  In multi-agent reinforcement learning, the problem of learning to act is
particularly difficult because the policies of co-players may be heavily
conditioned on information only observed by them. On the other hand, humans
readily form beliefs about the knowledge possessed by their peers and leverage
beliefs to inform decision-making. Such abilities underlie individual success
in a wide range of Markov games, from bluffing in Poker to conditional
cooperation in the Prisoner's Dilemma, to convention-building in Bridge.
Classical methods are usually not applicable to complex domains due to the
intractable nature of hierarchical beliefs (i.e. beliefs of other agents'
beliefs). We propose a scalable method to approximate these belief structures
using recursive deep generative models, and to use the belief models to obtain
representations useful to acting in complex tasks. Our agents trained with
belief models outperform model-free baselines with equivalent representational
capacity using common training paradigms. We also show that higher-order belief
models outperform agents with lower-order models.
