Robust approachability and regret minimization in games with partial monitoring

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 for this setup. We finally consider external and internal regret in repeated games with partial monitoring, for which we show efficient regret-minimizing strategies based on approachability theory.