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Max-Plus Linear Approximations for Deterministic Continuous-State Markov Decision Processes

Eloïse Berthier 1, 2 Francis Bach 1, 2 
1 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique - ENS Paris, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : We consider deterministic continuous-state Markov decision processes (MDPs). We apply a max-plus linear method to approximate the value function with a specific dictionary of functions that leads to an adequate state-discretization of the MDP. This is more efficient than a direct discretization of the state space, typically intractable in high dimension. We propose a simple strategy to adapt the discretization to a problem instance, thus mitigating the curse of dimensionality. We provide numerical examples showing that the method works well on simple MDPs.
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Eloïse Berthier, Francis Bach. Max-Plus Linear Approximations for Deterministic Continuous-State Markov Decision Processes. IEEE Control Systems Letters, 2020, 4 (3), pp.767-772. ⟨10.1109/LCSYS.2020.2973199⟩. ⟨hal-02617479⟩

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