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Information Trajectory of Optimal Learning

In: Dynamics of Information Systems

Author

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  • Roman V. Belavkin

    (Middlesex University)

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.

Suggested Citation

  • Roman V. Belavkin, 2010. "Information Trajectory of Optimal Learning," Springer Optimization and Its Applications, in: Michael J. Hirsch & Panos M. Pardalos & Robert Murphey (ed.), Dynamics of Information Systems, chapter 0, pages 29-44, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-5689-7_2
    DOI: 10.1007/978-1-4419-5689-7_2
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