Stochastic Online Learning with Feedback Graphs: Finite-Time and Asymptotic Optimality

We revisit the problem of stochastic online learning with feedbackgraphs, with the goal of devising algorithms that are optimal, up toconstants, both asymptotically and in finite time. We show that,surprisingly, the notion of optimal finite-time regret is not auniquely defined property in this context and that, in general, itis decoupled from the asymptotic rate. We discuss alternativechoices and propose a notion of finite-time optimality that we argueis \emph{meaningful}. For that notion, we give an algorithm thatadmits quasi-optimal regret both in finite-time and asymptotically.