On modelling non-stationary random environments using switching techniques

Learning automata are stochastic finite state machines that attempt to learn the characteristic of a random environment with which they interact. The fundamental problem is that of learning, through feedback, the action which has the highest probability of being rewarded by the environment. The problem of designing automata for stationary environments has been extensively studied. When the environment is non-stationary, the question of modelling the non-stationarity is, in itself, a very interesting problem. In this paper, the authors generalize the model used in Tsetlin (1961, 1963) to present models of non-stationarity. In the first the non-stationarity is modelled by a homogeneous Markov chain governing the way in which the characteristics change. The final model considers the more general case when the transition matrix of this chain itself changes with time in a geometric manner. In each case the authors have analyzed the stochastic properties of the resultant switching environment. The question of analyzing various automata interacting with these environments is open