Randomized Greedy Learning for Non-monotone Stochastic Submodular Maximization Under Full-bandit Feedback
Fares Fourati, Vaneet Aggarwal, Christopher Quinn, Mohamed-Slim Alouini
Abstract
We investigate the problem of unconstrained combinatorial multi-armed bandits with full-bandit feedback and stochastic rewards for submodular maximization. Previous works investigate the same problem assuming a submodular and monotone reward function. In this work, we study a more general problem, i.e., when the reward function is not necessarily monotone, and the submodularity is assumed only in expectation. We propose Randomized Greedy Learning (RGL) algorithm and theoretically prove that it achieves a $\frac{1}{2}$-regret upper bound of $\tilde{\mathcal{O}}(n T^{\frac{2}{3}})$ for horizon $T$ and number of arms $n$. We also show in experiments that RGL empirically outperforms other full-bandit variants in submodular and non-submodular settings.
BibTeX
@InProceedings{pmlr-v206-fourati23a,
title = {Randomized Greedy Learning for Non-monotone Stochastic Submodular Maximization Under Full-bandit Feedback},
author = {Fourati, Fares and Aggarwal, Vaneet and Quinn, Christopher and Alouini, Mohamed-Slim},
booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics},
pages = {7455--7471},
year = {2023},
editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem},
volume = {206},
series = {Proceedings of Machine Learning Research},
month = {25--27 Apr},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v206/fourati23a/fourati23a.pdf},
url = {https://proceedings.mlr.press/v206/fourati23a.html},
abstract = {We investigate the problem of unconstrained combinatorial multi-armed bandits with full-bandit feedback and stochastic rewards for submodular maximization. Previous works investigate the same problem assuming a submodular and monotone reward function. In this work, we study a more general problem, i.e., when the reward function is not necessarily monotone, and the submodularity is assumed only in expectation. We propose Randomized Greedy Learning (RGL) algorithm and theoretically prove that it achieves a $\frac{1}{2}$-regret upper bound of $\tilde{\mathcal{O}}(n T^{\frac{2}{3}})$ for horizon $T$ and number of arms $n$. We also show in experiments that RGL empirically outperforms other full-bandit variants in submodular and non-submodular settings.}
}