# Spectral risk-based learning using unbounded losses

arXiv: https://arxiv.org/abs/2105.04816 · HTML: https://mlsanity.com/paper/2105.04816/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 11 May 2021.

## Builds on (most cited first, 16 of 16)

- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Optimizing the CVaR via Sampling](https://mlsanity.com/paper/1404.3862/) (2014)
- [Learning with Average Top-k Loss](https://mlsanity.com/paper/1705.08826/) (2017)
- [Adaptive Sampling for Stochastic Risk-Averse Learning](https://mlsanity.com/paper/1910.12511/) (2019)
- [Scalable Kernel Methods via Doubly Stochastic Gradients](https://mlsanity.com/paper/1407.5599/) (2014)
- [Learning Bounds for Risk-sensitive Learning](https://mlsanity.com/paper/2006.08138/) (2020)
- [Minimizing the Maximal Loss: How and Why?](https://mlsanity.com/paper/1602.01690/) (2016)
- [Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits](https://mlsanity.com/paper/1401.1123/) (2014)
- [Statistical Learning with Conditional Value at Risk](https://mlsanity.com/paper/2002.05826/) (2020)
- [Functional Gradient Boosting based on Residual Network Perception](https://mlsanity.com/paper/1802.09031/) (2018)
- [Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions](https://mlsanity.com/paper/1501.07242/) (2015)
- [Estimation of Spectral Risk Measures](https://mlsanity.com/paper/1912.10398/) (2019)
- [Learning with risks based on M-location](https://mlsanity.com/paper/2012.02424/) (2020)
- [Better scalability under potentially heavy-tailed feedback](https://mlsanity.com/paper/2012.07346/) (2020)

## Built on by (most cited first, 8 of 8)

- [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)
- [A Survey of Learning Criteria Going Beyond the Usual Risk](https://mlsanity.com/paper/2110.04996/) (2021)
- [A policy gradient approach for optimization of smooth risk measures](https://mlsanity.com/paper/2202.11046/) (2022)
- [Tailoring to the Tails: Risk Measures for Fine-Grained Tail Sensitivity](https://mlsanity.com/paper/2208.03066/) (2022)
- [OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimation](https://mlsanity.com/paper/2606.06096/) (2026)
- [SOREL: A Stochastic Algorithm for Spectral Risks Minimization](https://mlsanity.com/paper/2407.14618/) (2024)
- [Optimizing Shortfall Risk Metric for Learning Regression Models](https://mlsanity.com/paper/2505.17777/) (2025)

## Abstract (arXiv)

In this work, we consider the setting of learning problems under a wide class of spectral risk (or "L-risk") functions, where a Lipschitz-continuous spectral density is used to flexibly assign weight to extreme loss values. We obtain excess risk guarantees for a derivative-free learning procedure under unbounded heavy-tailed loss distributions, and propose a computationally efficient implementation which empirically outperforms traditional risk minimizers in terms of balancing spectral risk and misclassification error.