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Cooperative Set Function Optimization Without Communication or Coordination

We introduce a new model for cooperative agents that seek to optimize a common goal without communication or coordination. Given a universe of elements V, a set of agents, and a set function f, we ask each agent i to select a subset Si ⊂ V such that the size of Si is constrained (i.e., |Si| < k). The goal is for the agents to cooperatively choose the sets Si to maximize the function evaluated at the union of these sets, ∪iSi; we seek max f(∪iSi). We assume the agents can neither communicate nor coordinate how they choose their sets. This model arises naturally in many real-world settings such as swarms of surveillance robots and colonies of foraging insects. Even for simple classes of set functions, there are strong lower bounds on the achievable performance of coordinating deterministic agents. We show, surprisingly, that for the fundamental class of submodular set functions, there exists a near-optimal distributed algorithm for this problem that does not require communication. We demonstrate that our algorithm performs nearly as well as recently published algorithms that allow full coordination.