A. Kontogiannis, V. Pollatos, P. Mertikopoulos, and I. Panageas. In AISTATS '26: Proceedings of the 29th International Conference on Artificial Intelligence and Statistics, 2026.
This paper addresses the problem of designing efficient no-swap regret algorithms for combinatorial bandits, where the number of actions $N$ is exponentially large in the dimensionality of the problem. In this setting, designing efficient no-swap regret translates to sublinear – in horizon $T$ – swap regret with polylogarithmic dependence on $N$. In contrast to the weaker notion of external regret minimization - a problem which is fairly well understood in the literature - achieving no-swap regret with a polylogarithmic dependence on $N$ has remained elusive in combinatorial bandits. Our paper resolves this challenge, by introducing a no-swap-regret learning algorithm with regret that scales polylogarithmically in $N$ and is tight for the class of combinatorial bandits. To ground our results, we also demonstrate how to implement the proposed algorithm efficiently – that is, with a per-iteration complexity that also scales polylogarithmically in $N$ – across a wide range of well-studied applications.
arXiv link: https://arxiv.org/abs/2602.02087