Bandit Multi-linear DR-Submodular Maximization and Its Applications on Adversarial Submodular Bandits

Zongqi Wan, Jialin Zhang, Wei Chen, Xiaoming Sun, Zhijie Zhang
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:35491-35524, 2023.

Abstract

We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm $\mathtt{BanditMLSM}$ that attains $O(T^{2/3}\log T)$ of $(1-1/e)$-regret. Then we reduce submodular bandit with partition matroid constraint and bandit sequential monotone maximization to the online bandit learning of the monotone multi-linear DR-submodular functions, attaining $O(T^{2/3}\log T)$ of $(1-1/e)$-regret in both problems, which improve the existing results. To the best of our knowledge, we are the first to give a sublinear regret algorithm for the submodular bandit with partition matroid constraint. A special case of this problem is studied by Streeter et al.(2009). They prove a $O(T^{4/5})$ $(1-1/e)$-regret upper bound. For the bandit sequential submodular maximization, the existing work proves an $O(T^{2/3})$ regret with a suboptimal $1/2$ approximation ratio (Niazadeh et al. 2021).

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-wan23e, title = {Bandit Multi-linear {DR}-Submodular Maximization and Its Applications on Adversarial Submodular Bandits}, author = {Wan, Zongqi and Zhang, Jialin and Chen, Wei and Sun, Xiaoming and Zhang, Zhijie}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {35491--35524}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/wan23e/wan23e.pdf}, url = {https://proceedings.mlr.press/v202/wan23e.html}, abstract = {We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm $\mathtt{BanditMLSM}$ that attains $O(T^{2/3}\log T)$ of $(1-1/e)$-regret. Then we reduce submodular bandit with partition matroid constraint and bandit sequential monotone maximization to the online bandit learning of the monotone multi-linear DR-submodular functions, attaining $O(T^{2/3}\log T)$ of $(1-1/e)$-regret in both problems, which improve the existing results. To the best of our knowledge, we are the first to give a sublinear regret algorithm for the submodular bandit with partition matroid constraint. A special case of this problem is studied by Streeter et al.(2009). They prove a $O(T^{4/5})$ $(1-1/e)$-regret upper bound. For the bandit sequential submodular maximization, the existing work proves an $O(T^{2/3})$ regret with a suboptimal $1/2$ approximation ratio (Niazadeh et al. 2021).} }
Endnote
%0 Conference Paper %T Bandit Multi-linear DR-Submodular Maximization and Its Applications on Adversarial Submodular Bandits %A Zongqi Wan %A Jialin Zhang %A Wei Chen %A Xiaoming Sun %A Zhijie Zhang %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-wan23e %I PMLR %P 35491--35524 %U https://proceedings.mlr.press/v202/wan23e.html %V 202 %X We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm $\mathtt{BanditMLSM}$ that attains $O(T^{2/3}\log T)$ of $(1-1/e)$-regret. Then we reduce submodular bandit with partition matroid constraint and bandit sequential monotone maximization to the online bandit learning of the monotone multi-linear DR-submodular functions, attaining $O(T^{2/3}\log T)$ of $(1-1/e)$-regret in both problems, which improve the existing results. To the best of our knowledge, we are the first to give a sublinear regret algorithm for the submodular bandit with partition matroid constraint. A special case of this problem is studied by Streeter et al.(2009). They prove a $O(T^{4/5})$ $(1-1/e)$-regret upper bound. For the bandit sequential submodular maximization, the existing work proves an $O(T^{2/3})$ regret with a suboptimal $1/2$ approximation ratio (Niazadeh et al. 2021).
APA
Wan, Z., Zhang, J., Chen, W., Sun, X. & Zhang, Z.. (2023). Bandit Multi-linear DR-Submodular Maximization and Its Applications on Adversarial Submodular Bandits. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:35491-35524 Available from https://proceedings.mlr.press/v202/wan23e.html.

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