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New research details SGD for operator learning in Hilbert spaces

By PulseAugur Editorial · [1 sources] ·

This research paper explores the application of stochastic gradient descent (SGD) for learning operators within Hilbert spaces. The study establishes convergence rate upper bounds and conducts a minimax lower bound analysis, quantifying the statistical difficulty of operator estimation under specific regularity conditions. The findings extend to nonlinear regression targets and offer refined convergence results for operator learning problems utilizing reproducing kernel Hilbert spaces. AI

IMPACT Provides theoretical underpinnings for operator learning, potentially improving machine learning model capabilities.

RANK_REASON The cluster contains an academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New research details SGD for operator learning in Hilbert spaces

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The cluster contains an academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Lei Shi, Jia-Qi Yang ·

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

    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…

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