Recursive Least Squares Policy Control with Echo State Network

The echo state network (ESN) is a special type of recurrent neural networks for processing the time-series dataset. However, limited by the strong correlation among sequential samples of the agent, ESN-based policy control algorithms are difficult to use the recursive least squares (RLS) algorithm to update the ESN's parameters. To solve this problem, we propose two novel policy control algorithms, ESNRLS-Q and ESNRLS-Sarsa. Firstly, to reduce the correlation of training samples, we use the leaky integrator ESN and the mini-batch learning mode. Secondly, to make RLS suitable for training ESN in mini-batch mode, we present a new mean-approximation method for updating the RLS correlation matrix. Thirdly, to prevent ESN from over-fitting, we use the L1 regularization technique. Lastly, to prevent the target state-action value from overestimation, we employ the Mellowmax method. Simulation results show that our algorithms have good convergence performance.