# Online Regularized Learning Algorithms in RKHS with β- and φ-Mixing Sequences

arXiv: https://arxiv.org/abs/2507.05929 · HTML: https://mlsanity.com/paper/2507.05929/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 38 references that are in the map.
- First posted on arXiv 8 Jul 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 an online regularized learning algorithm in a reproducing kernel Hilbert spaces (RKHS) based on a class of dependent processes. We choose such a process where the degree of dependence is measured by mixing coefficients. As a representative example, we analyze a strictly stationary Markov chain, where the dependence structure is characterized by the (φ)- and (β)-mixing coefficients. Under these assumptions, we derive probabilistic upper bounds as well as convergence rates for both the exponential and polynomial decay of the mixing coefficients.