Generative Adversarial Regression (GAR): Learning Conditional Risk Scenarios

2026-03-09

AI Summary

Existing methods struggle to generate conditional risk scenarios aligned with downstream risk objectives. This work proposes a Generative Adversarial Regression (GAR) framework that extends the elicitable regression properties of risk functionals—such as Value-at-Risk (VaR) and Expected Shortfall (ES)—from point prediction to generative modeling. GAR jointly optimizes a conditional generator and a strategy-aware discriminator through a minimax adversarial mechanism, ensuring risk consistency across a broad class of strategies without requiring a pre-specified set of candidate policies. The framework robustly produces scenarios that faithfully align with the true underlying risk distribution. Empirical experiments on S&P 500 data demonstrate that GAR-generated scenarios significantly outperform unconditional, econometric, and direct prediction baselines in terms of downstream risk accuracy, while maintaining stability under adversarial strategies.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

We propose Generative Adversarial Regression (GAR), a framework for learning conditional risk scenarios through generators aligned with downstream risk objectives. GAR builds on a regression characterization of conditional risk for elicitable functionals, including quantiles, expectiles, and jointly elicitable pairs. We extend this principle from point prediction to generative modeling by training generators whose policy-induced risk matches that of real data under the same context. To ensure robustness across all policies, GAR adopts a minimax formulation in which an adversarial policy identifies worst-case discrepancies in risk evaluation while the generator adapts to eliminate them. This structure preserves alignment with the risk functional across a broad class of policies rather than a fixed, pre-specified set. We illustrate GAR through a tail-risk instantiation based on jointly elicitable $(\mathrm{VaR}, \mathrm{ES})$ objectives. Experiments on S\&P 500 data show that GAR produces scenarios that better preserve downstream risk than unconditional, econometric, and direct predictive baselines while remaining stable under adversarially selected policies.

Problem

• conditional risk scenarios
• risk elicitation
• generative modeling
• adversarial robustness
• tail risk

Innovation

• Generative Adversarial Regression
• Conditional Risk Scenarios
• Elicitable Functionals
• Minimax Formulation
• Tail Risk