Sequential operator learning under dependent data

Abstract:Learning operators from sequentially collected data arises in adaptive experimental design, Bayesian optimization, and dynamical-system modelling, where observations may be dependent, and future inputs or sensing operators may depend on preceding data. We derive time-uniform self-normalized concentration bounds for stochastic processes in Hilbert spaces with vector-valued noise. We use these bounds to obtain regression-error guarantees for linear operators, including targets outside the Hilbert estimation space, and for nonlinear parametric operators trained with strongly convex losses and regularizers. Our results allow possibly infinite-dimensional inputs and outputs without independence or mixing assumptions, providing a major step towards convergence guarantees for adaptive operator learning and learning from stochastic dynamical data.

Under review. Work in progress

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2608.24426 [stat.ML]

(or arXiv:2608.24426v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2608.24426 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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