Universal Rates for Interactive Learning

Consider the task of learning an unknown concept from a given concept class; to what extent does interacting with a domain expert accelerate the learning process? It is common to measure the effectiveness of learning algorithms by plotting the "learning curve", that is, the decay of the error rate as a function of the algorithm's resources (examples, queries, etc). Thus, the overarching question in this work is whether (and which kind of) interaction accelerates the learning curve. Previous work in interactive learning focused on uniform bounds on the learning rates which only capture the upper envelope of the learning curves over families of data distributions. We thus formalize our overarching question within the distribution dependent framework of universal learning, which aims to understand the performance of learning algorithms on every data distribution, but without requiring a single upper bound which applies uniformly to all distributions.