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• W4376288907 abstract "In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most successful optimization methods in machine learning, imaging, and signal processing, to name a few. At each iteration SGD uses a single datum, or a small subset of data, resulting in highly scalable methods that are very attractive for large-scale inverse problems. Nonetheless, the theoretical analysis of SGD-based approaches for inverse problems has thus far been largely limited to Euclidean and Hilbert spaces. In this work we present a novel convergence analysis of SGD for linear inverse problems in general Banach spaces: we show the almost sure convergence of the iterates to the minimum norm solution and establish the regularizing property for suitable a priori stopping criteria. Numerical results are also presented to illustrate features of the approach." @default.
• W4376288907 created "2023-05-13" @default.
• W4376288907 creator A5039605463 @default.
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• W4376288907 date "2023-05-15" @default.
• W4376288907 modified "2023-09-24" @default.
• W4376288907 title "On the Convergence of Stochastic Gradient Descent for Linear Inverse Problems in Banach Spaces" @default.
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• W4376288907 doi "https://doi.org/10.1137/22m1518542" @default.
• W4376288907 hasPublicationYear "2023" @default.
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