A Unified Analysis of Dynamic Interactive Learning
This work addresses dynamic interactive learning for applications like clustering and recommender systems, but it is incremental as it builds directly on prior models.
The paper tackles the problem of learning evolving concepts over combinatorial structures, such as non-static user preferences in clustering or recommender systems, by providing a unified framework that captures previous models, closes the gap between upper and lower bounds on query complexity, and analyzes efficient algorithms with mistake bounds for specific graph types.
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.