Learning curves estimates

Iterative learning as learning in strictly repeating conditions is one of the simplest varieties of learning; it underlies the formation of human skills, conditioned reflexes in animals, the training of many technical (materialized) and cybernetic (abstract-logical) systems and is the subject of research in pedagogy, psychology and physiology of humans and animals, in control theory and in other sciences. For the model of individual learning in discrete time, upper and lower bounds for learning curves are obtained, their asymptotic behavior in time and parameter values is characterized. For the model of joint learning in continuous time, upper and lower bounds are obtained, as well as a lower asymptotic (by the number of agents) estimate of the aggregated level of learning. Stochastic asymptotic (in time) estimates of the learning process are presented, and confidence intervals for the values of the learning level are obtained.