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Approachability has become a standard tool in analyzing earning algorithms inthe adversarial online learning setup. We develop a variant of approachabilityfor games where there is ambiguity in the obtained reward that belongs to aset, rather than being a single vector. Using this variant we tackle theproblem of approachability in games with partial monitoring and develop simpleand efficient algorithms (i.e., with constant per-step complexity) for thissetup. We finally consider external regret and internal regret in repeatedgames with partial monitoring and derive regret-minimizing strategies based onapproachability theory.

Robust approachability and regret minimization in games with partial monitoring