A Study of Distributionally Robust Multistage Stochastic Optimization

Understand

In this paper, we focus on a data-driven risk-averse multistage stochastic programming (RMSP) model considering distributional robustness.

• We optimize the RMSP over the worst-case distribution within an ambiguity set of probability distributions constructed directly from historical data samples.
• The proposed RMSP is intractable due to the multistage nested minimax structure in its objective function, so we reformulate it into a deterministic equivalent that contains a series of convex combination of expectation and conditional value at risk (CVaR), which can be solved by a customized stochastic dual dynamic programming (SDDP) algorithm in this paper.
• As the size of collected data samples increases to infinity, we show the consistency of the RMSP with distributional robustness to the traditional multistage stochastic programming.