Decision Focused Scenario Learning for Contextual Stochastic Programming

Decision-focused scenario learning for contextual two-stage stochastic programming has emerged as a promising research direction, but open questions remain. A general theory for when scenario generators can yield optimal decision policies is currently lacking. Many existing methods require strict assumptions on which second-stage data are allowed to be random. Generally, the non-differentiability of the decision-focused objective is a source of difficulty. This paper makes three theoretical contributions, each aiming to remedy one of these challenges. First, we present a comprehensive theory for when scenario generators can induce optimal policies, showing that learning a single out-of-support scenario component is often sufficient. Second, we demonstrate a theoretical and methodological equivalence result between learning different second-stage data components, relaxing assumptions required for applying existing methods. Third, we study log-barrier smoothing enabled training, presenting representability and optimization results. Finally, leveraging the theory, we propose a novel method inspired by interior-point methods from classical optimization, and validate it on standard benchmarks.