UNIVERSITY OF HERTFORDSHIRE
COMPUTER SCIENCE RESEARCH COLLOQUIUM
presents
Variational Problems of Information Theory and Optimal Markov Evolution
Dr. Roman V. Belavkin
(School of Engineering and Information Sciences,
Middlesex University, UK)
28 March 2012 (Wednesday)
1 -2 pm
Hatfield, College Lane Campus
* * Room C152 * *
Everyone is Welcome to Attend
Refreshments will be available
Abstract:
Variational problems of information theory have played an important role
in defining theoretical bounds on various quantities, such as the average
length of codewords, capacity of a communication channel, probability of
error and so on. Here we study the relation between two such problems
in the context of evolutionary dynamics. The first is the problem
of minimizing information divergence between two probability measures
subject to a lower constraint on expected utility (linear functional).
Solutions to this problem form a one parameter family of probability
measures corresponding to a replicator dynamics with constant selection.
The second is the problem of finding optimal Markov operator maximizing
expected utility of the output measure subject to a constraint on
mutual information between the input and output. We demonstrate how
the semi-group of Markov operators solving the second problem can also
produce the one-parameter evolution of solutions to the first problem.
Understanding this relation is facilitated by the Pythagorean theorem
for Markov morphisms, and it can help in the development of optimal
control functions achieving information-theoretic bounds. An optimal
control of mutation rate in a simple genetic algorithm is shown as an
example demonstrating the principle.
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Hertfordshire Computer Science Research Colloquium
http://cs-colloq.stca.herts.ac.uk