mlsanityData to 13 Oct 2026

Proximally Guided Stochastic Subgradient Method for Nonsmooth, Nonconvex Problems

arXiv 1707.03505 ↗First posted 12 Jul 2017math.OC cs.LGcited by 30

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Abstract (arXiv)

In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes. At a high-level, the method is an inexact proximal point iteration in which the strongly convex proximal subproblems are quickly solved with a specialized stochastic projected subgradient method. The primary contribution of this paper is a simple proof that the proposed algorithm converges at the same rate as the stochastic gradient method for smooth nonconvex problems. This result appears to be the first convergence rate analysis of a stochastic (or even deterministic) subgradient method for the class of weakly convex functions.

Key facts. Cited by 30 papers in the map (data through 13 Oct 2026). First posted on arXiv 12 Jul 2017.

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 4; 2022: 4; 2023: 5; 2024: 7; 2025: 4; 2026: 6.

30 papers.

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  1. 2021Differentially Private Stochastic Optimization: New Results in Convex and Non-Convex Settingscited by 45
  2. 2021Stability and Convergence of Stochastic Gradient Clipping: Beyond Lipschitz Continuity and Smoothnesscited by 37
  3. 2024Towards Certified Unlearning for Deep Neural Networkscited by 30
  4. 2022Large-scale Optimization of Partial AUC in a Range of False Positive Ratescited by 15
  5. 2022Bridging Differential Privacy and Byzantine-Robustness via Model Aggregationcited by 12
  6. 2023Oracle Complexity of Single-Loop Switching Subgradient Methods for Non-Smooth Weakly Convex Functional Constrained Optimizationcited by 11
  7. 2024Taming Nonconvex Stochastic Mirror Descent with General Bregman Divergencecited by 11
  8. 2023Non-Smooth Weakly-Convex Finite-sum Coupled Compositional Optimizationcited by 10
  9. 2024Independent Learning in Constrained Markov Potential Gamescited by 10
  10. 2024Projected gradient methods for nonconvex and stochastic smooth optimization: new complexities and auto-conditioned stepsizescited by 6
  11. 2025Single-loop Algorithms for Stochastic Non-convex Optimization with Weakly-Convex Constraintscited by 5
  12. 2022Learning Proximal Operators to Discover Multiple Optimacited by 4
18 more
  1. 2023Differentially Private Non-Convex Optimization under the KL Condition with Optimal Ratescited by 4
  2. 2024Single-Loop Stochastic Algorithms for Difference of Max-Structured Weakly Convex Functionscited by 4
  3. 2024Stochastic Weakly Convex Optimization Beyond Lipschitz Continuitycited by 3
  4. 2021Coordinate Descent Methods for DC Minimization: Optimality Conditions and Global Convergencecited by 2
  5. 2022Coordinate Descent Methods for Fractional Minimizationcited by 2
  6. 2023Damped Proximal Augmented Lagrangian Method for weakly-Convex Problems with Convex Constraintscited by 2
  7. 2026Finding a stationary point of a stochastic convex problemcited by 2
  8. 2026Musec: MomentUm SpEctral Clipping for Stable Muon-type Trainingcited by 2
  9. 2025Stochastic Primal-Dual Double Block-Coordinate for Two-way Partial AUC Maximizationcited by 1
  10. 2026Singularity-aware Optimization via Randomized Geometric Probing: Towards Stable Non-smooth Optimizationcited by 1
  11. 2021Robust Regression via Model Based Methodscited by 0
  12. 2023Some Primal-Dual Theory for Subgradient Methods for Strongly Convex Optimizationcited by 0
  13. 2024On the Hardness of Meaningful Local Guarantees in Nonsmooth Nonconvex Optimizationcited by 0
  14. 2025Learning-Based Surrogate Method for Stochastic Optimization under Decision-Dependent Uncertainty with Adaptive Random Designscited by 0
  15. 2025Stochastic Momentum Methods for Non-smooth Non-Convex Finite-Sum Coupled Compositional Optimizationcited by 0
  16. 2026Global Optimality for Constrained Exploration via Penalty Regularizationcited by 0
  17. 2026Zeroth-Order Nonconvex Nonsmooth Optimization with Heavy-Tailed Noisecited by 0
  18. 2026A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Lojasiewicz conditioncited by 0