mlsanityData to 7 Oct 2026

UniXGrad: A Universal, Adaptive Algorithm with Optimal Guarantees for Constrained Optimization

arXiv 1910.13857 ↗First posted 30 Oct 2019math.OC cs.LGcited by 56

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Abstract (arXiv)

We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, simultaneously achieves the optimal rates for smooth/non-smooth problems with either deterministic/stochastic first-order oracles. This is done without any prior knowledge of the smoothness nor the noise properties of the problem. To the best of our knowledge, this is the first adaptive, unified algorithm that achieves the optimal rates in the constrained setting. We demonstrate the practical performance of our framework through extensive numerical experiments.

Key facts. Cited by 56 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Oct 2019.

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Citing papers per year: 2021: 4; 2022: 11; 2023: 7; 2024: 11; 2025: 14; 2026: 9.

56 papers.

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  1. 2024The Road Less Scheduledcited by 158
  2. 2023Prodigy: An Expeditiously Adaptive Parameter-Free Learnercited by 129
  3. 2022The Power of Adaptivity in SGD: Self-Tuning Step Sizes with Unbounded Gradients and Affine Variancecited by 60
  4. 2022Making SGD Parameter-Freecited by 50
  5. 2022High Probability Bounds for a Class of Nonconvex Algorithms with AdaGrad Stepsizecited by 40
  6. 2023DoWG Unleashed: An Efficient Universal Parameter-Free Gradient Descent Methodcited by 35
  7. 2023Parameter-Agnostic Optimization under Relaxed Smoothnesscited by 29
  8. 2023Two Sides of One Coin: the Limits of Untuned SGD and the Power of Adaptive Methodscited by 23
  9. 2021No-Regret Dynamics in the Fenchel Game: A Unified Framework for Algorithmic Convex Optimizationcited by 20
  10. 2022No-Regret Learning in Games with Noisy Feedback: Faster Rates and Adaptivity via Learning Rate Separationcited by 17
  11. 2022Nest Your Adaptive Algorithm for Parameter-Agnostic Nonconvex Minimax Optimizationcited by 16
  12. 2022Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimizationcited by 15
38 more
  1. 2024General framework for online-to-nonconvex conversion: Schedule-free SGD is also effective for nonconvex optimizationcited by 14
  2. 2021Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solutioncited by 13
  3. 2022On the Convergence of AdaGrad(Norm) on Rd: Beyond Convexity, Non-Asymptotic Rate and Accelerationcited by 13
  4. 2024Tuning-Free Stochastic Optimizationcited by 13
  5. 2024How Free is Parameter-Free Stochastic Optimization?cited by 12
  6. 2025SGD with Adaptive Preconditioning: Unified Analysis and Momentum Accelerationcited by 12
  7. 2024The Price of Adaptivity in Stochastic Convex Optimizationcited by 11
  8. 2024Fully Unconstrained Online Learningcited by 10
  9. 2022Extra-Newton: A First Approach to Noise-Adaptive Accelerated Second-Order Methodscited by 8
  10. 2024Adaptive and Optimal Second-order Optimistic Methods for Minimax Optimizationcited by 8
  11. 2022TiAda: A Time-scale Adaptive Algorithm for Nonconvex Minimax Optimizationcited by 7
  12. 2021Learning Under Delayed Feedback: Implicitly Adapting to Gradient Delayscited by 6
  13. 2025Analysis of an Idealized Stochastic Polyak Method and its Application to Black-Box Model Distillationcited by 5
  14. 2025Gradient-Variation Online Adaptivity for Accelerated Optimization with H"older Smoothnesscited by 5
  15. 2025A Tale of Two Geometries: Adaptive Optimizers and Non-Euclidean Descentcited by 5
  16. 2026Improved Dimension Dependence for Bandit Convex Optimization with Gradient Variationscited by 5
  17. 2021Adaptive first-order methods revisited: Convex optimization without Lipschitz requirementscited by 4
  18. 2022Adaptive Accelerated (Extra-)Gradient Methods with Variance Reductioncited by 4
  19. 2023SLowcal-SGD: Slow Query Points Improve Local-SGD for Stochastic Convex Optimizationcited by 4
  20. 2023μ2-SGD: Stable Stochastic Optimization via a Double Momentum Mechanismcited by 4
  21. 2025Nesterov Finds GRAAL: Optimal and Adaptive Gradient Method for Convex Optimizationcited by 4
  22. 2022Optimistic Optimisation of Composite Objective with Exponentiated Updatecited by 3
  23. 2024Fault Tolerant ML: Efficient Meta-Aggregation and Synchronous Trainingcited by 3
  24. 2024Private and Federated Stochastic Convex Optimization: Efficient Strategies for Centralized Systemscited by 3
  25. 2025Improving Online-to-Nonconvex Conversion for Smooth Optimization via Double Optimismcited by 3
  26. 2025Parameter-free Algorithms for the Stochastically Extended Adversarial Modelcited by 3
  27. 2023Distributed Extra-gradient with Optimal Complexity and Communication Guaranteescited by 2
  28. 2025Weight for Robustness: A Comprehensive Approach towards Optimal Fault-Tolerant Asynchronous MLcited by 2
  29. 2026Optimistic Dual Averaging Unifies Modern Optimizerscited by 2
  30. 2024Tracking solutions of time-varying variational inequalitiescited by 1
  31. 2024Towards Simple and Provable Parameter-Free Adaptive Gradient Methodscited by 1
  32. 2025Enhancing Parallelism in Decentralized Stochastic Convex Optimizationcited by 1
  33. 2025Privacy-Preserving Federated Convex Optimization: Balancing Partial-Participation and Efficiency via Noise Cancellationcited by 1
  34. 2025Online Learning-guided Learning Rate Adaptation via Gradient Alignmentcited by 1
  35. 2025Optimistic Online-to-Batch Conversions for Accelerated Convergence and Universalitycited by 1
  36. 2026Randomized Feasibility Methods for Constrained Optimization with Adaptive Step Sizescited by 1
  37. 2026Optimal Projection-Free Adaptive SGD for Matrix Optimizationcited by 1
  38. 2026Online Learning with Gradient-Variation Interval Regretcited by 1

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