Budgeted Prediction With Expert Advice

We consider a budgeted variant of the problem of learning from expert advice with N experts. Each queried expert incurs a cost and there is a given budget B on the total cost of experts that can be queried in any prediction round. We provide an online learning algorithm for this setting with regret after T prediction rounds bounded by O C B log(N)T, where C is the total cost of all experts. We complement this upper bound with a nearly matching lower bound Ω