Humans leverage shared conversational context to become increasingly successful and efficient at communicating over time. One manifestation of this is the formation of ad hoc linguistic conventions, which allow people to coordinate on short, less costly utterances that are understood using shared conversational context. We present a method to train large multimodal models to form conventions, enabling efficient communication. Our approach uses simulated reference games between models, and requires no additional human-produced data. In repeated reference games involving photographs and tangram images, our method enables models to communicate efficiently with people: reducing the message length by up to 41% while increasing success by 15% over the course of the interaction. Human listeners respond faster when interacting with our model that forms conventions. We also show that training based on success or cost alone is insufficient - both are necessary to elicit convention formation.