![[2602.18053] On the Generalization and Robustness in Conditional Value-at-Risk](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2602.18053] On the Generalization and Robustness in Conditional Value-at-Risk
Summary
This paper explores the generalization and robustness of Conditional Value-at-Risk (CVaR) in the context of heavy-tailed data, providing theoretical insights and practical implications for risk-sensitive learning.
Why It Matters
Understanding CVaR's behavior under heavy-tailed conditions is crucial for developing robust machine learning models, especially in finance and risk management. This research offers foundational insights that can improve decision-making processes in scenarios involving rare but significant losses.
Key Takeaways
- CVaR's statistical behavior under heavy-tailed data is not well understood, impacting risk-sensitive learning.
- The paper establishes generalization and excess risk bounds for CVaR-based empirical risk minimization.
- A new truncated median-of-means CVaR estimator is proposed, achieving optimal robustness under contamination.
- CVaR decisions can be unstable under heavy tails, highlighting limitations in decision robustness.
- The study provides a framework for understanding when CVaR learning is robust and when instability is unavoidable.
Statistics > Machine Learning arXiv:2602.18053 (stat) [Submitted on 20 Feb 2026] Title:On the Generalization and Robustness in Conditional Value-at-Risk Authors:Dinesh Karthik Mulumudi, Piyushi Manupriya, Gholamali Aminian, Anant Raj View a PDF of the paper titled On the Generalization and Robustness in Conditional Value-at-Risk, by Dinesh Karthik Mulumudi and 3 other authors View PDF HTML (experimental) Abstract:Conditional Value-at-Risk (CVaR) is a widely used risk-sensitive objective for learning under rare but high-impact losses, yet its statistical behavior under heavy-tailed data remains poorly understood. Unlike expectation-based risk, CVaR depends on an endogenous, data-dependent quantile, which couples tail averaging with threshold estimation and fundamentally alters both generalization and robustness properties. In this work, we develop a learning-theoretic analysis of CVaR-based empirical risk minimization under heavy-tailed and contaminated data. We establish sharp, high-probability generalization and excess risk bounds under minimal moment assumptions, covering fixed hypotheses, finite and infinite classes, and extending to $\beta$-mixing dependent data; we further show that these rates are minimax optimal. To capture the intrinsic quantile sensitivity of CVaR, we derive a uniform Bahadur-Kiefer type expansion that isolates a threshold-driven error term absent in mean-risk ERM and essential in heavy-tailed regimes. We complement these results with robustness g...