A Unified Analysis of Dynamic Interactive Learning

TL;DR

This paper presents a unified framework for analyzing dynamic interactive learning, addressing concept evolution over combinatorial structures, and provides new bounds and algorithms with practical mistake guarantees.

Contribution

It introduces a general model that encompasses previous models, closing the gap between upper and lower bounds on query complexity, and analyzes simple algorithms with mistake bounds.

Findings

Unified framework for dynamic concept learning

Closed gap between query complexity bounds

Mistake bounds for low diameter graphs

Abstract

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.