Robust approachability and regret minimization in games with partial monitoring

Shie Mannor, Vianney Perchet, Gilles Stoltz ; JMLR W&CP 19:515-536, 2011.

Abstract

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 efficientalgorithms (i.e., with constant per-step complexity) for this setup.We finally consider external and internal regret in repeated games with partial monitoring, for which we deriveregret-minimizing strategies based on approachability theory.

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