# Learning Bounds for Risk-sensitive Learning

arXiv: https://arxiv.org/abs/2006.08138 · HTML: https://mlsanity.com/paper/2006.08138/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 30 of 33)

- [Probable Domain Generalization via Quantile Risk Minimization](https://mlsanity.com/paper/2207.09944/) (2022)
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- [Off-Policy Risk Assessment in Contextual Bandits](https://mlsanity.com/paper/2104.08977/) (2021)
- [Rank-based Decomposable Losses in Machine Learning: A Survey](https://mlsanity.com/paper/2207.08768/) (2022)
- [Understanding Contrastive Learning via Distributionally Robust Optimization](https://mlsanity.com/paper/2310.11048/) (2023)
- [Almost Optimal Variance-Constrained Best Arm Identification](https://mlsanity.com/paper/2201.10142/) (2022)
- [Regret Bounds for Markov Decision Processes with Recursive Optimized Certainty Equivalents](https://mlsanity.com/paper/2301.12601/) (2023)
- [Quantile Risk Control: A Flexible Framework for Bounding the Probability of High-Loss Predictions](https://mlsanity.com/paper/2212.13629/) (2022)
- [Conformal Risk Training: End-to-End Optimization of Conformal Risk Control](https://mlsanity.com/paper/2510.08748/) (2025)
- [A Unifying Theory of Thompson Sampling for Continuous Risk-Averse Bandits](https://mlsanity.com/paper/2108.11345/) (2021)
- [Spectral risk-based learning using unbounded losses](https://mlsanity.com/paper/2105.04816/) (2021)
- [Stochastic Optimization for Spectral Risk Measures](https://mlsanity.com/paper/2212.05149/) (2022)
- [Supervised Learning with General Risk Functionals](https://mlsanity.com/paper/2206.13648/) (2022)
- [Towards Efficient Risk-Sensitive Policy Gradient: An Iteration Complexity Analysis](https://mlsanity.com/paper/2403.08955/) (2024)
- [Pessimism Meets Risk: Risk-Sensitive Offline Reinforcement Learning](https://mlsanity.com/paper/2407.07631/) (2024)
- [Risk-Aware Learning for Scalable Voltage Optimization in Distribution Grids](https://mlsanity.com/paper/2110.01490/) (2021)
- [Online Estimation and Optimization of Utility-Based Shortfall Risk](https://mlsanity.com/paper/2111.08805/) (2021)
- [A Survey of Learning Criteria Going Beyond the Usual Risk](https://mlsanity.com/paper/2110.04996/) (2021)
- [Revisiting adversarial training for the worst-performing class](https://mlsanity.com/paper/2302.08872/) (2023)
- [Generalization and Robustness of the Tilted Empirical Risk](https://mlsanity.com/paper/2409.19431/) (2024)
- [Flexible risk design using bi-directional dispersion](https://mlsanity.com/paper/2203.14434/) (2022)
- [Soft ascent-descent as a stable and flexible alternative to flooding](https://mlsanity.com/paper/2310.10006/) (2023)
- [Thompson Sampling for Gaussian Entropic Risk Bandits](https://mlsanity.com/paper/2105.06960/) (2021)
- [Concentration Bounds for Optimized Certainty Equivalent Risk Estimation](https://mlsanity.com/paper/2405.20933/) (2024)
- [Neural Network Pruning Through Constrained Reinforcement Learning](https://mlsanity.com/paper/2110.08558/) (2021)
- [Robust Federated Learning with Global Sensitivity Estimation for Financial Risk Management](https://mlsanity.com/paper/2502.17694/) (2025)
- [PAC-Bayesian Bounds on Constrained f-Entropic Risk Measures](https://mlsanity.com/paper/2510.11169/) (2025)
- [Robust variance-regularized risk minimization with concomitant scaling](https://mlsanity.com/paper/2301.11584/) (2023)
- [Criterion Collapse and Loss Distribution Control](https://mlsanity.com/paper/2402.09802/) (2024)
- [Making Robust Generalizers Less Rigid with Loss Concentration](https://mlsanity.com/paper/2408.03619/) (2024)

## Abstract (arXiv)

In risk-sensitive learning, one aims to find a hypothesis that minimizes a risk-averse (or risk-seeking) measure of loss, instead of the standard expected loss. In this paper, we propose to study the generalization properties of risk-sensitive learning schemes whose optimand is described via optimized certainty equivalents (OCE): our general scheme can handle various known risks, e.g., the entropic risk, mean-variance, and conditional value-at-risk, as special cases. We provide two learning bounds on the performance of empirical OCE minimizer. The first result gives an OCE guarantee based on the Rademacher average of the hypothesis space, which generalizes and improves existing results on the expected loss and the conditional value-at-risk. The second result, based on a novel variance-based characterization of OCE, gives an expected loss guarantee with a suppressed dependence on the smoothness of the selected OCE. Finally, we demonstrate the practical implications of the proposed bounds via exploratory experiments on neural networks.