Abstract:Are we running out of learning signal? Predicting the next word in an existing text has turned out to be a powerful signal, at least at scale. But there are signs that we are running out of this resource. In recent months, interaction between learner and feedback-giver has come into focus, both for "alignment" (with a reward model judging the quality of instruction following attempts) and for improving "reasoning" (process- and outcome-based verifiers judging reasoning steps). In this paper, we explore to what extent synthetic interaction in what we call Dialogue Games -- goal-directed and rule-governed activities driven predominantly by verbal actions -- can provide a learning signal, and how this signal can be used. We introduce an environment for producing such interaction data (with the help of a Large Language Model as counterpart to the learner model), both offline and online. We investigate the effects of supervised fine-tuning on this data, as well as reinforcement learning setups such as DPO, and GRPO; showing that all of these approaches achieve some improvements in in-domain games, but only GRPO demonstrates the ability to generalise to out-of-domain games as well as retain competitive performance in reference-based tasks. We release the framework and the baseline training setups in the hope that this can foster research in this promising new direction.