On the Influence of Informed Agents on Learning and Adaptation over Networks

Adaptive networks consist of a collection of agents with adaptation and learning abilities. The agents interact with each other on a local level and diffuse information across the network through their collaborations. In this work, we consider two types of agents: informed agents and uninformed agents. The former receive new data regularly and perform consultation and in-network tasks, while the latter do not collect data and only participate in the consultation tasks. We examine the performance of adaptive networks as a function of the proportion of informed agents and their distribution in space. The results reveal some interesting and surprising trade-offs between convergence rate and mean-square performance. In particular, among other results, it is shown that the performance of adaptive networks does not necessarily improve with a larger proportion of informed agents. Instead, it is established that the larger the proportion of informed agents is, the faster the convergence rate of the network becomes albeit at the expense of some deterioration in mean-square performance. The results further establish that uninformed agents play an important role in determining the steady-state performance of the network, and that it is preferable to keep some of the highly connected agents uninformed. The arguments reveal an important interplay among three factors: the number and distribution of informed agents in the network, the convergence rate of the learning process, and the estimation accuracy in steady-state. Expressions that quantify these relations are derived, and simulations are included to support the theoretical findings. We further apply the results to two models that are widely used to represent behavior over complex networks, namely, the Erdos-Renyi and scale-free models.

💡 Research Summary

The paper investigates how the presence and placement of “informed agents” – nodes that regularly acquire fresh data – affect the learning dynamics of diffusion adaptive networks. In a diffusion network each node performs two steps at every iteration: an adaptation step, where it updates its estimate using locally observed data, and a combination step, where it fuses its intermediate estimate with those of its neighbors according to a left‑stochastic combination matrix A. The authors distinguish two classes of agents. Informed agents execute both adaptation and combination, while uninformed agents skip the adaptation step and only participate in the combination. This distinction reflects realistic constraints such as limited sensing capability, power budget, or privacy restrictions.

The authors first formulate the global error dynamics. By stacking the individual weight vectors into a single vector w(i) and linearizing around the optimal solution, they obtain a recursion of the form

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