  Assuming humans are (approximately) rational enables robots to infer reward
functions by observing human behavior. But people exhibit a wide array of
irrationalities, and our goal with this work is to better understand the effect
they can have on reward inference. The challenge with studying this effect is
that there are many types of irrationality, with varying degrees of
mathematical formalization. We thus operationalize irrationality in the
language of MDPs, by altering the Bellman optimality equation, and use this
framework to study how these alterations would affect inference.
  We find that wrongly modeling a systematically irrational human as
noisy-rational performs a lot worse than correctly capturing these biases -- so
much so that it can be better to skip inference altogether and stick to the
prior! More importantly, we show that an irrational human, when correctly
modelled, can communicate more information about the reward than a perfectly
rational human can. That is, if a robot has the correct model of a human's
irrationality, it can make an even stronger inference than it ever could if the
human were rational. Irrationality fundamentally helps rather than hinder
reward inference, but it needs to be correctly accounted for.
