Learning and optimization in biological systems

Abstract

A model of sequential actions implying learning is proposed, starting from the concept of acybernetical action introduced in a previous paper (Teodorescu, 1977). Sequential actions of this kind (e.g. defence actions occurring repeatedly in a biological population, some motor subroutines such as walking, swimming etc.) are always goal-oriented ones. Furthermore, in performing them, some constraints must be observed. Finally, each action must be optimal with respect to a given criterion, otherwise it becomes highly expensive (or, perhaps, inefficient) for the living organism(s). To take into account these rather natural features of any cybernetical action, a specific tool is used, namely, themessage operator defined in (Teodorescu, 1976b). The procedure of deriving an action model with the aid of message operators is illustrated by means of an experimental paradigm concerning the visually induced behaviour in insects (Reichardt and Poggio, 1976). Next, by taking into account certain recovery processes, the concept of alearning sequence (i.e. model of sequential action involving learning) is defined, and some examples are given to illustrate learning in biological systems. The related concepts offull subsequence, node andmemory cycle are also defined, and some theorems concerning memory cycles are stated and proved. Furthermore,a measure of the learning effort is suggested. It is used to show that, under certain conditions, learning occurs even in the case of many different active messages. Finally, by using the proposed models, the relationship between learning and optimization is investigated, proving thatoptimization is deeply implicated in any learning process. More exctly, as far as sequential actions with recovery are concerned, optimization is a necessary (but not sufficient) condition for learning. Thus, the proposed model of action may be regarded as a useful tool, which enables to investigate some unknown aspects related to learning in living organisms, in a general, computeroriented way.