Submodular maximization problems are a relevant model set for many real-world applications. Since these problems are generally NP-Hard, many methods have been developed to approximate the optimal solution in polynomial time. One such approach uses an agent-based greedy algorithm, where the goal is for each agent to choose an action from its action set such that the union of all actions chosen is as high-valued as possible. Recent work has shown how the performance of the greedy algorithm degrades as the amount of information shared among the agents decreases, whereas this work addresses the scenario where agents are capable of sharing more information than allowed in the greedy algorithm. Specifically, we show how performance guarantees increase as agents are capable of passing messages, which can augment the allowable decision set for each agent. Under these circumstances, we show a near-optimal method for message passing, and how much such an algorithm could increase performance for any given problem instance.

中文翻译：

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基于代理的子模块最大化中消息传递的影响

子模块最大化问题是许多实际应用的相关模型集。由于这些问题通常是 NP-Hard 问题，因此已经开发了许多方法来在多项式时间内逼近最优解。一种这样的方法使用基于代理的贪心算法，其目标是让每个代理从其动作集中选择一个动作，使得所有选择的动作的联合尽可能高。最近的工作表明贪心算法的性能如何随着代理之间共享的信息量减少而降低，而这项工作解决了代理能够共享比贪婪算法允许的更多信息的情况。具体来说，我们展示了性能保证如何随着代理能够传递消息而增加，这可以增加每个代理的允许决策集。