Nonzero-sum Adversarial Hypothesis Testing Games
This work addresses adversarial classification problems for machine learning and statistics, offering theoretical insights into equilibrium behavior and error rates, though it appears incremental as it extends classical results to an adversarial setting.
The paper tackles nonzero-sum hypothesis testing games in adversarial classification, showing they admit mixed strategy Nash equilibria and analyzing concentration phenomena, with main results providing exponential convergence rates of classification errors at equilibrium analogous to classical error exponents but derived from adversarial parameters, 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.