mlsanityData to 7 Oct 2026

Algorithms of Robust Stochastic Optimization Based on Mirror Descent Method

arXiv 1907.02707 ↗First posted 5 Jul 2019math.ST math.OC stat.THcited by 32

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Abstract (arXiv)

We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds under weak assumptions about the tails of the noise distribution in convex and strongly convex settings. Robust estimates of the accuracy of general stochastic algorithms are also proposed.

Key facts. Cited by 32 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Jul 2019.

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Citing papers per year: 2021: 5; 2022: 7; 2023: 5; 2024: 5; 2025: 5; 2026: 5.

32 papers.

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  1. 2023High Probability Convergence of Stochastic Gradient Methodscited by 48
  2. 2024From Gradient Clipping to Normalization for Heavy Tailed SGDcited by 48
  3. 2021Convergence Rates of Stochastic Gradient Descent under Infinite Noise Variancecited by 34
  4. 2022Mirror Descent Strikes Again: Optimal Stochastic Convex Optimization under Infinite Noise Variancecited by 22
  5. 2022Stochastic linear optimization never overfits with quadratically-bounded losses on general datacited by 16
  6. 2022Nonlinear gradient mappings and stochastic optimization: A general framework with applications to heavy-tail noisecited by 16
  7. 2022Clipped Stochastic Methods for Variational Inequalities with Heavy-Tailed Noisecited by 13
  8. 2025Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under (L0, L1)-Smoothnesscited by 12
  9. 2024The Price of Adaptivity in Stochastic Convex Optimizationcited by 11
  10. 2024Taming Nonconvex Stochastic Mirror Descent with General Bregman Divergencecited by 11
  11. 2021Heavy-tailed Streaming Statistical Estimationcited by 10
  12. 2023Clip21: Error Feedback for Gradient Clippingcited by 10
20 more
  1. 2022High Probability Bounds for Stochastic Subgradient Schemes with Heavy Tailed Noisecited by 9
  2. 2022Large deviations rates for stochastic gradient descent with strongly convex functionscited by 9
  3. 2023Differentially Private Stochastic Convex Optimization in (Non)-Euclidean Space Revisitedcited by 8
  4. 2023General Tail Bounds for Non-Smooth Stochastic Mirror Descentcited by 7
  5. 2025Efficient Distributed Optimization under Heavy-Tailed Noisecited by 7
  6. 2021Robust Online Convex Optimization in the Presence of Outlierscited by 4
  7. 2022Flexible risk design using bi-directional dispersioncited by 3
  8. 2023Robust Stochastic Optimization via Gradient Quantile Clippingcited by 3
  9. 2025Stochastic Bilevel Optimization with Heavy-Tailed Noisecited by 3
  10. 2025Second-order Optimization under Heavy-Tailed Noise: Hessian Clipping and Sample Complexity Limitscited by 3
  11. 2026Why is Normalization Preferred? A Worst-Case Complexity Theory for Stochastically Preconditioned SGD under Heavy-Tailed Noisecited by 2
  12. 2021Parameter-free Gradient Temporal Difference Learningcited by 1
  13. 2024Variance Reduction and Low Sample Complexity in Stochastic Optimization via Proximal Point Methodcited by 1
  14. 2026Shuffling the Stochastic Mirror Descent via Dual Lipschitz Continuity and Kernel Conditioningcited by 1
  15. 2021Robust learning with anytime-guaranteed feedbackcited by 0
  16. 2024Making Robust Generalizers Less Rigid with Loss Concentrationcited by 0
  17. 2025Stress-Aware Learning under KL Drift via Trust-Decayed Mirror Descentcited by 0
  18. 2026Stability and Generalization of Stochastic Nonconvex Optimization under Heavy-Tailed Noise: From Gradient Norm to Goldstein Stationaritycited by 0
  19. 2026Asynchronous Heavy-Tailed Optimizationcited by 0
  20. 2026Online Distributional Prediction via Latent Cluster Geometry Under Drift and Corruptioncited by 0