Best-of-Both-Worlds FTRL for Linear Bandits: The Interplay of Information Acquisition, Corruption, and Geometry
Canzhe Zhao, Vincent Y. F. Tan
Abstract
We study \textit{best-of-both-worlds} (BOBW) algorithms for linear bandits, which aim to simultaneously guarantee $\gO(\sqrt T)$ regret in the adversarial regime and $\gO(\log T)$ regret in the stochastic regime over $T$ rounds. For finite action sets, we introduce \emph{information-acquisition follow-the-regularized-leader} (\IAFTRL{}), the first BOBW algorithm based purely on the follow-the-regularized-leader (FTRL) framework that attains an $\gO(\cstar\log T)$-type regret in the stochastic regime, where $\cstar$ is the information-acquisition complexity that characterizes instance-dependent optimality in linear bandits, while retaining the $\gO(\sqrt{T})$ regret guarantee in the adversarial regime. This resolves the open problem posed in~\cite{LeeEtAl2021,KongZ023,ItoT23,ZhaoItoLi2025}.