  Recent work (Xu et al., 2020) has suggested that numeral systems in different
languages are shaped by a functional need for efficient communication in an
information-theoretic sense. Here we take a learning-theoretic approach and
show how efficient communication emerges via reinforcement learning. In our
framework, two artificial agents play a Lewis signaling game where the goal is
to convey a numeral concept. The agents gradually learn to communicate using
reinforcement learning and the resulting numeral systems are shown to be
efficient in the information-theoretic framework of Regier et al. (2015);
Gibson et al. (2017). They are also shown to be similar to human numeral
systems of same type. Our results thus provide a mechanistic explanation via
reinforcement learning of the recent results in Xu et al. (2020) and can
potentially be generalized to other semantic domains.
