  In this paper we consider the adversarial contextual bandit problem in metric
spaces. The paper "Nearest neighbour with bandit feedback" tackled this problem
but when there are many contexts near the decision boundary of the comparator
policy it suffers from a high regret. In this paper we eradicate this problem,
designing an algorithm in which we can hold out any set of contexts when
computing our regret term. Our algorithm builds on that of "Nearest neighbour
with bandit feedback" and hence inherits its extreme computational efficiency.
