Information trajectory of optimal learning.

Belavkin, Roman V. ORCID: https://orcid.org/0000-0002-2356-1447 (2010) Information trajectory of optimal learning. In: Dynamics of information systems: theory and applications. Hirsch, Michael J., Pardalos, Panos M. and Murphey, Robert, eds. Springer Optimization and Its Applications (40) . Springer, pp. 29-44. ISBN 9781441956880. [Book Section]

Abstract

The paper outlines some basic principles of a geometric and
non-asymptotic 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 optimization 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 interpretation of the classical information value theory and statistical mechanics. In addition, theoretical predictions are evaluated experimentally by comparing performance of agents learning in a non-stationary stochastic environment.

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