The status of the theory of adaptive systems

Despite the extensive literature on adaptive systems, relatively little progress has been made so far toward the development of a general theory of adaptation. Among the more promising and mathematically concrete approaches to the design of adaptive systems are the dynamic programming formulation due to Bellman and Kalaba, the empirical Bayes and stochastic approximation methods developed by Robbins, and the learning algorithms used in pattern recognition. The advantages and shortcomings of these approaches are pointed out and alternative points of view are briefly analyzed.