Optimal control under uncertainty and Bayesian parameters adjustments

N. Baradel (1, 2) , Bruno Bouchard (2) , Ngoc Minh M Dang (3)

1 CREST - Centre de Recherche en Économie et Statistique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 inconnu

We propose a general framework for studying 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 non trivial way on the initial data through the filtration itself.

Mots clés: Bayesian filtering MSC 2010: 49L20; Optimal control; uncertainty; Bayesian filtering

Domaines: Probabilités [math.PR]

N. Baradel, Bruno Bouchard, Ngoc Minh M Dang. Optimal control under uncertainty and Bayesian parameters adjustments. SIAM Journal on Control and Optimization, 2018, 56 (2), pp.1038-1057. ⟨10.1137/16M1070815⟩. ⟨hal-01304018v2⟩