Exogenous control and dynamical reduction of echo state networks

In this paper, we demonstrate that a Q-Learning control policy with a Growing Neural Gas state space approximation is sufficient to control echo state neural networks of arbitrary dynamical complexity in a discrete time model, given sufficient input gain. We control through a single input unit fully connected to an echo state reservoir; our influence of the system is constrained to the input only - no weights are modified after the network is initialized. Our methodology is successful for both temporal and spatial control goals. However, control of increasingly complex systems requires increasing saturation of units´ activation function non-linearities, which we achieve by increasing the input gain. We find that when subjected to the minimal gain needed for control goals, systems of varying levels of dynamical complexity are reduced to very similar levels. However, even in such reduced circumstances, our control framework is still advantageous or necessary to achieve performance above chance levels.