mlsanityData to 7 Oct 2026

Stochastic variance reduced extragradient methods for solving hierarchical variational inequalities

arXiv 2602.13510 ↗First posted 13 Feb 2026math.OC cs.GT cs.LGcited by 1

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Abstract (arXiv)

We are concerned with optimization in a broad sense through the lens of solving variational inequalities (VIs) -- a class of problems that are so general that they cover as particular cases minimization of functions, saddle-point (minimax) problems, Nash equilibrium problems, and many others. The key challenges in our problem formulation are the two-level hierarchical structure and finite-sum representation of the smooth operators in each level. For this setting, we are the first to prove convergence rates and complexity statements for variance-reduced stochastic algorithms approaching the solution of hierarchical VIs in Euclidean and Bregman setups.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 27 of its 58 references that are in the map. First posted on arXiv 13 Feb 2026.

Builds on

27 of 58 references.

References · 27

  1. 2018Bilevel Programming for Hyperparameter Optimization and Meta-Learningcited by 403
  2. 2020Bilevel Optimization: Convergence Analysis and Enhanced Designcited by 219
  3. 2019On the convergence of single-call stochastic extra-gradient methodscited by 88
  4. 2019Reducing Noise in GAN Training with Variance Reduced Extragradientcited by 61
  5. 2016Error bounds, quadratic growth, and linear convergence of proximal methodscited by 59
  6. 2016Stochastic Variance Reduction Methods for Saddle-Point Problemscited by 57
  7. 2021Stochastic Variance Reduction for Variational Inequality Methodscited by 46
  8. 2023On Finding Small Hyper-Gradients in Bilevel Optimization: Hardness Results and Improved Analysiscited by 39
  9. 2018Golden Ratio Algorithms for Variational Inequalitiescited by 38
  10. 2020Simple and optimal methods for stochastic variational inequalities, I: operator extrapolationcited by 35
  11. 2017Extragradient method with variance reduction for stochastic variational inequalitiescited by 33
  12. 2021Stability and Generalization of Bilevel Programming in Hyperparameter Optimizationcited by 31
15 more
  1. 2021Stochastic Extragradient: General Analysis and Improved Ratescited by 31
  2. 2023Projection-Free Methods for Stochastic Simple Bilevel Optimization with Convex Lower-level Problemcited by 13
  3. 2021The Last-Iterate Convergence Rate of Optimistic Mirror Descent in Stochastic Variational Inequalitiescited by 12
  4. 2022Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Surveycited by 10
  5. 2024Penalty-based Methods for Simple Bilevel Optimization under H"olderian Error Boundscited by 7
  6. 2021First-Order Methods for Convex Optimizationcited by 4
  7. 2022Stochastic Approximation for Estimating the Price of Stability in Stochastic Nash Gamescited by 2
  8. 2023Convergence of Extragradient SVRG for Variational Inequalities: Error Bounds and Increasing Iterate Averagingcited by 2
  9. 2023Improved guarantees for optimal Nash equilibrium seeking and bilevel variational inequalitiescited by 2
  10. 2025Regularized Operator Extrapolation Method For Stochastic Bilevel Variational Inequality Problemscited by 2
  11. 2013Forward-Backward and Tseng's Type Penalty Schemes for Monotone Inclusion Problemscited by 1
  12. 2021On the solution of monotone nested variational inequalitiescited by 1
  13. 2025Hierarchical Variational Inequality Problem for Noncooperative Game-Theoretic Selection of Generalized Nash Equilibriumcited by 1
  14. 2025Accelerating Diagonal Methods for Bilevel Optimization: Unified Convergence via Continuous-Time Dynamicscited by 1
  15. 2025Extragradient methods with complexity guarantees for hierarchical variational inequalitiescited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problemscited by 1