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Generative Adversarial Regression (GAR): Learning Conditional Risk Scenarios

Saeed Asadi, Jonathan Yu-Meng Li

TL;DR

Generative Adversarial Regression is proposed, a framework for learning conditional risk scenarios through generators aligned with downstream risk objectives that produces scenarios that better preserve downstream risk than unconditional, econometric, and direct predictive baselines while remaining stable under adversarially selected policies.

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.

Generative Adversarial Regression (GAR): Learning Conditional Risk Scenarios

TL;DR

Generative Adversarial Regression is proposed, a framework for learning conditional risk scenarios through generators aligned with downstream risk objectives that produces scenarios that better preserve downstream risk than unconditional, econometric, and direct predictive baselines while remaining stable under adversarially selected policies.

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 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.
Paper Structure (25 sections, 44 equations, 4 figures, 3 tables, 1 algorithm)

This paper contains 25 sections, 44 equations, 4 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Generative Adversarial Regression (GAR)
  3. Conditional Risk Scenario Generation
  4. Elicitable risk functional
  5. Elements of GAR
  6. Step 1: Conditional risk as regression
  7. Step 2: Generative regression
  8. Step 3: Adversarial policy robustification (GAR)
  9. End-to-End Training and Optimization of GAR
  10. Risk Targets and Strictly Consistent Scores
  11. Remark
  12. Estimation of Generator-Implied Conditional Risk
  13. Policy Class and Alternating Min--Max Optimization
  14. Policy parameterization.
  15. Optimization (alternating stochastic min--max).
  16. ...and 10 more sections

Figures (4)

  • Figure 1: Comparison of training pipelines. (\ref{['fig:pipeline:baseline']}) Baseline framework: an unconditional generator produces scenarios that are evaluated under a fixed set of policies to obtain outcomes. (\ref{['fig:pipeline:robust']}) Proposed framework: the generator conditions on context and is trained in a min--max game against an adversarial policy, encouraging risk estimates that are robust to worst-case policies.
  • Figure 2: Training/validation score curves for two generator architectures. Each experiment is repeated five times with different random seeds. The dotted line indicates the lowest attainable in-sample score. Scores are visualized with mean (solid lines) and standard deviation (shaded areas).
  • Figure 3: Sensitivity to conditioning information at PnL-level. Kernel density estimates of PnL for two strategy classes (mean reversion, trend following) under two market conditioning sample A and B, for fixed-policy and adversarial-policy training. Bottom panels: full PnL distribution; top panels: left tail (5% quantile region).
  • Figure 4: Sensitivity to conditioning information at Trajectory-level. For each asset and time step, densities of extreme scenarios contributing to the left tail of the PnL under two conditioning samples A and B, for adversarial-policy (top rows) and fixed-policy (bottom rows) training.