  For an autonomous system to be helpful to humans and to pose no unwarranted
risks, it needs to align its values with those of the humans in its environment
in such a way that its actions contribute to the maximization of value for the
humans. We propose a formal definition of the value alignment problem as
cooperative inverse reinforcement learning (CIRL). A CIRL problem is a
cooperative, partial-information game with two agents, human and robot; both
are rewarded according to the human's reward function, but the robot does not
initially know what this is. In contrast to classical IRL, where the human is
assumed to act optimally in isolation, optimal CIRL solutions produce behaviors
such as active teaching, active learning, and communicative actions that are
more effective in achieving value alignment. We show that computing optimal
joint policies in CIRL games can be reduced to solving a POMDP, prove that
optimality in isolation is suboptimal in CIRL, and derive an approximate CIRL
algorithm.
