# Asymptotic Bias of Stochastic Gradient Search

arXiv: https://arxiv.org/abs/1709.00291 · HTML: https://mlsanity.com/paper/1709.00291/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2017.

## Built on by (most cited first, 19 of 19)

- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Implicit Diffusion: Efficient Optimization through Stochastic Sampling](https://mlsanity.com/paper/2402.05468/) (2024)
- [Plug-and-Play image restoration with Stochastic deNOising REgularization](https://mlsanity.com/paper/2402.01779/) (2024)
- [Convergence Rates for Stochastic Approximation: Biased Noise with Unbounded Variance, and Applications](https://mlsanity.com/paper/2312.02828/) (2023)
- [On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descent](https://mlsanity.com/paper/2201.06133/) (2022)
- [Stability and Generalization for Markov Chain Stochastic Gradient Methods](https://mlsanity.com/paper/2209.08005/) (2022)
- [BR-SNIS: Bias Reduced Self-Normalized Importance Sampling](https://mlsanity.com/paper/2207.06364/) (2022)
- [Stochastic Approximation Beyond Gradient for Signal Processing and Machine Learning](https://mlsanity.com/paper/2302.11147/) (2023)
- [Conditionally Gaussian PAC-Bayes](https://mlsanity.com/paper/2110.11886/) (2021)
- [Convergence of First-Order Methods for Constrained Nonconvex Optimization with Dependent Data](https://mlsanity.com/paper/2203.15797/) (2022)
- [Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradients](https://mlsanity.com/paper/2206.06295/) (2022)
- [Constrained Stochastic Nonconvex Optimization with State-dependent Markov Data](https://mlsanity.com/paper/2206.11346/) (2022)
- [Non-asymptotic Analysis of Biased Adaptive Stochastic Approximation](https://mlsanity.com/paper/2402.02857/) (2024)
- [Stochastic Approximation with Biased MCMC for Expectation Maximization](https://mlsanity.com/paper/2402.17870/) (2024)
- [Inexact subgradient methods for semialgebraic functions](https://mlsanity.com/paper/2404.19517/) (2024)
- [Equivariant Denoisers for Image Restoration](https://mlsanity.com/paper/2412.05343/) (2024)
- [Convergence of Batch Asynchronous Stochastic Approximation With Applications to Reinforcement Learning](https://mlsanity.com/paper/2109.03445/) (2021)
- [Derivatives of Stochastic Gradient Descent in parametric optimization](https://mlsanity.com/paper/2405.15894/) (2024)
- [Stability and Generalization for Decentralized Markov SGD](https://mlsanity.com/paper/2605.01701/) (2026)

## Abstract (arXiv)

The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and Lojasiewicz inequality), tight bounds on the asymptotic bias of the iterates generated by such an algorithm are derived. The obtained results hold under mild conditions and cover a broad class of high-dimensional nonlinear algorithms. Using these results, the asymptotic properties of the policy-gradient (reinforcement) learning and adaptive population Monte Carlo sampling are studied. Relying on the same results, the asymptotic behavior of the recursive maximum split-likelihood estimation in hidden Markov models is analyzed, too.