The learning convergence of CMAC in cyclic learning

Discusses the learning convergence of the cerebellar model articulation controller (CMAC) in cyclic learning. The authors prove the following results. First, if the training samples are noiseless, the learning algorithm converges if and only if the learning rate is chosen from (0, 2). Second, when the training samples have noises, the learning algorithm will converge with probability one if the learning rate is dynamically decreased. Third, in the noise case, with a small but fixed learning rate ε the mean square error of the weight sequences generated by the CMAC learning algorithm will be bounded by O(ε). Some simulation experiments are carried out to test these results.