The current big data deluge requires innovative solutions for performing efficient inference on large, heterogeneous amounts of information. Apart from the known challenges deriving from high volume and velocity, real-world big data applications may impose additional technological constraints, including the need for a fully decentralized training architecture. While several alternatives exist for training feed-forward neural networks in such a distributed setting, less attention has been devoted to the case of decentralized training of recurrent neural networks (RNNs). In this paper, we propose such an algorithm for a class of RNNs known as Echo State Networks. The algorithm is based on the well-known Alternating Direction Method of Multipliers optimization procedure. It is formulated only in terms of local exchanges between neighboring agents, without reliance on a coordinating node. Additionally, it does not require the communication of training patterns, which is a crucial component in realistic big data implementations. Experimental results on large scale artificial datasets show that it compares favorably with a fully centralized implementation, in terms of speed, efficiency and generalization accuracy.