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Article Dans Une Revue Journal of Optimization Theory and Applications Année : 2015

Dynamic Programming for Mean-Field Type Control

Résumé

We investigate a model problem for optimal resource management. The problem is a stochastic control problem of mean-field type. We compare an 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.
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hal-01558745 , version 1 (09-07-2017)

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Mathieu Lauriere, Olivier Pironneau. Dynamic Programming for Mean-Field Type Control. Journal of Optimization Theory and Applications, 2015, 169 (3), pp.902-924. ⟨10.1007/s10957-015-0785-x⟩. ⟨hal-01558745⟩
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