New Algorithm Maximizes Submodular Functions in Distributed Bandit Settings.

Optimizing submodular functions in distributed, online settings, especially when agents have limited information (bandit feedback), presents significant challenges. This paper addresses the problem where multiple agents sequentially select actions from their own subsets to maximize a cumulative objective, subject to partition matroid constraints. The researchers developed a comprehensive algorithmic framework that works effectively with both full-information and bandit feedback models. A key achievement is proving that these algorithms can achieve sublinear regret guarantees, matching the performance of existing centralized solutions. Furthermore, the framework tackles the practical issue of sampling violations that often arise from continuous relaxation and rounding in optimization. It introduces a novel bounded stochastic pipage rounding scheme, demonstrating that the probability of such violations diminishes asymptotically, keeping cumulative violations sublinear. This theoretical finding is supported by numerical results.