This paper presents an algorithm for learning the meaning of messages communicated between agents that interact while acting optimally towards a cooperative goal. Our reinforcement-learning method is based on Bayesian filtering and has been adapted for a decentralized control process. Empirical results shed light on the complexity of the learning problem, and on factors affecting the speed of convergence. Designing intelligent agents able to adapt their mutual interpretation of messages exchanged, in order to improve overall task-oriented performance, introduces an essential cognitive capability that can upgrade the current state of the art in multi-agent and human-machine systems to the next level. Learning to communicate while acting will add to the robustness and flexibility of these systems and hence to a more efficient and productive performance.