mlsanityData to 14 Oct 2026

Asymptotic normality and optimality in nonsmooth stochastic approximation

arXiv 2301.06632 ↗First posted 16 Jan 2023math.OC math.ST stat.MLcited by 14

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Abstract (arXiv)

In their seminal work, Polyak and Juditsky showed that stochastic approximation algorithms for solving smooth equations enjoy a central limit theorem. Moreover, it has since been argued that the asymptotic covariance of the method is best possible among any estimation procedure in a local minimax sense of H'ajek and Le Cam. A long-standing open question in this line of work is whether similar guarantees hold for important non-smooth problems, such as stochastic nonlinear programming or stochastic variational inequalities. In this work, we show that this is indeed the case.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Builds on 7 of its 39 references that are in the map. First posted on arXiv 16 Jan 2023.

Builds on

7 of 39 references.

References · 7

  1. 2018Stochastic subgradient method converges on tame functionscited by 124
  2. 2018Stochastic (Approximate) Proximal Point Methods: Convergence, Optimality, and Adaptivitycited by 61
  3. 2016Asymptotic Optimality in Stochastic Optimizationcited by 38
  4. 2019Stochastic algorithms with geometric step decay converge linearly on sharp functionscited by 14
  5. 2022Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimalitycited by 12
  6. 2021Active manifolds, stratifications, and convergence to local minima in nonsmooth optimizationcited by 11
  7. 2015Generic minimizing behavior in semi-algebraic optimizationcited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 3; 2025: 6; 2026: 2.

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  1. 2023Online covariance estimation for stochastic gradient descent under Markovian samplingcited by 7
  2. 2023High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariancecited by 6
  3. 2025Online Covariance Estimation in Nonsmooth Stochastic Approximationcited by 4
  4. 2025Stopping Rules for Stochastic Gradient Descent via Anytime-Valid Confidence Sequencescited by 4
  5. 2024The Stochastic Conjugate Subgradient Algorithm For Kernel Support Vector Machinescited by 3
  6. 2025Stochastic Optimization with Optimal Importance Samplingcited by 2
  7. 2025Statistical Inference for Online Algorithmscited by 2
  8. 2023Statistical Inference for Linear Functionals of Online SGD in High-dimensional Linear Regressioncited by 1
  9. 2024Stochastic Optimization with Constraints: A Non-asymptotic Instance-Dependent Analysiscited by 1
  10. 2024The radius of statistical efficiencycited by 1
  11. 2025Statistical Inference for Linear Functionals of Online Least-squares SGD when t gtrsim d1+δcited by 1
  12. 2026Non-Asymptotic Convergence of Stochastic Iterative Algorithms: A Lyapunov Frameworkcited by 1
2 more
  1. 2025Online Statistical Inference of Constrained Stochastic Optimization via Random Scalingcited by 0
  2. 2026Local linear convergence of gradient methods for overparameterized Gaussian mixturescited by 0