Towards Sharp Minimax Risk Bounds for Operator Learning
Ben Adcock; Gregor Maier; Rahul Parhi · 2025 · arXiv
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Abstract (excerpt)
We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove information-theoretic lower bounds together with matching or near-matching upper bounds, covering both fixed and random designs under Hilbert-valued Gaussian noise and Gaussian white noise errors. The rates are controlled by the spectrum of the covariance operator of the measure that defines the error metric. Our setup is very general and allows for measures with u
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Metadata source: arXiv