LC-Tsallis-INF: Generalized Best-of-Both-Worlds Linear Contextual Bandits

Masahiro Kato, Shinji Ito
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3655-3663, 2025.

Abstract

We investigate the \emph{linear contextual bandit problem} with independent and identically distributed (i.i.d.) contexts. In this problem, we aim to develop a \emph{Best-of-Both-Worlds} (BoBW) algorithm with regret upper bounds in both stochastic and adversarial regimes. We develop an algorithm based on \emph{Follow-The-Regularized-Leader} (FTRL) with Tsallis entropy, referred to as the $\alpha$-\emph{Linear-Contextual (LC)-Tsallis-INF}. We show that its regret is at most $O(\log(T))$ in the stochastic regime under the assumption that the suboptimality gap is uniformly bounded from below, and at most $O(\sqrt{T})$ in the adversarial regime. Furthermore, our regret analysis is extended to more general regimes characterized by the \emph{margin condition} with a parameter $\beta \in (1, \infty]$, which imposes a milder assumption on the suboptimality gap than in previous studies. We show that the proposed algorithm achieves $O\left(\log(T)^{\frac{1+\beta}{2+\beta}}T^{\frac{1}{2+\beta}}\right)$ regret under the margin condition.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-kato25a, title = {LC-Tsallis-INF: Generalized Best-of-Both-Worlds Linear Contextual Bandits}, author = {Kato, Masahiro and Ito, Shinji}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3655--3663}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/kato25a/kato25a.pdf}, url = {https://proceedings.mlr.press/v258/kato25a.html}, abstract = {We investigate the \emph{linear contextual bandit problem} with independent and identically distributed (i.i.d.) contexts. In this problem, we aim to develop a \emph{Best-of-Both-Worlds} (BoBW) algorithm with regret upper bounds in both stochastic and adversarial regimes. We develop an algorithm based on \emph{Follow-The-Regularized-Leader} (FTRL) with Tsallis entropy, referred to as the $\alpha$-\emph{Linear-Contextual (LC)-Tsallis-INF}. We show that its regret is at most $O(\log(T))$ in the stochastic regime under the assumption that the suboptimality gap is uniformly bounded from below, and at most $O(\sqrt{T})$ in the adversarial regime. Furthermore, our regret analysis is extended to more general regimes characterized by the \emph{margin condition} with a parameter $\beta \in (1, \infty]$, which imposes a milder assumption on the suboptimality gap than in previous studies. We show that the proposed algorithm achieves $O\left(\log(T)^{\frac{1+\beta}{2+\beta}}T^{\frac{1}{2+\beta}}\right)$ regret under the margin condition.} }
Endnote
%0 Conference Paper %T LC-Tsallis-INF: Generalized Best-of-Both-Worlds Linear Contextual Bandits %A Masahiro Kato %A Shinji Ito %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-kato25a %I PMLR %P 3655--3663 %U https://proceedings.mlr.press/v258/kato25a.html %V 258 %X We investigate the \emph{linear contextual bandit problem} with independent and identically distributed (i.i.d.) contexts. In this problem, we aim to develop a \emph{Best-of-Both-Worlds} (BoBW) algorithm with regret upper bounds in both stochastic and adversarial regimes. We develop an algorithm based on \emph{Follow-The-Regularized-Leader} (FTRL) with Tsallis entropy, referred to as the $\alpha$-\emph{Linear-Contextual (LC)-Tsallis-INF}. We show that its regret is at most $O(\log(T))$ in the stochastic regime under the assumption that the suboptimality gap is uniformly bounded from below, and at most $O(\sqrt{T})$ in the adversarial regime. Furthermore, our regret analysis is extended to more general regimes characterized by the \emph{margin condition} with a parameter $\beta \in (1, \infty]$, which imposes a milder assumption on the suboptimality gap than in previous studies. We show that the proposed algorithm achieves $O\left(\log(T)^{\frac{1+\beta}{2+\beta}}T^{\frac{1}{2+\beta}}\right)$ regret under the margin condition.
APA
Kato, M. & Ito, S.. (2025). LC-Tsallis-INF: Generalized Best-of-Both-Worlds Linear Contextual Bandits. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3655-3663 Available from https://proceedings.mlr.press/v258/kato25a.html.

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