Stochastic Online Learning with Feedback Graphs: Finite-Time and Asymptotic Optimality
This work addresses theoretical gaps in online learning for researchers, offering a novel framework for optimality, though it is incremental in refining existing concepts.
The paper tackles the problem of stochastic online learning with feedback graphs by showing that optimal finite-time regret is not uniquely defined and is decoupled from asymptotic rates, proposing a meaningful notion of finite-time optimality and providing an algorithm with quasi-optimal regret in both finite-time and asymptotically.
We revisit the problem of stochastic online learning with feedback graphs, with the goal of devising algorithms that are optimal, up to constants, both asymptotically and in finite time. We show that, surprisingly, the notion of optimal finite-time regret is not a uniquely defined property in this context and that, in general, it is decoupled from the asymptotic rate. We discuss alternative choices and propose a notion of finite-time optimality that we argue is \emph{meaningful}. For that notion, we give an algorithm that admits quasi-optimal regret both in finite-time and asymptotically.