Dynamic Programming for Mean-Field Type Control

Mathieu Laurière and Olivier Pironneau ()
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Mathieu Laurière: Université Denis Diderot (Paris 7)
Olivier Pironneau: Université Pierre et Marie Curie (Paris 6)

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 3, No 10, 902-924

Abstract: Abstract We investigate a model problem for optimal resource management. The problem is a stochastic control problem of mean-field type. We compare a Hamilton–Jacobi–Bellman fixed-point algorithm to a steepest descent method issued from calculus of variations. For mean-field type control problems, stochastic dynamic programming requires adaptation. The problem is reformulated as a distributed control problem by using the Fokker–Planck equation for the probability distribution of the stochastic process; then, an extended Bellman’s principle is derived by a different argument than the one used by P. L. Lions. Both algorithms are compared numerically.

Keywords: Stochastic control; Mean-field game; Hamilton–Jacobi–Bellman; 35Q93; 37N35; 49J20 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0785-x

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