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(√C/B T) on the regret of any algorithm for this problem. We also provide experimental validation of our algorithm.