Distributed Online Bandit Submodular Maximization with Bounded Sampling Violations
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Computer Science > Machine Learning
Title:Distributed Online Bandit Submodular Maximization with Bounded Sampling Violations
Abstract:We study distributed online submodular maximization under partition matroid constraints, in which multiple agents select a limited number of actions from their own subsets sequentially to maximize the cumulative value of a sequence of objective functions. We develop a unified algorithmic framework that accommodates full-information and bandit feedback models. For both feedback models, we prove that the proposed algorithms achieve sublinear $(1-1/e)$-regret guarantees, which are comparable to those achieved by existing centralized counterparts. Furthermore, to tackle the sampling violation issue caused by continuous relaxation and rounding, we develop a bounded stochastic pipage rounding scheme and show that the probability of sampling violation vanishes asymptotically. As a result, the cumulative sampling violation remains sublinear in $T$, which is further shown to be not improvable under certain conditions. Numerical results validate the theoretical findings in this paper.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2607.00680 [cs.LG] |
| (or arXiv:2607.00680v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.00680
arXiv-issued DOI via DataCite (pending registration)
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