mlsanityData to 7 Oct 2026

Graphical Convergence of Subgradients in Nonconvex Optimization and Learning

arXiv 1810.07590 ↗First posted 17 Oct 2018math.OC cs.LGcited by 17

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Abstract (arXiv)

We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such losses. We analyze the estimation quality of such nonsmooth and nonconvex problems by their sample average approximations. Our main results establish dimension-dependent rates on subgradient estimation in full generality and dimension-independent rates when the loss is a generalized linear model. As an application of the developed techniques, we analyze the nonsmooth landscape of a robust nonlinear regression problem.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Oct 2018.

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Citing papers per year: 2021: 3; 2022: 4; 2023: 0; 2024: 3; 2025: 3; 2026: 4.

17 papers.

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  1. 2022Stability and Generalization of Stochastic Optimization with Nonconvex and Nonsmooth Problemscited by 25
  2. 2021Sign-RIP: A Robust Restricted Isometry Property for Low-rank Matrix Recoverycited by 10
  3. 2022Generalization Bounds of Nonconvex-(Strongly)-Concave Stochastic Minimax Optimizationcited by 6
  4. 2022PAC-Bayesian Learning of Optimization Algorithmscited by 4
  5. 2024On the Uniform Convergence of Subdifferentials in Stochastic Optimization and Learningcited by 3
  6. 2025Failure of uniform laws of large numbers for subdifferentials and beyondcited by 3
  7. 2026Finding a stationary point of a stochastic convex problemcited by 2
  8. 2021Improved Learning Rates for Stochastic Optimizationcited by 0
  9. 2021Learning Rates for Nonconvex Pairwise Learningcited by 0
  10. 2022Consistent Approximations in Composite Optimizationcited by 0
  11. 2024Loss Gradient Gaussian Width based Generalization and Optimization Guaranteescited by 0
  12. 2024Towards Sharper Risk Bounds for Minimax Problemscited by 0
5 more
  1. 2025Stability-based Generalization Analysis of Randomized Coordinate Descent for Pairwise Learningcited by 0
  2. 2025Unregularized limit of stochastic gradient method for Wasserstein distributionally robust optimizationcited by 0
  3. 2026Stability and Generalization of Stochastic Nonconvex Optimization under Heavy-Tailed Noise: From Gradient Norm to Goldstein Stationaritycited by 0
  4. 2026Unveiling High-Probability Generalization in Decentralized SGDcited by 0
  5. 2026Lipschitzian SLLNs for random functionscited by 0