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Approximative Policy Iteration for Exit Time Feedback Control Problems driven by Stochastic Differential Equations using Tensor Train format

  • We consider a stochastic optimal exit time feedback control problem. The Bellman equation is solved approximatively via the Policy Iteration algorithm on a polynomial ansatz space by a sequence of linear equations. As high degree multi-polynomials are needed, the corresponding equations suffer from the curse of dimensionality even in moderate dimensions. We employ tensor-train methods to account for this problem. The approximation process within the Policy Iteration is done via a Least-Squares ansatz and the integration is done via Monte-Carlo methods. Numerical evidences are given for the (multi dimensional) double well potential and a three-hole potential.

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Author:Konstantin FackeldeyORCiD, Mathias Oster, Leon Sallandt, Reinhold Schneider
Document Type:Article
Parent Title (English):SIAM Journal on Multiscale Modeling and Simulation
First Page:379
Last Page:403
Year of first publication:2022
ArXiv Id:http://arxiv.org/abs/2010.04465
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