Convergence of Teams and Hierarchies of Learning Automata in Connectionist Systems

Learning algorithms for feedforward connectionist systems in a reinforcement learning environment are developed and analyzed in this paper. The connectionist system is made of units of groups of learning automata. The learning algorithm used is the $L_{R-I}$ and the asymptotic behavior of this algorithm is approximated by an Ordinary Differential Equation (ODE) for low values of the learning parameter. This is done using weak convergence techniques. The reinforcement learning model is used to pose the goal of the system as a constrained optimization problem. It is shown that the ODE, and hence the algorithm exhibits local convergence properties, converging to local solutions of the related optimization problem. The three layer pattern recognition network is used as an example to show that the system does behave as predicted and reasonable rates of convergence are obtained. Simulations also show that the algorithm is robust to noise