On the coevolutionary construction of learnable gradients

“The best way for adaptive agents to learn is to be exposed to problems that are just a little more difficult than those they already know how to solve”. While this has been a guiding concept in developing algorithms for gradient construction in coevolution, it has remained largely an intuition rather than a formal concept. In this paper, we build on the ordertheoretic formulation of coevolution to develop some preliminary formal concepts towards clarifying the nature of the relation between the variational structure imposed by the representation and coevolutionary learning. By explicitly marrying the learnability problem to the variational structure of the learner space, we describe a basic idealization of how coevolution with an Ideal Teacher could inherently address the problem of appropriate gradient creation with the intent that this could serve as a basis to developing practical algorithmic mechanisms that approximate this idealized behavior.