Towards Sharp Minimax Risk Bounds for Operator Learning

arXiv — stat.MLMonday, December 22, 2025 at 5:00:00 AM
  • A new minimax theory for operator learning has been developed, focusing on estimating unknown operators between separable Hilbert spaces using limited noisy input-output samples. The research establishes information-theoretic lower bounds and corresponding upper bounds for uniformly bounded Lipschitz operators, addressing both fixed and random designs under Gaussian noise conditions.
  • This advancement is significant as it highlights the limitations of sample complexity in operator learning, demonstrating that the minimax risk for generic Lipschitz operators cannot decrease at any algebraic rate with increased sample size.
  • The findings resonate with ongoing discussions in the field of machine learning regarding the balance between model complexity and data availability, as well as the implications of noise in learning algorithms, which are critical for applications in various domains including statistics and data science.
— via World Pulse Now AI Editorial System

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