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 meaningful. For that notion, we give an a…