  In this paper we investigate the problem of learning evolving concepts over a
combinatorial structure. Previous work by Emamjomeh-Zadeh et al. [2020]
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
both of the models analyzed by [Emamjomeh-Zadeh et al., 2020], which allows us
to study any type of concept evolution and matches the same query complexity
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 query complexity. 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(log n)
diameter graphs by using a Markov Chain model.
