A new learning automaton for interaction with triple level environments

Heretofore, the most presented Learning Automata (LA) is invented to interact with double level environments (one level for reward and the other for penalty). Those LA are often expedient, optimal or both of them and can minimize their mean value of receiving penalties (or at least converge to the minimum point) during time an d work much better than a pure-chance automaton. However, in many operational applications, the environment has three level responses; one for reward, one for small scale penalty and the last one for large scale penalty. In these applications, the old LA not only can not minimize the mean value of receiving penalties, but also in some cases their mean value of receiving penalties are even more than a pure-chance automaton. In this paper, first the triple level environments with illustrative example are described precisely. Then, the new fixed structure stochastic LA (called TILA) is introduced and its properties are considered mathematically. The simulation results show the old LA can not converge to the minimum value of the mean value of receiving penalties, but TILA receives fewer penalties in comparison with the older ones.