Max-Plus Matching Pursuit for Deterministic Markov Decision Processes - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Max-Plus Matching Pursuit for Deterministic Markov Decision Processes

Résumé

We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The setup naturally leads to novel theoretical results which are simply formulated due to the max-plus algebra structure. For example, when considering a fixed (non adaptive) finite basis, the computational complexity of approximating the optimal value function is not directly related to the number of states, but to notions of covering numbers of the state space. In order to break the curse of dimensionality in factored state-spaces, we consider adaptive basis that can adapt to particular problems leading to an algorithm similar to matching pursuit from signal processing. They currently come with no theoretical guarantees but work empirically well on simple deterministic MDPs derived from low-dimensional continuous control problems. We focus primarily on deterministic MDPs but note that the framework can be applied to all MDPs by considering measure-based formulations.
Fichier principal
Vignette du fichier
maxplus_final_hal.pdf (2.28 Mo) Télécharger le fichier
maxplus_final_hal.synctex.gz (193.06 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02155865 , version 1 (19-06-2019)

Identifiants

Citer

Francis Bach. Max-Plus Matching Pursuit for Deterministic Markov Decision Processes. 2019. ⟨hal-02155865⟩
321 Consultations
136 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More