Strategizing against Learners in Bayesian Games

Yishay Mansour, Mehryar Mohri, Jon Schneider, Balasubramanian Sivan

Research output: Contribution to journalConference articlepeer-review


We study repeated two-player games where one of the players, the learner, employs a no-regret learning strategy, while the other, the optimizer, is a rational utility maximizer. We consider general Bayesian games, where the payoffs of both the optimizer and the learner could depend on the type, which is drawn from a publicly known distribution, but revealed privately to the learner. We address the following questions: (a) what is the bare minimum that the optimizer can guarantee to obtain regardless of the no-regret learning algorithm employed by the learner? (b) are there learning algorithms that cap the optimizer payoff at this minimum? (c) can these algorithms be implemented efficiently? While building this theory of optimizer-learner interactions, we define a new combinatorial notion of regret called polytope swap regret, that could be of independent interest in other settings.

Original languageEnglish (US)
Pages (from-to)5221-5252
Number of pages32
JournalProceedings of Machine Learning Research
StatePublished - 2022
Event35th Conference on Learning Theory, COLT 2022 - London, United Kingdom
Duration: Jul 2 2022Jul 5 2022


  • Bayesian games
  • Stackelberg value
  • swap regret

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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