English(EN) Stochastic Gradient Descent for Operator Learning in Hilbert Spaces: Convergence Rates and Minimax Lower Bounds

新研究详细介绍了希尔伯特空间中算子学习的 SGD

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-15 04:00

本研究论文探讨了在希尔伯特空间中使用随机梯度下降 (SGD) 学习算子的应用。该研究建立了收敛速度上界，并进行了 minimax 下界分析，在特定正则性条件下量化了算子估计的统计难度。研究结果扩展到非线性回归目标，并为使用再生核希尔伯特空间的算子学习问题提供了更精细的收敛结果。 AI

影响为算子学习提供了理论基础，可能提高机器学习模型的能力。

排序理由该集群包含一篇在 arXiv 上发表的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

AI 生成摘要 · Google Gemini · 来自 1 个来源。我们如何撰写摘要 →

本文如何被排名

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arXiv cs.LG TIER_1 English(EN) · Lei Shi, Jia-Qi Yang · 2026-09-15 04:00

希尔伯特空间算子学习的随机梯度下降：收敛速度与minimax下界

arXiv:2402.04691v5 Announce Type: replace-cross Abstract: This study investigates the use of stochastic gradient descent (SGD) to learn operators between general Hilbert spaces. We study weak and strong regularity conditions for the target operator that characterize its structure…