Switching models for nonstationary random environments

Learning automata are stochastic finite state machines that attempt to learn the characteristic of an unknown 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 nonstationary, the question of modeling the nonstationarity is, in itself, a very interesting problem. In this paper, the authors generalize the model used in Tsetlin (1971, 1973) to present three models of nonstationarity. In the first two cases, the nonstationarity is modeled 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 analyze the stochastic properties of the resultant switching environment. The question of analyzing the various learning machines when interacting with these environments introduces an entire new avenue of open research problems