Differentiability and Regularization of Parametric Convex Value Functions in Stochastic Multistage Optimization - Archive ouverte HAL Accéder directement au contenu
Rapport Année : 2022

Differentiability and Regularization of Parametric Convex Value Functions in Stochastic Multistage Optimization

Résumé

In multistage decision problems, it is often the case that an initial strategic decision (such as investment) is followed by many operational ones (operating the investment). Such initial strategic decision can be seen as a parameter affecting a multistage decision problem. More generally, we study in this paper a standard multistage stochastic optimization problem depending on a parameter. When the parameter is fixed, Stochastic Dynamic Programming provides a way to compute the optimal value of the problem. Thus, the value function depends both on the state (as usual) and on the parameter. Our aim is to investigate on the possibility to efficiently compute gradients of the value function with respect to the parameter, when these objects exist. When nondifferentiable, we propose a regularization method based on the Moreau-Yosida envelope. We present a numerical test case from day-ahead power scheduling.
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Dates et versions

hal-03903218 , version 1 (16-12-2022)
hal-03903218 , version 2 (11-01-2023)

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Adrien Le Franc, Jean-Philippe Chancelier, Pierre Carpentier, Michel de Lara. Differentiability and Regularization of Parametric Convex Value Functions in Stochastic Multistage Optimization. ENPC - École des Ponts ParisTech. 2022. ⟨hal-03903218v1⟩
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