Learning from examples, agent teams and the concept of reflection

Learning from examples has a number of distinct algebraic forms, depending on what is to be learned from the available information. One of these forms is [GRAPHICS] where the input-output tuple (x, y) is the available information, and G represents the process determining the mapping from x to y. Various models, y = f(x), of G can be constructed using the information from the (x, y) tuples. In general, and for real-world problems, it is not reasonable to expect the exact representation of G to be found (i.e. a formula that is correct for all possible (x, y)). The modeling procedure involves finding a satisfactory set of basis functions, their combination, a coding for (x, y) and then to adjust all free parameters in an approximation process, to construct a final model. The approximation process can bring the accuracy of the model to a certain level, after which it becomes increasingly expensive to improve further. Further improvement may be gained through constructing a number of agents {alpha}, each of which develops its own model f(alpha). These may then be combined in a second modeling phase to synthesize a team model. If each agent has the ability for internal reflection the combination in a team framework becomes more profitable. We describe reflection and the generation of a confidence function: the agent's estimate of the correctness of each of its predictions. The presence of reflective information is shown to increase significantly the performance of a team.