Optimality of pocket algorithm

Many constructive methods use the pocket algorithm as a basic component in the training of multilayer perceptrons. This is mainly due to the good properties of the pocket algorithm confirmed by a proper convergence theorem which asserts its optimality. Unfortunately the original proof holds vacuously and does not ensure the asymptotical achievement of an optimal weight vector in a general situation. This inadequacy can be overcome by a different approach that leads to the desired result. Moreover, a modified version of this learning method, called pocket algorithm with ratchet, is shown to obtain an optimal configuration within a finite number of iterations independently of the given training set.