Discretized pursuit learning automata

The problem of a stochastic learning automaton interacting with an unknown random environment is considered. The fundamental problem is that of learning, through interaction, the best action allowed by the environment (i.e. the action that is rewarded optimally). By using running estimates of reward probabilities to learn the optimal action, an extremely efficient pursuit algorithm (PA), which is presently among the fastest algorithms known, was reported in earlier works. The improvements gained by rendering the PA discrete are investigated. 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 experimental results seem to indicate that the algorithm presented is faster than the fastest nonestimator learning automata reported to date, and also faster than the continuous pursuit automaton