Distributed Online Bandit Submodular Maximization with Bounded Sampling Violations

2026-07-01

AI Summary

This work addresses the challenge of sampling violations arising from continuous relaxation and rounding in distributed online submodular maximization under partition matroid constraints across multi-agent systems. The authors propose a unified algorithmic framework applicable to both full-information and bandit feedback settings. Its key innovation lies in a bounded stochastic pipage rounding scheme, for which they establish— for the first time—that the probability of sampling violations asymptotically vanishes and the cumulative violation remains sublinear. Under both feedback models, the method achieves tight sublinear $(1-1/e)$-regret bounds, matching the performance of centralized optimal algorithms. These theoretical guarantees are corroborated by numerical experiments.

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.

Problem

• distributed online optimization
• submodular maximization
• bandit feedback
• sampling violations
• partition matroid constraints

Innovation

• distributed online learning
• submodular maximization
• bandit feedback
• bounded sampling violation
• stochastic pipage rounding