Stochastic Gradient in Hilbert Spaces

What it does

We develop an end-to-end, fully rigorous theory of stochastic gradient methods in infinite-dimensional Hilbert spaces. After assembling the minimal functional-analytic and measure-theoretic toolkit (including the key inequalities used throughout), we show that the many ways practitioners define a “stochastic gradient” in function spaces in fact agree under mild assumptions. On this foundation we e

You are using an outdated browser. Please upgrade your browser to improve your experience. Zenodo is currently experiencing slowness and intermittent outages due to heavy automated traffic from bots and AI crawlers. We are aware of the problem, and our team is focused on stabilizing the service. Thank you for your patience. We develop an end-to-end, fully rigorous theory of stochastic gradient methods in infinite-dimensional Hilbert spaces. After assembling the minimal functional-analytic and measure-theoretic toolkit (including the key inequalities used throughout), we show that the many ways practitioners define a “stochastic gradient” in function spaces in fact agree under…from zenodo.org

In the maker’s words, at launch

I wrote a free, proof-complete monograph on stochastic gradient methods in infinite-dimensional Hilbert spaces. It starts from the functional-analysis foundations (Riesz, Radon–Nikodym), gives five equivalent definitions of stochastic gradients, proves existence/uniqueness of the dynamics, connects the continuum…

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