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Optimal Control Under Uncertainty and Bayesian Parameters Adjustments

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Date
2018
Link to item file
https://hal.archives-ouvertes.fr/hal-01590606
Dewey
Probabilités et mathématiques appliquées
Sujet
optimal control; uncertainty; Bayesian filtering
Journal issue
SIAM Journal on Control and Optimization
Volume
56
Number
2
Publication date
2018
Article pages
1038-1057
Publisher
SIAM - Society for Industrial and Applied Mathematics
DOI
http://dx.doi.org/10.1137/16M1070815
URI
https://basepub.dauphine.fr/handle/123456789/17618
Collections
  • CEREMADE : Publications
Metadata
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Author
Baradel, Nicolas
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
2579 Centre de Recherche en Économie et Statistique [CREST]
Bouchard, Bruno
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dang, Ngoc Minh
Type
Article accepté pour publication ou publié
Abstract (EN)
We propose a general framework for studying the optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the classical Bayesian rule after each impulse. Taking these progressive prior-adjustments into account, we characterize the optimal policy through a quasi-variational parabolic equation, which can be solved numerically. The derivation of the dynamic programming equation seems to be new in this context. The main difficulty lies in the nature of the set of controls which depends in a nontrivial way on the initial data through the filtration itself.

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