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arXiv · 2607.00680

Distributed Online Bandit Submodular Maximization with Bounded Sampling Violations

Bin Du·Chang Liu·Dingqi Zhu·Lintao Ye·Dengfeng Sun
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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.

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Bin Du, Chang Liu, Dingqi Zhu, Lintao Ye, Dengfeng Sun. 2026-07-01. Distributed Online Bandit Submodular Maximization with Bounded Sampling Violations. https://arxiv.org/abs/2607.00680

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