A robust locally adaptive learning algorithm is developed via two enhancements of the Resilient Propagation (RPROP) method. Remaining drawbacks of the gradient-based approach are addressed by hybridization with gradient-independent Local Search. Finally, a global optimization method based on recursion of the hybrid is constructed, making use of tabu neighborhoods to accelerate the search for minima through diver-sification. Enhanced RPROP is shown to be faster and more accurate than the standard RPROP in solving classification tasks based on natural data sets taken from the UCI repository of machine learning databases. Furthermore, the use of Local Search is shown to improve Enhanced RPROP by solving the same classification tasks as part of the global optimization method.