Approachability has become a standard tool in analyzing learning algorithms
in the adversarial online learning setup. We develop a variant of
approachability for games where there is ambiguity in the obtained reward that
belongs to a set, rather than being a single vector. Using this variant we
tackle the problem of approachability in games with partial monitoring and
develop simple and efficient algorithms (i.e., with constant per-step
complexity) for this setup.