Information Trajectory of Optimal Learning

Roman V. Belavkin ()
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Roman V. Belavkin: Middlesex University

Chapter Chapter 2 in Dynamics of Information Systems, 2010, pp 29-44 from Springer

Abstract: Summary The paper outlines some basic principles of geometric and nonasymptotic 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 nonstationary stochastic environment.

Keywords: Utility Function; Probability Measure; Path Integral; Learning System; Optimal Trajectory (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-5689-7_2

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DOI: 10.1007/978-1-4419-5689-7_2

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