  Despite the considerable success enjoyed by machine learning techniques in
practice, numerous studies demonstrated that many approaches are vulnerable to
attacks. An important class of such attacks involves adversaries changing
features at test time to cause incorrect predictions. Previous investigations
of this problem pit a single learner against an adversary. However, in many
situations an adversary's decision is aimed at a collection of learners, rather
than specifically targeted at each independently. We study the problem of
adversarial linear regression with multiple learners. We approximate the
resulting game by exhibiting an upper bound on learner loss functions, and show
that the resulting game has a unique symmetric equilibrium. We present an
algorithm for computing this equilibrium, and show through extensive
experiments that equilibrium models are significantly more robust than
conventional regularized linear regression.
