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

2025/07/08 by Priyanka Roy, Roy, Priyanka, Susanne Saminger‐Platz +1
Engineering · Mathematics · #60J20 #62H05 #62L20 #68Q32 #68T05 #Advanced Adaptive Filtering Techniques #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2507.05929

openalex publication_date 2025/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Stochastic Gradient Descent under Markovian Sampling Schemes
• Adapting to Mixing Time in Stochastic Optimization with Markovian Data
• Least Squares Regression with Markovian Data: Fundamental Limits and Algorithms
• On Markov Chain Gradient Descent
• The Generalization Ability of Online Algorithms for Dependent Data
• Stability Bound for Stationary Phi-mixing and Beta-mixing Processes

Related

• Online Regularized Statistical Learning in Reproducing Kernel Hilbert Space With Non-Stationary Data
• Online Learning as Stochastic Approximation of Regularization Paths
• Fast and Strong Convergence of Online Learning Algorithms
• The Generalization Ability of Online Algorithms for Dependent Data
• Convergence of Unregularized Online Learning Algorithms