Distributed Alignment Processes With Samples of Group Average

Reaching agreement despite noise in communication is a fundamental problem multi-agent systems. Here we study this under an idealized model, where it assumed that agents can sense the general tendency system. More specifically, consider $n$ agents, each being associated with real-valued number. In round, agent receives noisy measurement of average value, and then updates its which turn perturbed by random drift. We assume both noises measurements drift follow Gaussian distributions. What should be updating policy if their goal to minimize expected deviation agents' values from value? prove distributed weighted-average algorithm optimally minimizes for agent, any round. Interestingly, optimality holds even centralized setting, master gather all instruct move agent.We find result surprising since shown total obtained contain strictly more information about Agent $i$ than contained alone. Although relevant $i$, not processed when running algorithm. Nevertheless, optimal, it, other manage fully process way perfectly benefits $i$.Finally, also analyze center mass show no achieve as small one achieved best light this, our incurs relatively overhead over possible setting.