mlsanityData to 14 Oct 2026

Stochastic subgradient method converges at the rate O(k-1/4) on weakly convex functions

arXiv 1802.02988 ↗First posted 8 Feb 2018math.OC cs.LGcited by 32

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Abstract (arXiv)

We prove that the proximal stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate O(k-1/4). As a consequence, we resolve an open question on the convergence rate of the proximal stochastic gradient method for minimizing the sum of a smooth nonconvex function and a convex proximable function.

Key facts. Cited by 32 papers in the map (data through 14 Oct 2026). First posted on arXiv 8 Feb 2018.

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Citing papers per year: 2021: 8; 2022: 7; 2023: 3; 2024: 5; 2025: 4; 2026: 5.

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  2. 2021Global Convergence of Multi-Agent Policy Gradient in Markov Potential Gamescited by 93
  3. 2021A Single-Timescale Method for Stochastic Bilevel Optimizationcited by 69
  4. 2021Amortized Implicit Differentiation for Stochastic Bilevel Optimizationcited by 63
  5. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
  6. 2021Proximal and Federated Random Reshufflingcited by 33
  7. 2022When AUC meets DRO: Optimizing Partial AUC for Deep Learning with Non-Convex Convergence Guaranteecited by 29
  8. 2023Escaping limit cycles: Global convergence for constrained nonconvex-nonconcave minimax problemscited by 21
  9. 2024Plug-and-Play image restoration with Stochastic deNOising REgularizationcited by 17
  10. 2025Can SGD Handle Heavy-Tailed Noise?cited by 17
  11. 2022Large-scale Optimization of Partial AUC in a Range of False Positive Ratescited by 15
  12. 2021Outlier-Robust Sparse Estimation via Non-Convex Optimizationcited by 14
20 more
  1. 2024Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisationcited by 14
  2. 2022Weighted Distillation with Unlabeled Examplescited by 13
  3. 2023Oracle Complexity of Single-Loop Switching Subgradient Methods for Non-Smooth Weakly Convex Functional Constrained Optimizationcited by 11
  4. 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10
  5. 2022Min-Max Bilevel Multi-objective Optimization with Applications in Machine Learningcited by 9
  6. 2021Minimax Optimization with Smooth Algorithmic Adversariescited by 8
  7. 2021Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domaincited by 8
  8. 2024Provable Policy Gradient Methods for Average-Reward Markov Potential Gamescited by 5
  9. 2022Blessing of Nonconvexity in Deep Linear Models: Depth Flattens the Optimization Landscape Around the True Solutioncited by 3
  10. 2023Damped Proximal Augmented Lagrangian Method for weakly-Convex Problems with Convex Constraintscited by 2
  11. 2025Stochastic Primal-Dual Double Block-Coordinate for Two-way Partial AUC Maximizationcited by 1
  12. 2026Oracle-Robust Online Alignment for Large Language Modelscited by 1
  13. 2026Risk-Conditioned Fine-Tuning of Large Language Modelscited by 1
  14. 2022ScaLA: Accelerating Adaptation of Pre-Trained Transformer-Based Language Models via Efficient Large-Batch Adversarial Noisecited by 0
  15. 2024Stochastic First-Order Methods with Non-smooth and Non-Euclidean Proximal Terms for Nonconvex High-Dimensional Stochastic Optimizationcited by 0
  16. 2025Stochastic Weakly Convex Optimization Under Heavy-Tailed Noisescited by 0
  17. 2025The Measure of Deception: An Analysis of Data Forging in Machine Unlearningcited by 0
  18. 2026Sample Complexity Analysis for Constrained Bilevel Reinforcement Learningcited by 0
  19. 2026Global Optimality for Constrained Exploration via Penalty Regularizationcited by 0
  20. 2026The Role of Gradient Modification in Heavy-Tailed Nonconvex Stochastic Min-Max Optimizationcited by 0