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

TL;DR

This paper investigates stochastic online learning with feedback graphs, proposing algorithms that achieve near-optimal regret both in finite time and asymptotically, and discusses the nuanced differences in defining finite-time optimality.

Contribution

The paper introduces a meaningful notion of finite-time optimality for feedback graph learning and provides an algorithm that is nearly optimal in both finite and asymptotic regimes.

Findings

Proposes a new, meaningful definition of finite-time optimality.

Develops an algorithm with quasi-optimal regret in finite and asymptotic settings.

Highlights the decoupling between finite-time and asymptotic optimality in feedback graph learning.

Abstract

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.