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 (VaR,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
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.
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 Sα (↓)
VaR viol. rate (%)
Train
Validation
Test
(at α=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 Sα (Boldface indicates the best value in each column) and the VaR violation rate at α=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 VaR0.05 .
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 Sα(⋅) (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.
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.
Andrey Vasilyev, Yikai Wang, Xiaocheng Li +1
Imperial College Business School, Imperial College London · Department of Statistics and Operations Research, UNC-Chapel Hill
Optimization problems routinely depend on uncertain parameters that must be predicted before a decision is made. Classical robust and regret formulations are designed to handle erroneous predictions and can provide statistical error bounds in simple settings. However, when predictions lack rigorous error bounds (as is typical of modern machine learning methods) classical robust models often yield vacuous guarantees, while regret formulations can paradoxically produce decisions that are more optimistic than even a nominal solution. We introduce Globalized Adversarial Regret Optimization (GARO), a decision framework that controls adversarial regret, defined as the gap between the worst-case cost and the oracle robust cost, uniformly across all possible uncertainty set sizes. By design, GARO delivers absolute or relative performance guarantees against an oracle with full knowledge of the prediction error, without requiring any probabilistic calibration of the uncertainty set. We show that GARO equipped with a relative rate function generalizes the classical adaptation method of Lepski to downstream decision problems. We derive exact tractable reformulations for problems with affine worst-case cost functions and polyhedral norm uncertainty sets, and provide a discretization and a constraint-generation algorithm with convergence guarantees for general settings. Finally, experiments demonstrate that GARO yields solutions with a more favorable trade-off between worst-case and mean out-of-sample performance, as well as stronger global performance guarantees.
Reliable decision making pipelines powered by machine learning models require uncertainty quantification (UQ) methods that come with explicit safety guarantees. Conformal prediction provides such UQ by wrapping ML predictions into prediction sets, and recent work by Kiyani et al. (2025b) established that these sets can be translated into optimal risk-averse decision policies -- yet only inheriting marginal safety guarantees. We generalize and strengthen their results by (i) introducing action-conditional conformal prediction, which yields safety guarantees conditioned explicitly on each action taken by the decision maker, (ii) showing that action-conditional prediction sets serve as a proxy for the feasible decision space for risk-averse decision makers aiming to optimize action-conditional value-at-risk, and (iii) proposing a principled finite-sample algorithm based on pinball-loss minimization, connecting the framework of Gibbs et al. (2025) to action-conditional guarantees. Experiments on two real-world datasets confirm that our approach significantly improves action-conditional performance over conformal baselines.