Tropical numerical methods for solving stochastic control problems
Résumé
We consider Dynamic programming equations associated to discrete time stochastic control problems with continuous state space, which arise in particular from monotone time discretizations of Hamilton-Jacobi-Bellman equations. We develop and study several numerical algorithms for solving such equations, combining tropical numerical methods and stochastic dual dynamic programming methods. We also compare these algorithms with the point based methods for solving Partially Observable Markov Decision Processes (POMDP).
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