Generative models for decision-making under distributional shift

TL;DR

This paper reviews how modern generative models, especially flow- and score-based methods, can be used to construct and transform distributions for decision-making under distributional shifts, emphasizing robustness and uncertainty quantification.

Contribution

It introduces a unified framework using transport maps and related mathematical tools to leverage generative models for robust decision-making and scenario generation under distributional shifts.

Findings

Generative models can learn nominal uncertainty and stressed distributions.

The framework includes theoretical guarantees like convergence and error bounds.

Applications include scenario generation, robustness, and uncertainty quantification.

Abstract

Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced. This tutorial presents modern generative models, particularly flow- and score-based methods, as mathematical tools for constructing decision-relevant distributions. From an operations research perspective, their primary value lies not in unconstrained sample synthesis but in representing and transforming distributions through transport maps, velocity fields, score fields, and guided stochastic dynamics. We present a unified framework based on pushforward maps, continuity, Fokker-Planck equations, Wasserstein geometry, and optimization in probability space. Within this framework, generative models can be used to learn nominal uncertainty, construct stressed or least-favorable distributions for robustness, and produce conditional or posterior distributions under side information and partial observation. We also highlight representative theoretical guarantees, including forward-reverse convergence for iterative flow models, first-order minimax analysis in transport-map space, and error-transfer bounds for posterior sampling with generative priors. The tutorial provides a principled introduction to using generative models for scenario generation, robust decision-making, uncertainty quantification, and related problems under distributional shift.