  Given two sources of evidence about a latent variable, one can combine the
information from both by multiplying the likelihoods of each piece of evidence.
However, when one or both of the observation models are misspecified, the
distributions will conflict. We study this problem in the setting with two
conflicting reward functions learned from different sources. In such a setting,
we would like to retreat to a broader distribution over reward functions, in
order to mitigate the effects of misspecification. We assume that an agent will
maximize expected reward given this distribution over reward functions, and
identify four desiderata for this setting. We propose a novel algorithm,
Multitask Inverse Reward Design (MIRD), and compare it to a range of simple
baselines. While all methods must trade off between conservatism and
informativeness, through a combination of theory and empirical results on a toy
environment, we find that MIRD and its variant MIRD-IF strike a good balance
between the two.
