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# Bayesian Games for Adversarial Regression Problems

*Proceedings of the 30th International Conference on Machine Learning*, PMLR 28(3):55-63, 2013.

#### Abstract

We study regression problems in which an adversary can exercise some control over the data generation process. Learner and adversary have conflicting but not necessarily perfectly antagonistic objectives. We study the case in which the learner is not fully informed about the adversary’s objective; instead, any knowledge of the learner about parameters of the adversary’s goal may be reflected in a Bayesian prior. We model this problem as a Bayesian game, and characterize conditions under which a unique Bayesian equilibrium point exists. We experimentally compare the Bayesian equilibrium strategy to the Nash equilibrium strategy, the minimax strategy, and regular linear regression.