Efficient Swap Regret Minimization in Combinatorial Bandits

Andreas Kontogiannis, Vasilis Pollatos, Panayotis Mertikopoulos, Ioannis Panageas
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1963-1971, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-kontogiannis26a, title = { Efficient Swap Regret Minimization in Combinatorial Bandits }, author = {Kontogiannis, Andreas and Pollatos, Vasilis and Mertikopoulos, Panayotis and Panageas, Ioannis}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1963--1971}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/kontogiannis26a/kontogiannis26a.pdf}, url = {https://proceedings.mlr.press/v300/kontogiannis26a.html}, abstract = { 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. } }
Endnote
%0 Conference Paper %T Efficient Swap Regret Minimization in Combinatorial Bandits %A Andreas Kontogiannis %A Vasilis Pollatos %A Panayotis Mertikopoulos %A Ioannis Panageas %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-kontogiannis26a %I PMLR %P 1963--1971 %U https://proceedings.mlr.press/v300/kontogiannis26a.html %V 300 %X 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.
APA
Kontogiannis, A., Pollatos, V., Mertikopoulos, P. & Panageas, I.. (2026). Efficient Swap Regret Minimization in Combinatorial Bandits . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1963-1971 Available from https://proceedings.mlr.press/v300/kontogiannis26a.html.

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