  Applications of machine learning inform human decision makers in a broad
range of tasks. The resulting problem is usually formulated in terms of a
single decision maker. We argue that it should rather be described as a
two-player learning problem where one player is the machine and the other the
human. While both players try to optimize the final decision, the setup is
often characterized by (1) the presence of private information and (2) opacity,
that is imperfect understanding between the decision makers. We prove that both
properties can complicate decision making considerably. A lower bound
quantifies the worst-case hardness of optimally advising a decision maker who
is opaque or has access to private information. An upper bound shows that a
simple coordination strategy is nearly minimax optimal. More efficient learning
is possible under certain assumptions on the problem, for example that both
players learn to take actions independently. Such assumptions are implicit in
existing literature, for example in medical applications of machine learning,
but have not been described or justified theoretically.
