Optimization on discrete probability spaces and applications to probabilistic control design

This paper addresses the iterative optimization of discrete probability distributions using a information geometry framework. Discrete probability distributions can be represented both as a mixture family or an exponential family. A Riemannian metric is introduced in these spaces given by the Fisher information matrix. The natural gradient is then computed with respect to this metric and is used in a iterative procedure for optimization. Properties of both formulations are given, and examples are presented. Finally, the formulation is illustrated in a probabilistic control design for a gene regulatory network problem.