Unified Algorithms for Online Learning and Competitive Analysis

Online learning and competitive analysis are two widely studied frameworks for online decisionmaking settings. Despite the frequent similarity of the problems they study, there are significant differences in their assumptions, goals and techniques, hindering a unified analysis and richer interplay between the two. In this paper, we provide several contributions in this direction. We provide a single unified algorithm which by parameter tuning, interpolates between optimal regret for learning from experts (in online learning) and optimal competitive ratio for the metrical task systems problem (MTS) (in competitive analysis), improving on the results of Blum and Burch (1997). The algorithm also allows us to obtain new regret bounds against “drifting” experts, which might be of independent interest. Moreover, our approach allows us to go beyond experts/MTS, obtaining similar unifying results for structured action sets and “combinatorial experts”, whenever the setting has a certain matroid structure.