Strategizing against Learners in Bayesian Games

Yishay Mansour, Mehryar Mohri, Jon Schneider, Balasubramanian Sivan

Research output: Contribution to journalConference articlepeer-review

8 Scopus citations


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
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: 2 Jul 20225 Jul 2022


FundersFunder number
Yandex Initiative for Machine Learning
Horizon 2020 Framework Programme882396
European Research Council
Israel Science Foundation993/17
Tel Aviv University


    • Bayesian games
    • Stackelberg value
    • swap regret


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