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arXiv · 2509.22981

MDP modeling for multi-stage stochastic programs

David P. Morton·Oscar Dowson·Bernardo K. Pagnoncelli
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Abstract

We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include decision-dependent uncertainty for one-step transition probabilities as well as a limited form of statistical learning. We focus on the expressiveness of our modeling approach, illustrating ideas with a series of examples of increasing complexity. As a solution method, we develop new variants of stochastic dual dynamic programming, including approximations to handle non-convexities.

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David P. Morton, Oscar Dowson, Bernardo K. Pagnoncelli. 2025-09-26. MDP modeling for multi-stage stochastic programs. https://arxiv.org/abs/2509.22981

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