mlsanityData to 7 Oct 2026

Spectral risk-based learning using unbounded losses

arXiv 2105.04816 ↗First posted 11 May 2021stat.ML cs.LGcited by 8

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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.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 16 of its 45 references that are in the map. First posted on arXiv 11 May 2021.

Builds on

16 of 45 references.

References · 16

  1. 2014Convex Optimization: Algorithms and Complexitycited by 569
  2. 2019Online Learning: A Modern Introduction Using Convex Optimizationcited by 407
  3. 2016Variance-based regularization with convex objectivescited by 153
  4. 2014Optimizing the CVaR via Samplingcited by 98
  5. 2017Learning with Average Top-k Losscited by 52
  6. 2019Adaptive Sampling for Stochastic Risk-Averse Learningcited by 39
  7. 2014Scalable Kernel Methods via Doubly Stochastic Gradientscited by 36
  8. 2020Learning Bounds for Risk-sensitive Learningcited by 33
  9. 2016Minimizing the Maximal Loss: How and Why?cited by 30
  10. 2014Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Banditscited by 26
  11. 2020Statistical Learning with Conditional Value at Riskcited by 19
  12. 2018Functional Gradient Boosting based on Residual Network Perceptioncited by 14
4 more
  1. 2015Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functionscited by 9
  2. 2019Estimation of Spectral Risk Measurescited by 9
  3. 2020Learning with risks based on M-locationcited by 6
  4. 2020Better scalability under potentially heavy-tailed feedbackcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 0; 2024: 1; 2025: 1; 2026: 1.

8 papers.

  1. 2022Stochastic Optimization for Spectral Risk Measurescited by 7
  2. 2022Supervised Learning with General Risk Functionalscited by 6
  3. 2021A Survey of Learning Criteria Going Beyond the Usual Riskcited by 4
  4. 2022A policy gradient approach for optimization of smooth risk measurescited by 2
  5. 2022Tailoring to the Tails: Risk Measures for Fine-Grained Tail Sensitivitycited by 2
  6. 2026OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimationcited by 1
  7. 2024SOREL: A Stochastic Algorithm for Spectral Risks Minimizationcited by 0
  8. 2025Optimizing Shortfall Risk Metric for Learning Regression Modelscited by 0