# Information trajectory of optimal learning.

Belavkin, Roman V.
(2010)
*Information trajectory of optimal learning.*
In:
Dynamics of information systems: theory and applications.
Hirsch, Michael J. and Pardalos, Panos M. and Murphey, Robert, eds.
Springer Optimization and Its Applications
(40).
Springer, pp. 29-44.
ISBN 9781441956880

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## 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.

Item Type: | Book Section |
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Research Areas: | School of Science and Technology > Design Engineering and Mathematics School of Science and Technology > Computer and Communications Engineering |

ID Code: | 3490 |

Useful Links: | |

Deposited On: | 24 Mar 2010 13:40 |

Last Modified: | 13 May 2014 15:47 |

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