, L., and Schaal, S.
TitleStochastic Differential Games and Their Relation to Risk Sensitive Control: A Path Integral Control Formalism
Abstract Recent work on path integral stochastic optimal control theory [1], [2] and [3] has shown promising results in planning and control of nonlinear systems in high dimensional state spaces. The path integral control framework relies on the transformation of the nonlinear Hamilton Jacobi Bellman (HJB) partial differential equation (PDE) into a linear PDE and the approximation of its solution via the use of the Feynman Kac lemma. Given these characteristics of path integral control, in this work, we derive the conditions so that the path integral control formalism is applied to stochastic differential games. Moreover we derive the corresponding conditions for the case of path integral risk sensitive control. Finally we specify the necessary transformations under which the relation between stochastic differential games and risk sensitivity holds for the case of the path integral control framework.

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