We study adversarial online learning with expert recommendations in a totally ordered action space, where the experts' recommendations may change and be reordered arbitrarily. Our focus is two-point feedback: on each round the learner plays two current recommendations, observes both, and pays their average. We study two problems.
Separated monotone problem
In the separated monotone problem, the loss is the sum of a hidden nondecreasing component and a hidden nonincreasing component, and a query reveals the two components separately.
BV problem
In the BV problem, the losses are bounded and have bounded