Echo State Networks for Reinforcement Learning

Echo State Networks (ESNs) are a type of single-layer recurrent neural network with randomly-chosen internal weights and a trainable output layer. We prove under mild conditions that a sufficiently large Echo State Network (ESN) can approximate the value function of a broad class of stochastic and deterministic control problems. Such control problems are generally non-Markovian. We describe how the ESN can form the basis for novel (and computationally efficient) reinforcement learning algorithms in a non-Markovian framework. We demonstrate this theory with two examples. In the first, we use an ESN to solve a deterministic, partially observed, control problem which is a simple game we call `Bee World'. In the second example, we consider a stochastic control problem inspired by a market making problem in mathematical finance. In both cases we can compare the dynamics of the algorithms with analytic solutions to show that even after only a single reinforcement policy iteration the algorithms perform with reasonable skill.