{"ID":2844176,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.07604","arxiv_id":"2511.07604","title":"Infinite-Dimensional Operator/Block Kaczmarz Algorithms: Regret Bounds and $λ$-Effectiveness","abstract":"We present a variety of projection-based linear regression algorithms with a focus on modern machine-learning models and their algorithmic performance. We study the role of the relaxation parameter in generalized Kaczmarz algorithms and establish a priori regret bounds with explicit $λ$-dependence to quantify how much an algorithm's performance deviates from its optimal performance. A detailed analysis of relaxation parameter is also provided. Applications include: explicit regret bounds for the framework of Kaczmarz algorithm models, non-orthogonal Fourier expansions, and the use of regret estimates in modern machine learning models, including for noisy data, i.e., regret bounds for the noisy Kaczmarz algorithms. Motivated by machine-learning practice, our wider framework treats bounded operators (on infinite-dimensional Hilbert spaces), with updates realized as (block) Kaczmarz algorithms, leading to new and versatile results.","short_abstract":"We present a variety of projection-based linear regression algorithms with a focus on modern machine-learning models and their algorithmic performance. We study the role of the relaxation parameter in generalized Kaczmarz algorithms and establish a priori regret bounds with explicit $λ$-dependence to quantify how much...","url_abs":"https://arxiv.org/abs/2511.07604","url_pdf":"https://arxiv.org/pdf/2511.07604v1","authors":"[\"Halyun Jeong\",\"Palle E. T. Jorgensen\",\"Hyun-Kyoung Kwon\",\"Myung-Sin Song\"]","published":"2025-11-10T20:21:32Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.FA\"]","methods":"[]","has_code":false}