  Existing observational approaches for learning human preferences, such as
inverse reinforcement learning, usually make strong assumptions about the
observability of the human's environment. However, in reality, people make many
important decisions under uncertainty. To better understand preference learning
in these cases, we study the setting of inverse decision theory (IDT), a
previously proposed framework where a human is observed making non-sequential
binary decisions under uncertainty. In IDT, the human's preferences are
conveyed through their loss function, which expresses a tradeoff between
different types of mistakes. We give the first statistical analysis of IDT,
providing conditions necessary to identify these preferences and characterizing
the sample complexity -- the number of decisions that must be observed to learn
the tradeoff the human is making to a desired precision. Interestingly, we show
that it is actually easier to identify preferences when the decision problem is
more uncertain. Furthermore, uncertain decision problems allow us to relax the
unrealistic assumption that the human is an optimal decision maker but still
identify their exact preferences; we give sample complexities in this
suboptimal case as well. Our analysis contradicts the intuition that partial
observability should make preference learning more difficult. It also provides
a first step towards understanding and improving preference learning methods
for uncertain and suboptimal humans.
