Optimal measures and Markov transition kernels

Belavkin, Roman V. (2012) Optimal measures and Markov transition kernels. Journal of Global Optimization, 55 (2). pp. 387-416. ISSN 0925-5001

This is the latest version of this item.

[img]
Preview
PDF
318kB

Official URL: http://dx.doi.org/10.1007/s10898-012-9851-1

This item is available in the Library Catalogue

Abstract

We study optimal solutions to an abstract optimization problem for measures, which is a generalization of classical variational problems in information theory and statistical physics. In the classical problems, information and relative entropy are defined using the Kullback-Leibler divergence, and for this reason optimal measures belong to a one-parameter exponential family. Measures within such a family have the property of mutual absolute continuity. Here we show that this property characterizes other families of optimal positive measures if a functional representing information has a strictly convex dual. Mutual absolute continuity of optimal probability measures allows us to strictly separate deterministic and non-deterministic Markov transition kernels, which play an important role in theories of decisions, estimation, control, communication and computation. We show that deterministic transitions are strictly sub-optimal, unless information resource with a strictly convex dual is unconstrained. For illustration, we construct an example where, unlike non-deterministic, any deterministic kernel either has negatively infinite expected utility (unbounded expected error) or communicates infinite information.

Item Type:Article
Research Areas:Middlesex University Schools and Centres > School of Science and Technology > Computer Science
Middlesex University Schools and Centres > School of Science and Technology > Computer Science > Artificial Intelligence group
ID Code:8531
Permissions granted by publisher:The final publication is available at www.springerlink.com
Useful Links:
Deposited On:01 Mar 2012 05:30
Last Modified:13 Nov 2014 16:16

Available Versions of this Item

  • Optimal measures and Markov transition kernels. (deposited 01 Mar 2012 05:30) [Currently Displayed]

Repository staff only: item control page

Full text downloads (NB count will be zero if no full text documents are attached to the record)

Downloads per month over the past year