# Convergence of sequences: a survey

arXiv: https://arxiv.org/abs/2111.11374 · HTML: https://mlsanity.com/paper/2111.11374/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2021.

## Built on by (most cited first, 10 of 10)

- [Convergence Rates for Stochastic Approximation: Biased Noise with Unbounded Variance, and Applications](https://mlsanity.com/paper/2312.02828/) (2023)
- [Convergence of Stochastic Approximation via Martingale and Converse Lyapunov Methods](https://mlsanity.com/paper/2205.01303/) (2022)
- [A quantitative Robbins-Siegmund theorem](https://mlsanity.com/paper/2410.15986/) (2024)
- [Convergence of the Stochastic Heavy Ball Method With Approximate Gradients and/or Block Updating](https://mlsanity.com/paper/2303.16241/) (2023)
- [Distributed Bayesian Estimation in Sensor Networks: Consensus on Marginal Densities](https://mlsanity.com/paper/2312.01227/) (2023)
- [A Mathematical Model of the Hidden Feedback Loop Effect in Machine Learning Systems](https://mlsanity.com/paper/2405.02726/) (2024)
- [Solving Hidden Monotone Variational Inequalities with Surrogate Losses](https://mlsanity.com/paper/2411.05228/) (2024)
- [An abstract effective convergence theorem for stochastic processes, with applications to stochastic approximation](https://mlsanity.com/paper/2504.12922/) (2025)
- [Convergence of Momentum-Based Optimization Algorithms with Time-Varying Parameters](https://mlsanity.com/paper/2506.11904/) (2025)
- [Convergence of Batch Updating Methods with Approximate Gradients and/or Noisy Measurements: Theory and Computational Results](https://mlsanity.com/paper/2209.05372/) (2022)

## 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.