Chapter 2 Information Trajectory of Optimal Learning

Summary The paper outlines some basic principles of geometric and nonasymp-totic theory of learning systems. An evolution of such a system is represented by points on a statistical manifold, and a topology related to information dynamics is introduced to define trajectories continuous in information. It is shown that opti-mization of learning with respect to a given utility function leads to an evolution described by a continuous trajectory. Path integrals along the trajectory define the optimal utility and information bounds. Closed form expressions are derived for two important types of utility functions. The presented approach is a generalization of the use of Orlicz spaces in information geometry, and it gives a new, geometric in-terpretation of the classical information value theory and statistical mechanics. In addition, theoretical predictions are evaluated experimentally by comparing perfor-mance of agents learning in a nonstationary stochastic environment. The ability to learn and adapt the behavior with respect to changes in the environ-ment is arguably one of the most important characteristics of intelligent systems