The limits and robustness of reinforcement learning in Lewis signalling games

Lewis signalling games are a standard model to study the emergence of language. We introduce win-stay/lose-inaction, a random process that only updates behaviour on success and never deviates from what was once successful, prove that it always ends up in a state of optimal communication in all Lewis signalling games, and predict the number of interactions it needs to do so: N-3 interactions for Lewis signalling games with N equiprobable types. We show three reinforcement learning algorithms (Roth-Erev learning, Q-learning, and Learning Automata) that can imitate win-stay/lose-inaction and can even cope with errors in Lewis signalling games.