Convergence of Trajectory Following Dynamic Programming algorithms for multistage stochastic problems without finite support assumptions

Maël Forcier (1) , Vincent Leclère (1)

1 ENPC - École des Ponts ParisTech

We introduce a class of algorithms, called Trajectory Following Dynamic Programming (TFDP) algorithms, that iteratively refines approximation of cost-to-go functions of multistage stochastic problems with independent random variables. This framework encompasses most variants of the Stochastic Dual Dynamic Programming algorithm. Leveraging a Lipschitz assumption on the expected cost-to-go functions, we provide a new convergence and complexity proof that allows random variables with non-finitely supported distributions. In particular, this leads to new complexity results for numerous known algorithms. Further, we detail how TFDP algorithms can be implemented without the finite support assumption, either through approximations or exact computations.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Maël Forcier, Vincent Leclère. Convergence of Trajectory Following Dynamic Programming algorithms for multistage stochastic problems without finite support assumptions. 2022. ⟨hal-03683697⟩