  We consider the following question: in a nonatomic routing game, can the
tolls that induce the minimum latency flow be computed without knowing the
latency functions? Since the latency functions are unknown, we assume we are
given an oracle that has access to the underlying routing game. A query to the
oracle consists of tolls on edges, and the response is the resulting
equilibrium flow. We show that in this model, it is impossible to obtain
optimal tolls. However, if we augment the oracle so that it returns the total
latency of the equilibrium flow induced by the tolls in addition to the flow
itself, then the required tolls can be computed with a polynomial number of
queries.
