mlsanityData to 7 Oct 2026

Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

arXiv 1706.04957 ↗First posted 15 Jun 2017math.OC cs.CV cs.NAcited by 29

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Abstract (arXiv)

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Jun 2017.

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Citing papers per year: 2021: 10; 2022: 6; 2023: 6; 2024: 5; 2025: 2.

29 papers.

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  1. 2021Stochastic Variance Reduction for Variational Inequality Methodscited by 46
  2. 2022Sharper Rates for Separable Minimax and Finite Sum Optimization via Primal-Dual Extragradient Methodscited by 14
  3. 2021Variance Reduction via Primal-Dual Accelerated Dual Averaging for Nonsmooth Convex Finite-Sumscited by 10
  4. 2021Coordinate Linear Variance Reduction for Generalized Linear Programmingcited by 10
  5. 2021A Continuous-time Stochastic Gradient Descent Method for Continuous Datacited by 7
  6. 2025Deep Equilibrium models for Poisson Imaging Inverse problems via Mirror Descentcited by 7
  7. 2022On the Complexity of a Practical Primal-Dual Coordinate Methodcited by 6
  8. 2023Empirical Risk Minimization with Shuffled SGD: A Primal-Dual Perspective and Improved Boundscited by 6
  9. 2023Towards a Better Theoretical Understanding of Independent Subnetwork Trainingcited by 6
  10. 2022Fast Kernel Methods for Generic Lipschitz Losses via p-Sparsified Sketchescited by 5
  11. 2021Stochastic Primal-Dual Deep Unrollingcited by 4
  12. 2021A Stochastic Bregman Primal-Dual Splitting Algorithm for Composite Optimizationcited by 4
17 more
  1. 2021Cyclic Coordinate Dual Averaging with Extrapolationcited by 3
  2. 2023Accelerated Cyclic Coordinate Dual Averaging with Extrapolation for Composite Convex Optimizationcited by 3
  3. 2023Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methodscited by 2
  4. 2024A primal-dual algorithm for image reconstruction with input-convex neural network regularizerscited by 2
  5. 2024Learning a Single Neuron Robustly to Distributional Shifts and Adversarial Label Noisecited by 2
  6. 2021WARPd: A linearly convergent first-order method for inverse problems with approximate sharpness conditionscited by 1
  7. 2021Nearly Optimal Linear Convergence of Stochastic Primal-Dual Methods for Linear Programmingcited by 1
  8. 2022Semi-Implicit Hybrid Gradient Methods with Application to Adversarial Robustnesscited by 1
  9. 2023Enhanced Federated Optimization: Adaptive Unbiased Client Sampling with Reduced Variancecited by 1
  10. 2023Fast Minimization of Expected Logarithmic Loss via Stochastic Dual Averagingcited by 1
  11. 2024Hypergraph p-Laplacian regularization on point clouds for data interpolationcited by 1
  12. 2024Hypergraph p-Laplacian equations for data interpolation and semi-supervised learningcited by 1
  13. 2021Accelerated nonlinear primal-dual hybrid gradient methods with applications to supervised machine learningcited by 0
  14. 2022Operator Sketching for Deep Unrolling Networkscited by 0
  15. 2022Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoisingcited by 0
  16. 2024Stochastic First-Order Methods with Non-smooth and Non-Euclidean Proximal Terms for Nonconvex High-Dimensional Stochastic Optimizationcited by 0
  17. 2025Multi-Timescale Primal Dual Hybrid Gradient with Application to Distributed Optimizationcited by 0