Generative models for decision-making under distributional shift

2026-06-18 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Data Science & Analytics · Depth: Expert, extended

Summary

This tutorial explores modern generative models, specifically flow- and score-based methods, as mathematical tools for constructing decision-relevant distributions under distributional shift. It addresses operations research problems where nominal distributions from historical data differ from deployment distributions due to context, partial observation, or stress. The framework unifies pushforward maps, continuity, Fokker–Planck equations, Wasserstein geometry, and optimization in probability space. Generative models are presented for learning nominal uncertainty, constructing robust or least-favorable distributions, and producing conditional or posterior distributions. The paper highlights theoretical guarantees like forward–reverse convergence and first-order minimax analysis, providing a principled introduction to scenario generation, robust decision-making, and uncertainty quantification.

Key takeaway

For AI and Data Scientists developing data-driven decision systems, understanding how generative models construct and transform uncertainty distributions is crucial. You should consider flow- and score-based models to move beyond nominal data, enabling robust planning, accurate scenario generation, and dynamic inference under real-world distributional shifts. This approach enhances decision quality by capturing the correct uncertainty law.

Key insights

Generative models transform nominal data distributions into decision-relevant uncertainty distributions for OR problems.

Principles

• Generative models support uncertainty representation.
• They enable robustness via stress scenario generation.
• They facilitate inference through conditional updates.

Method

Distribution learning and perturbation can be viewed as iterative algorithms in probability space, realized through transport maps, velocity fields, or guided stochastic dynamics, often implemented via particle-based schemes.

In practice

• Generate stress scenarios for robust planning.
• Update distributions with new side information.
• Transport between arbitrary sample-defined distributions.

Topics

• Generative Models
• Distributional Shift
• Operations Research
• Wasserstein Geometry
• Robust Optimization
• Normalizing Flows
• Diffusion Models

Best for: Research Scientist, AI Scientist, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.