Title: Neighborhood Learning in Weighted Beeping Networks
Primary area: learning on graphs and other geometries & topologies
Keywords: Neighborhood Learning, Multiagent Systems, Weighted Beeping Networks

Abstract: Neighborhood Learning (NL) is a fundamental tool in Multiagent Systems (MAS). The task is for each autonomous agent to learn, in parallel, some information (e.g., agent identifier, message, etc.) from every neighboring agent, according to some notion of vicinity. NL thus requires communication among neighboring agents, which is particularly challenging if agents are tiny devices with very limited capabilities (for instance, biological systems) and may interrupt each other.
In this work, we study how the speed of learning depends on the system topology. We model the communication environment as a Weighted Beeping Network (WBN). In a WBN, network nodes (one for each agent) communicate by deciding whether to beep or stay silent -- all the beeps are then scaled by weights on the corresponding links, and a threshold function is applied at each idle node to check if they heard a beep or not.
We introduce a novel characteristic of a WBN topology, called Maximum Average Influence (MaxAveInf), and we prove almost tight upper and lower bounds on the running time to accomplish NL task by a Multiagent System, as a linear function of that characteristic. Although MaxAveInf is a global characteristic and it could be as large as the number of all agents in some networks, even with small neighborhoods,
for networks with small value of MaxAveInf we succeeded to give a provably-efficient nearly-optimal algorithmic solution.