  Natural language is an intuitive and expressive way to communicate reward
information to autonomous agents. It encompasses everything from concrete
instructions to abstract descriptions of the world. Despite this, natural
language is often challenging to learn from: it is difficult for machine
learning methods to make appropriate inferences from such a wide range of
input. This paper proposes a generalization of reward design as a unifying
principle to ground linguistic communication: speakers choose utterances to
maximize expected rewards from the listener's future behaviors. We first extend
reward design to incorporate reasoning about unknown future states in a linear
bandit setting. We then define a speaker model which chooses utterances
according to this objective. Simulations show that short-horizon speakers
(reasoning primarily about a single, known state) tend to use instructions,
while long-horizon speakers (reasoning primarily about unknown, future states)
tend to describe the reward function. We then define a pragmatic listener which
performs inverse reward design by jointly inferring the speaker's latent
horizon and rewards. Our findings suggest that this extension of reward design
to linguistic communication, including the notion of a latent speaker horizon,
is a promising direction for achieving more robust alignment outcomes from
natural language supervision.
