The duality of utility and information in optimally learning systems

Abstract

The paper considers learning systems as optimisation systems with dynamical information constraints, and general optimality conditions are derived using the duality between the space of utility functions and probability measures. The increasing dynamics of the constraints is used to parametrise the optimal solutions which form a trajectory in the space of probability measures. Stochastic processes following such trajectories describe systems achieving the maximum possible utility gain with respect to a given information. The theory is discussed on examples for finite and uncountable sets and in relation to existing applications and cognitive models of learning.