Reference:
J. van Ast,
R. Babuska, and
B. De Schutter,
"Convergence analysis of ant colony learning," Proceedings of the
18th IFAC World Congress, Milan, Italy, pp. 14693-14698,
Aug.-Sept. 2011.
Abstract:
In this paper, we study the convergence of the pheromone levels of Ant
Colony Learning (ACL) in the setting of discrete state spaces and
noiseless state transitions. ACL is a multi-agent approach for
learning control policies that combines some of the principles found
in ant colony optimization and reinforcement learning. Convergence of
the pheromone levels in expected value is a necessary requirement for
the convergence of the learning process to optimal control policies.
In this paper, we derive upper and lower bounds for the pheromone
levels and relate those to the learning parameters and the number of
ants used in the algorithm. We also derive upper and lower bounds on
the expected value of the pheromone levels.