  We study a non-linear statistical inverse learning problem, where we observe
the noisy image of a quantity through a non-linear operator at some random
design points. We consider the widely used Tikhonov regularization (or method
of regularization, MOR) approach to reconstruct the estimator of the quantity
for the non-linear ill-posed inverse problem. The estimator is defined as the
minimizer of a Tikhonov functional, which is the sum of a data misfit term and
a quadratic penalty term. We develop a theoretical analysis for the minimizer
of the Tikhonov regularization scheme using the ansatz of reproducing kernel
Hilbert spaces. We discuss optimal rates of convergence for the proposed
scheme, uniformly over classes of admissible solutions, defined through
appropriate source conditions.
