# Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with φ- and β-Mixing

arXiv: https://arxiv.org/abs/2502.03551 · HTML: https://mlsanity.com/paper/2502.03551/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 34 references that are in the map.
- First posted on arXiv 5 Feb 2025.

## Builds on (most cited first, 4 of 4)

- [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)

## Abstract (arXiv)

In this paper, we study a strictly stationary Markov chain gradient descent algorithm operating in general Hilbert spaces. Our analysis focuses on the mixing coefficients of the underlying process, specifically the φ- and β-mixing coefficients. Under these assumptions, we derive probabilistic upper bounds on the convergence behavior of the algorithm based on the exponential as well as the polynomial decay of the mixing coefficients.