Finite and infinite memory range learning processes in stationary and nonstationary environments

A generalized Bush-Mosteller learning model is discussed simulating both finite memory range learning and infinite memory range imprinting processes, as well as an ideal learning scheme storing all experiences with equal weight. The learning and imprinting dynamics in stationary and non-stationary environments is studied using as a performance criterion the relative entropy of the true with respect to the system´s subjective environmental probabilities. For the stationary case learning and imprinting schemes exhibit a symmetrical performance which is nearly optimal for small deviations from the ideal learning scheme. In the non-stationary case imprinting schemes perform poorly, while proper learning processes are capable of keeping the relative entropy at a low level. Their optimal memory range is calculated in terms of the environmental fluctuation time.