Learning over social networks via diffusion adaptation

We propose a diffusion strategy to enable social learning over networks. Individual agents observe signals influenced by the state of the environment. The individual measurements are not sufficient to enable the agents to detect the true state of the environment on their own. Agents are then encouraged to cooperate through a diffusive process of self-learning and social-learning. We show that the diffusion algorithm converges almost surely to the true state. Simulation results also illustrate the superior convergence rate of the diffusion strategy over consensus-based strategies since diffusion schemes allow information to diffuse more thoroughly through the network.