A Unified Analysis of Dynamic Interactive Learning

In this paper we investigate the problem of learning evolving concepts over a combinatorial structure. Previous work by Emamjomeh-Zadeh et al. [1] introduced dynamics into interactive learning as a way to model non-static user preferences in clustering problems or recommender systems. We provide many useful contributions to this problem. First, we give a framework that captures the two different models analyzed by Emamjomeh-Zadeh et al. [1], which allows us to study any type of concept evolution and matches the same mistake bounds and running time guarantees of the previous models. Using this general model we solve the open problem of closing the gap between the upper and lower bounds on the number of mistakes. Finally, we study an efficient algorithm where the learner simply follows the feedback at each round, and we provide mistake bounds for low diameter graphs such as cliques, stars, and general o(logn) diameter graphs by using a Markov Chain model.