We study nonzero-sum hypothesis testing games that arise in the context of adversarial classification, in both the Bayesian as well as the Neyman-Pearson frameworks. We first show that these games admit mixed strategy Nash equilibria, and then we examine some interesting concentration phenomena of these equilibria. Our main results are on the exponential rates of convergence of classification errors at equilibrium, which are analogous to the well-known Chernoff-Stein lemma and Chernoff information that describe the error exponents in the classical binary hypothesis testing problem, but with parameters derived from the adversarial model. The results are validated through numerical experiments.

Summary of the model: A set of samples is either drawn from p or from some q chosen by an attacker from a set Q. The defended must look at the samples and decide which is the case. The attacker gets utility if the defender decides incorrectly, but pays some cost for drawing the samples that depends on the choice of q. Summary of results: Shows existence of a mixed-strategy Nash equilibrium. Leaves open existence of pure strategy, or natural conditions under which the equilibrium is pure (it seems to me this would be a very nice and likely result, given some strengthening of the assumptions). Shows that in equilibrium, error rates concentrate to zero as the number of samples n grows large.

The paper proposes a new adversarial framework for hypothesis testing, in a game-theoretic setup. The main positives are: the formulation bridges many fields including statistics, property testing, game-theory, and has the potential to inspire much future work. The theoretical results are reasonable but somewhat unsurprising.

We study nonzero-sum hypothesis testing games that arise in the context of adversarial classification, in both the Bayesian as well as the Neyman-Pearson frameworks. We first show that these games admit mixed strategy Nash equilibria, and then we examine some interesting concentration phenomena of these equilibria. Our main results are on the exponential rates of convergence of classification errors at equilibrium, which are analogous to the well-known Chernoff-Stein lemma and Chernoff information that describe the error exponents in the classical binary hypothesis testing problem, but with parameters derived from the adversarial model. The results are validated through numerical experiments.

We study nonzero-sum hypothesis testing games that arise in the context of adversarial classification, in both the Bayesian as well as the Neyman-Pearson frameworks. We first show that these games admit mixed strategy Nash equilibria, and then we examine some interesting concentration phenomena of these equilibria. Our main results are on the exponential rates of convergence of classification errors at equilibrium, which are analogous to the well-known Chernoff-Stein lemma and Chernoff information that describe the error exponents in the classical binary hypothesis testing problem, but with parameters derived from the adversarial model. The results are validated through numerical experiments. Papers published at the Neural Information Processing Systems Conference.