This paper deals with the analysis of nonlinear reinforcement schemes
for learning automata. The learning automaton is connected in feedback
loop to a random environment. The correction term of the action proba
bility vector depends on a nonlinear function phi(x). Results concerni
ng the convergence, the convergence rate, and the effect of the functi
on phi(x) are stated. A comparison between the convergence rate of non
linear and linear reinforcement schemes is presented.