Generative Adversarial Regression (GAR): Learning Conditional Risk Scenarios

Saeed Asadi; Jonathan Yu-Meng Li

stat.MLMar 9, 2026

Generative Adversarial Regression (GAR): Learning Conditional Risk Scenarios

Authors: Saeed Asadi, Jonathan Yu-Meng Li

Organizations: Telfer School of Management University of Ottawa

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.

Figures & tables

Panel of Figure 1 — Figure 1: Comparison of training pipelines. ( 1(a) ) Baseline framework: an unconditional generator produces scenarios that are evaluated under a fixed set of policies to obtain outcomes. ( 1(b) ) 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.

Panel of Figure 2 — 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).

Model	VaR–ES score $S_{\alpha}$ (↓)			VaR viol. rate (%)
Model	Train	Validation	Test	(at $\alpha=5\%$ )
Unconditional	$-3.747$	$-3.806$	$-3.765$	$1.2$
DCC–GARCH	$-3.545$	$-3.754$	$-3.774$	$14.8$
Direct	$-3.669$	$-3.744$	$-3.760$	$1.5$
Encoder–LSTM	-3.932	-3.950	-3.929	$6.6$
Encoder–Linear	$-3.911$	$-3.922$	$-3.920$	$2.5$

Table 1: Comparison of conditional generators and baselines on the joint VaR–ES score

S_{\alpha}

(Boldface indicates the best value in each column) and the VaR violation rate at

\alpha=5\%

(closer to

5\%

indicates better calibration). The violation rate is the fraction of periods in which the realized PnL falls below the model’s

\mathrm{VaR}_{0.05}

		Training Phase		Evaluation Phase
		Train	Validation	Benchmark	Worst-Case
Encoder-LSTM	Adversarial	-3.864	-3.885	-3.921	-3.888
	Fixed	-3.932	-3.950	-3.929	-3.558
Encoder-Linear	Adversarial	-3.762	-3.806	-3.921	-3.781
	Fixed	-3.911	-3.922	-3.920	-1.349
Simple-Linear	Adversarial	-3.799	-3.858	-3.855	-3.761

Table 2: Performance of conditional generators under Fixed and Adversarial training using the joint VaR–ES score

S_{\alpha}(\cdot)

(lower is better). Columns under Training Phase report train/validation scores obtained during each model’s own training regime (fixed-policy objective ( 7 ) for Fixed , min–max objective ( 8 ) for Adversarial ). Columns under Evaluation Phase report test scores under benchmark (mean-reversion and trend-following) and worst-case strategies. Boldface in the Evaluation Phase highlights the better value (lower score) between Fixed and Adversarial for each architecture.

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.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

	Configuration	Values
Optimization	Initial learning rate	$10^{-10}$
	Learning rate schedule	OneCycleLR ( Smith and Topin, 2017 )
	Batch size	128
	Optimization algorithm	Adam ( Kingma and Ba, 2017 )
Data setup	Number of assets	9
	Conditioning window length	5

Appendix

Table 3: Model and experiment configuration details.

Adversarial Scenario Generation

Adversarial scenario generation creates challenging, targeted situations to expose weaknesses and improve the robustness of AI systems.

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Calibrating conditional risk

Andrey Vasilyev, Yikai Wang, Xiaocheng Li, Guanting Chen

Imperial College Business School, Imperial College London · Department of Statistics and Operations Research, UNC-Chapel Hill

Open paper AskPDF arXiv

We introduce and study the problem of calibrating conditional risk, which involves estimating the expected loss of a prediction model conditional on input features. We analyze this problem in both classification and regression settings and show that it is fundamentally equivalent to a standard regression task. For classification settings, we further establish a connection between conditional risk calibration and individual/conditional probability calibration, and develop theoretical insights for the performance metric. This reveals that while conditional risk calibration is related to existing uncertainty quantification problems, it remains a distinct and standalone machine learning problem. Empirically, we validate our theoretical findings and demonstrate the practical implications of conditional risk calibration in the learning to defer (L2D) framework. Our systematic experiments provide both qualitative and quantitative assessments, offering guidance for future research in uncertainty-aware decision-making.

Abstract

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