Generative Adversarial Regression (GAR): Learning Conditional Risk Scenarios

• URL: http://arxiv.org/abs/2603.08553v1
• Date: Mon, 09 Mar 2026 16:16:59 GMT
• Title: Generative Adversarial Regression (GAR): Learning Conditional Risk Scenarios
• Abstract summary: We propose Generative Adversarial Regression (GAR), a framework for learning conditional risk scenarios through generators aligned with downstream risk objectives.<n>GAR builds on a regression characterization of conditional risk for elicitable functionals, including quantiles, expectiles, and jointly elicitable pairs.<n>We extend this principle to generative modeling by training generators whose policy-induced risk matches that of real data under the same context.
• Score: 0.2864713389096699
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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