mlsanityData to 7 Oct 2026

Convergence of Stochastic Proximal Gradient Algorithm

arXiv 1403.5074 ↗First posted 20 Mar 2014math.OCcited by 17

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Abstract (arXiv)

We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth component. We consider the iterates convergence and derive O(1/n) non asymptotic bounds in expectation in the strongly convex case, as well as almost sure convergence results under weaker assumptions. Our approach allows to avoid averaging and weaken boundedness assumptions which are often considered in theoretical studies and might not be satisfied in practice.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Mar 2014.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 5; 2023: 3; 2024: 5; 2025: 0; 2026: 2.

17 papers.

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  1. 2023Beyond Uniform Smoothness: A Stopped Analysis of Adaptive SGDcited by 41
  2. 2024Implicit Diffusion: Efficient Optimization through Stochastic Samplingcited by 22
  3. 2021A Bregman Learning Framework for Sparse Neural Networkscited by 15
  4. 2022A Unified Convergence Theorem for Stochastic Optimization Methodscited by 12
  5. 2022Lifted Bregman Training of Neural Networkscited by 10
  6. 2022Stochastic Zeroth order Descent with Structured Directionscited by 8
  7. 2024Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networkscited by 8
  8. 2023A Normal Map-Based Proximal Stochastic Gradient Method: Convergence and Identification Propertiescited by 5
  9. 2021Universal Regular Conditional Distributionscited by 4
  10. 2023A New Random Reshuffling Method for Nonsmooth Nonconvex Finite-sum Optimizationcited by 4
  11. 2026Sparse Training of Neural Networks based on Multilevel Mirror Descentcited by 3
  12. 2024Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Ratescited by 2
5 more
  1. 2022Sharper Bounds for Proximal Gradient Algorithms with Errorscited by 1
  2. 2022Iterative regularization in classification via hinge loss diagonal descentcited by 0
  3. 2024Stochastic First-Order Methods with Non-smooth and Non-Euclidean Proximal Terms for Nonconvex High-Dimensional Stochastic Optimizationcited by 0
  4. 2024Proximal Iteration for Nonlinear Adaptive Lassocited by 0
  5. 2026Learning Theory of the SVRG: Generalization and Convergence Analysiscited by 0