Adversarially Robust Control of Conditional Value-at-Risk via Rockafellar-Uryasev Conformal Inference

Catherine Chen, Jingyan Shen, Zhun Deng, Lihua Lei
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:16581-16608, 2026.

Abstract

We present an online, distribution-free framework for controlling the Conditional Value-at-Risk ($\operatorname{CVaR}$), extending conformal tail risk control to non-stationary and adversarial environments. Unlike classical risk control methods, which rely on stationarity or linearity of expectation, our approach provides provable safety guarantees for a nonlinear tail risk functional under arbitrary data-generating processes that may drift or shift strategically over time. By leveraging deep connections between conformal tail risk control, online learning, and the variational representation of $\operatorname{CVaR}$ introduced by Rockafellar and Uryasev, we develop a novel procedure for online $\operatorname{CVaR}$ control with adversarial regret guarantees. The proposed method operates without assumptions on the underlying data-generating process, making it broadly applicable in modern high-stakes deployment settings. We prove that the realized empirical $\operatorname{CVaR}$ is asymptotically controlled at the target level, and that the resulting control is asymptotically tight up to a finite-sample ${O}(1/\sqrt{T})$ conservatism gap. We demonstrate the effectiveness of our approach on portfolio risk management and toxicity mitigation for Large Language Models (LLMs), where rare but catastrophic failures dominate system risk.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26ds, title = {Adversarially Robust Control of Conditional Value-at-Risk via Rockafellar-Uryasev Conformal Inference}, author = {Chen, Catherine and Shen, Jingyan and Deng, Zhun and Lei, Lihua}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {16581--16608}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chen26ds/chen26ds.pdf}, url = {https://proceedings.mlr.press/v306/chen26ds.html}, abstract = {We present an online, distribution-free framework for controlling the Conditional Value-at-Risk ($\operatorname{CVaR}$), extending conformal tail risk control to non-stationary and adversarial environments. Unlike classical risk control methods, which rely on stationarity or linearity of expectation, our approach provides provable safety guarantees for a nonlinear tail risk functional under arbitrary data-generating processes that may drift or shift strategically over time. By leveraging deep connections between conformal tail risk control, online learning, and the variational representation of $\operatorname{CVaR}$ introduced by Rockafellar and Uryasev, we develop a novel procedure for online $\operatorname{CVaR}$ control with adversarial regret guarantees. The proposed method operates without assumptions on the underlying data-generating process, making it broadly applicable in modern high-stakes deployment settings. We prove that the realized empirical $\operatorname{CVaR}$ is asymptotically controlled at the target level, and that the resulting control is asymptotically tight up to a finite-sample ${O}(1/\sqrt{T})$ conservatism gap. We demonstrate the effectiveness of our approach on portfolio risk management and toxicity mitigation for Large Language Models (LLMs), where rare but catastrophic failures dominate system risk.} }
Endnote
%0 Conference Paper %T Adversarially Robust Control of Conditional Value-at-Risk via Rockafellar-Uryasev Conformal Inference %A Catherine Chen %A Jingyan Shen %A Zhun Deng %A Lihua Lei %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chen26ds %I PMLR %P 16581--16608 %U https://proceedings.mlr.press/v306/chen26ds.html %V 306 %X We present an online, distribution-free framework for controlling the Conditional Value-at-Risk ($\operatorname{CVaR}$), extending conformal tail risk control to non-stationary and adversarial environments. Unlike classical risk control methods, which rely on stationarity or linearity of expectation, our approach provides provable safety guarantees for a nonlinear tail risk functional under arbitrary data-generating processes that may drift or shift strategically over time. By leveraging deep connections between conformal tail risk control, online learning, and the variational representation of $\operatorname{CVaR}$ introduced by Rockafellar and Uryasev, we develop a novel procedure for online $\operatorname{CVaR}$ control with adversarial regret guarantees. The proposed method operates without assumptions on the underlying data-generating process, making it broadly applicable in modern high-stakes deployment settings. We prove that the realized empirical $\operatorname{CVaR}$ is asymptotically controlled at the target level, and that the resulting control is asymptotically tight up to a finite-sample ${O}(1/\sqrt{T})$ conservatism gap. We demonstrate the effectiveness of our approach on portfolio risk management and toxicity mitigation for Large Language Models (LLMs), where rare but catastrophic failures dominate system risk.
APA
Chen, C., Shen, J., Deng, Z. & Lei, L.. (2026). Adversarially Robust Control of Conditional Value-at-Risk via Rockafellar-Uryasev Conformal Inference. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:16581-16608 Available from https://proceedings.mlr.press/v306/chen26ds.html.

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