  We study the convergence speed of the batch learning algorithm, and compare
its speed to that of the memoryless learning algorithm and of learning with
memory (as analyzed in joint work with N. Komarova). We obtain precise results
and show in particular that the batch learning algorithm is never worse than
the memoryless learning algorithm (at least asymptotically). Its performance
vis-a-vis learning with full memory is less clearcut, and depends on
certainprobabilistic assumptions. These results necessitate theintroduction of
the moment zeta function of a probability distribution and the study of some of
its properties.
