# Behavior Representation by Growing a Learning Tree

Abstract: The work presented in this thesis is based on the basic idea of learning by reinforcement, within the theory of behaviorism. The reason for this choice is the generality of such an approach, especially that the reinforcement learning paradigm allows systems to be designed which can improve their behavior beyond that of their teacher. The role of the teacher is to define the reinforcement function, which acts as a description of the problem the machine is to solve.Learning is considered to be a bootstrapping procedure. Fragmented past experience, of what to do when performing well, is used for response generation. The new response, in its turn, adds more information to the system about the environment. Gained knowledge is represented by a behavior probability density function. This density function is approximated with a number of normal distributions which are stored in the nodes of a binary tree. The tree structure is grown by applying a recursive algorithm to the stored stimuli-response combinations, called decisions. By considering both the response and the stimulus, the system is able to bring meaning to structures in the input signal. The recursive algorithm is first applied to the whole set of stored decisions. A mean decision vector and a covariance matrix are calculated and stored in the root node. The decision space is then partitioned into two halves across the direction of maximal data variation. This procedure is now repeated recursively for each of the two halves of the decision space, forming a binary tree with mean vectors and covariance matrices in its nodes.The tree is the system's guide to response generation. Given a stimulus, the system searches for responses likely to result in highly reinforced decisions. This is accomplished by treating the sum of the normal distributions in the leaves as distribution describing the behavior of the system. The sum of normal distributions, with the current stimulus held fixed, is finally used for random generation of the response.This procedure makes it possible for the system to have several equally plausible responses to one stimulus. Not applying maximum likelihood principles will make the system more explorative and reduce its risk of being trapped in local minima.The performance and complexity of the learning tree is investigated and compared to some well known alternative methods. Presented are also some simple, yet principally important, experiments verifying the behavior of the proposed algorithm.

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