# Statistical Learning with Conditional Value at Risk

arXiv: https://arxiv.org/abs/2002.05826 · HTML: https://mlsanity.com/paper/2002.05826/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2020.

## Built on by (most cited first, 19 of 19)

- [On Tilted Losses in Machine Learning: Theory and Applications](https://mlsanity.com/paper/2109.06141/) (2021)
- [Non-convex Distributionally Robust Optimization: Non-asymptotic Analysis](https://mlsanity.com/paper/2110.12459/) (2021)
- [Off-Policy Risk Assessment in Contextual Bandits](https://mlsanity.com/paper/2104.08977/) (2021)
- [On Empirical Risk Minimization with Dependent and Heavy-Tailed Data](https://mlsanity.com/paper/2109.02224/) (2021)
- [Spectral risk-based learning using unbounded losses](https://mlsanity.com/paper/2105.04816/) (2021)
- [Risk-Averse No-Regret Learning in Online Convex Games](https://mlsanity.com/paper/2203.08957/) (2022)
- [A Model-Based Method for Minimizing CVaR and Beyond](https://mlsanity.com/paper/2305.17498/) (2023)
- [Multiplicative Reweighting for Robust Neural Network Optimization](https://mlsanity.com/paper/2102.12192/) (2021)
- [A Survey of Learning Criteria Going Beyond the Usual Risk](https://mlsanity.com/paper/2110.04996/) (2021)
- [Improved Stochastic Optimization of LogSumExp](https://mlsanity.com/paper/2509.24894/) (2025)
- [A Zeroth-Order Momentum Method for Risk-Averse Online Convex Games](https://mlsanity.com/paper/2209.02838/) (2022)
- [Distributionally Time-Varying Online Stochastic Optimization under Polyak-Lojasiewicz Condition with Application in Conditional Value-at-Risk Statistical Learning](https://mlsanity.com/paper/2309.09411/) (2023)
- [Large-Scale Non-convex Stochastic Constrained Distributionally Robust Optimization](https://mlsanity.com/paper/2404.01200/) (2024)
- [Tailoring to the Tails: Risk Measures for Fine-Grained Tail Sensitivity](https://mlsanity.com/paper/2208.03066/) (2022)
- [Risk-averse Learning with Non-Stationary Distributions](https://mlsanity.com/paper/2404.02988/) (2024)
- [Safe Collaborative Filtering](https://mlsanity.com/paper/2306.05292/) (2023)
- [Distributionally Robust Safety Verification of Neural Networks via Worst-Case CVaR](https://mlsanity.com/paper/2509.17413/) (2025)
- [Instantiating Bayesian CVaR lower bounds in Interactive Decision Making Problems](https://mlsanity.com/paper/2604.12519/) (2026)
- [Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk](https://mlsanity.com/paper/2604.18546/) (2026)

## Abstract (arXiv)

We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss. We devise algorithms based on stochastic gradient descent for this framework. While existing studies of CVaR optimization require direct access to the underlying distribution, our algorithms make a weaker assumption that only i.i.d. samples are given. For convex and Lipschitz loss functions, we show that our algorithm has O(1/√n)-convergence to the optimal CVaR, where n is the number of samples. For nonconvex and smooth loss functions, we show a generalization bound on CVaR. By conducting numerical experiments on various machine learning tasks, we demonstrate that our algorithms effectively minimize CVaR compared with other baseline algorithms.