Data-driven Multistage Distributionally Robust Linear Optimization with Nested Distance

Understand

We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance.

• The resulting minimax problem is notoriously difficult to solve due to its inherent non-convexity.
• In this paper, we demonstrate that, under mild conditions, the robust risk evaluation of a given policy can be expressed in an equivalent recursive form.
• Furthermore, assuming stagewise independence, we derive equivalent dynamic programming reformulations to find an optimal robust policy that is time-consistent and well-defined on unseen sample paths.