Proofs of Reinforcement Learning Algorithms

Hi,

I'm suggesting a new reinforcement learning algorithm applied in my
case on robots, please see:
http://www.compactech.com/kartoun/articles/html/Kartoun_RA_2005_September_3_2005_Accepted.htm

I would like to describe the algorithm more scientifically; define it
mathematically much better than described in the paper.

I'm asking for guidance of how to prove an algorithm, for example in
the form of convergence or superiority. How can I demonstrate
advantages or disadvantages of an algorithm mathematically? How can I
prove convergence or divergence? How can I show if it is better or
worse than other algorithms?

I've already tested the algorithm on a mobile robot for navigation,
please see:

http://www.compactech.com/kartoun/videos/Uri_Kartoun_CQ (lamda)_Reinforcment_Learning_August_7_2005.wmv

I intend applying it for the task of finding optimal grasping, lifting
and shaking policies of suspicious bags (contain anthrax, Ebola
microbes or SARS), please see an initial experiment:

http://www.compactech.com/kartoun/videos/Uri_Kartoun_Plastic_Bag_Experiment_January_2_2006.wmv

Thanks a lot!

Uri Kartoun.

http://www.compactech.com/kartoun/