# Markov Chain Gradient Descent in Hilbert Spaces

arXiv: https://arxiv.org/abs/2410.08361 · HTML: https://mlsanity.com/paper/2410.08361/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Builds on (most cited first, 9 of 9)

- [On Markov Chain Gradient Descent](https://mlsanity.com/paper/1809.04216/) (2018)
- [Least Squares Regression with Markovian Data: Fundamental Limits and Algorithms](https://mlsanity.com/paper/2006.08916/) (2020)
- [Stochastic Gradient Descent under Markovian Sampling Schemes](https://mlsanity.com/paper/2302.14428/) (2023)
- [Adapting to Mixing Time in Stochastic Optimization with Markovian Data](https://mlsanity.com/paper/2202.04428/) (2022)
- [Finite-Time Analysis of Stochastic Gradient Descent under Markov Randomness](https://mlsanity.com/paper/2003.10973/) (2020)
- [Convergence Rates of Accelerated Markov Gradient Descent with Applications in Reinforcement Learning](https://mlsanity.com/paper/2002.02873/) (2020)
- [Stability and Generalization for Markov Chain Stochastic Gradient Methods](https://mlsanity.com/paper/2209.08005/) (2022)
- [Large-scale Analysis and Simulation of Traffic Flow using Markov Models](https://mlsanity.com/paper/2007.02681/) (2020)
- [Markov Chain Models of Refugee Migration Data](https://mlsanity.com/paper/1903.08255/) (2019)

## Abstract (arXiv)

In this paper, we study a Markov chain-based stochastic gradient algorithm in general Hilbert spaces, aiming at approximating the optimal solution of a quadratic loss function. We establish probabilistic upper bounds on its convergence. We further extend these results to an online regularized learning algorithm in reproducing kernel Hilbert spaces, where the samples are drawn along a Markov chain trajectory.