mlsanityData to 7 Oct 2026

Convergence of sequences: a survey

arXiv 2111.11374 ↗First posted 22 Nov 2021math.OC cs.MAcited by 10

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Abstract (arXiv)

Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an overview of the literature on convergence theorems and their connection with Fejer monotonicity in the deterministic and stochastic settings, and we show how to exploit these results.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Nov 2021.

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Citing papers per year: 2022: 2; 2023: 3; 2024: 3; 2025: 2.

10 papers.

  1. 2023Convergence Rates for Stochastic Approximation: Biased Noise with Unbounded Variance, and Applicationscited by 15
  2. 2022Convergence of Stochastic Approximation via Martingale and Converse Lyapunov Methodscited by 8
  3. 2024A quantitative Robbins-Siegmund theoremcited by 4
  4. 2023Convergence of the Stochastic Heavy Ball Method With Approximate Gradients and/or Block Updatingcited by 2
  5. 2023Distributed Bayesian Estimation in Sensor Networks: Consensus on Marginal Densitiescited by 1
  6. 2024A Mathematical Model of the Hidden Feedback Loop Effect in Machine Learning Systemscited by 1
  7. 2024Solving Hidden Monotone Variational Inequalities with Surrogate Lossescited by 1
  8. 2025An abstract effective convergence theorem for stochastic processes, with applications to stochastic approximationcited by 1
  9. 2022Convergence of Batch Updating Methods with Approximate Gradients and/or Noisy Measurements: Theory and Computational Resultscited by 0
  10. 2025Convergence of Momentum-Based Optimization Algorithms with Time-Varying Parameterscited by 0