Optimal rates for the regularized learning algorithms under general source condition
This work provides theoretical foundations for machine learning practitioners dealing with regularization in vector-valued function settings, though it appears incremental as it extends existing analysis to more general conditions.
The paper tackles the problem of determining optimal convergence rates for regularized learning algorithms under general source conditions, establishing upper bounds for Tikhonov regularization and addressing the minimax error for any learning algorithm.
We consider the learning algorithms under general source condition with the polynomial decay of the eigenvalues of the integral operator in vector-valued function setting. We discuss the upper convergence rates of Tikhonov regularizer under general source condition corresponding to increasing monotone index function. The convergence issues are studied for general regularization schemes by using the concept of operator monotone index functions in minimax setting. Further we also address the minimum possible error for any learning algorithm.