Optimal non-linear reinforcement schemes for stochastic automata

Abstract

Two optimal non-linear reinforcement schemes-the Reward-Inaction and the Penalty-Inaction-for the two-state automaton functioning in a stationary random environment are considered. Very simple conditions of symmetry of the non-linear function figuring in the reinforcement scheme are shown to be necessary and sufficient for optimality. General expressions for the variance and rate of learning are derived. These schemes are compared with the already existing optimal linear schemes in the light of average variance and average rate of learning.