Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels

תקציר מקורי באנגליתarXiv:2504.18184v5 Announce Type: replace-cross Abstract: We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a vector-valued reproducing kernel Hilbert space induced by an operator-valued kernel. To address the associated ill-posedness, we analyze regularized stochastic gradient descent (SGD) algorithms in both online and finite-horizon settings. The former uses polynomially decaying step sizes and regularization parameters, while the latter adopts fixed values. Under suitable structural and distributional assumptions, we establish prediction and estimation error bounds with no explicit dependence on the dimension of the output space. The resulting convergence rates