  Centaurs are half-human, half-AI decision-makers where the AI's goal is to
complement the human. To do so, the AI must be able to recognize the goals and
constraints of the human and have the means to help them. We present a novel
formulation of the interaction between the human and the AI as a sequential
game where the agents are modelled using Bayesian best-response models. We show
that in this case the AI's problem of helping bounded-rational humans make
better decisions reduces to a Bayes-adaptive POMDP. In our simulated
experiments, we consider an instantiation of our framework for humans who are
subjectively optimistic about the AI's future behaviour. Our results show that
when equipped with a model of the human, the AI can infer the human's bounds
and nudge them towards better decisions. We discuss ways in which the machine
can learn to improve upon its own limitations as well with the help of the
human. We identify a novel trade-off for centaurs in partially observable
tasks: for the AI's actions to be acceptable to the human, the machine must
make sure their beliefs are sufficiently aligned, but aligning beliefs might be
costly. We present a preliminary theoretical analysis of this trade-off and its
dependence on task structure.
