Learning Operators with Stochastic Gradient Descent in General Hilbert Spaces

This study investigates leveraging stochastic gradient descent (SGD) to learn operators between general Hilbert spaces. We propose weak and strong regularity conditions for the target operator to depict its intrinsic structure and complexity. Under these conditions, we establish upper bounds for convergence rates of the SGD algorithm and conduct a minimax lower bound analysis, further illustrating that our convergence analysis and regularity conditions quantitatively characterize the tractability of solving operator learning problems using the SGD algorithm. It is crucial to …

algorithm complexity convergence cs.lg general gradient intrinsic learn math.fa math.st operators spaces stat.ml stat.th stochastic study