Learning on a response continuum: Comparison of a linear change and a functional learning model

Two reinforcement schedules were used to compare the predictive validity of a linear change model with a functional learning model. In one schedule, termed “convergent,” the linear change model predicts convergence to the optimum response, while in the other, termed “divergent,” this model predicts that a subject's response will not converge. The functional learning model predicts convergence in both cases. Another factor that was varied was presence or absence of random error or “noise” in the relationship between response and outcome. In the “noiseless” condition, in which no noise is added, a subject could discover the optimum response by chance, so that some subjects could appear to have converged fortuitously. In the “noisy” conditions such chance apparent convergence could not occur.The results did not unequivocally favor either model. While the linear change model's prediction of nonconvergence in the divergent conditions (particularly the “noisy” divergent condition) was not sustained, there was a clear difference in speed of convergence, counter to the prediction inferred from the functional learning model. Evidence that at least some subjects were utilizing a functional learning strategy was adduced from the fact that subjects were able to “map out” the relation between response and outcome quite accurately in a follow-up task. Almost all subjects in the “noisy” conditions had evidently “learned” a strong linear relation, with slope closely matching the veridical one.The data were consistent with a hybrid model assuming a “hierarchy of cognitive strategies” in which more complex strategies (e.g., functional learning) are utilized only when the simpler ones (e.g., a linear change strategy) fail to solve the problem.