Epsilon-optimal discretized pursuit learning automata

The authors consider the problem of a stochastic learning automaton interacting with an unknown random environment. The fundamental problem is that of learning, through interaction, the best action (that is, the action which is rewarded optimally) allowed by the environment. By using running estimates of reward probabilities to learn the optimal action, an extremely efficient pursuit algorithm was obtained by M.A.L. Thathachar et al. (1986, 1989) which is presently among the fastest-growing algorithms known. In the present work, the authors investigate the improvements gained by rendering the pursuit algorithm discrete. This is done by restricting the probability of selecting an action to a finite and, hence, discrete subset of [0,1]. This improved scheme is proven to be ε-optimal in all stationary environments. Furthermore, the authors´ experimental results seem to indicate that the algorithm is the fastest-absorbing learning automaton reported in the literature to date. Comparison with the continuous form of the pursuit algorithm is also presented