Infinite-Dimensional Operator/Block Kaczmarz Algorithms: Regret Bounds and $\lambda$-Effectiveness

The recent publication on arXiv presents a comprehensive analysis of projection-based linear regression algorithms, particularly emphasizing the generalized Kaczmarz algorithms. This study investigates the role of the relaxation parameter, providing a priori regret bounds that quantify how much an algorithm's performance can deviate from its optimal performance. Such insights are vital for improving algorithmic efficiency in modern machine learning applications, especially when dealing with noisy data. The framework discussed treats bounded operators on infinite-dimensional Hilbert spaces, leading to versatile results that can be applied across various machine learning models. By establishing explicit regret bounds, this research not only contributes to theoretical advancements but also has practical implications for enhancing the robustness of algorithms in real-world scenarios.