Controlled Sequential Information Fusion with Social Sensors

A network of social sensors estimate an unknown state of nature by performing Bayesian Social Learning, and myopically optimize individual reward functions. The decisions of the social sensors contain quantized information about the underlying state. How should a fusion center dynamically incentivize the social sensors for acquiring the information about the underlying state? This paper presents four results. First, sufficient conditions on the model parameters are provided under which the optimal policy for the fusion center has a threshold structure. The optimal policy is determined in closed form, and is such that it switches between two exactly specified incentive policies at the threshold. Second, a sample path characterization of the optimal threshold policy is provided, i.e, the nature of the incentives (average trend over time) resulting from the fusion center employing the optimal threshold policy. It is shown that the optimal incentive sequence is a sub-martingale, i.e, the optimal incentives increase on average over time. Third, it is shown that it is possible for the fusion center to learn the true state asymptotically by employing a sub-optimal policy; in other words, controlled information fusion with social sensors can be consistent. Finally, uniform bounds on the average additional cost incurred by the fusion center for employing a sub-optimal policy are provided. This characterizes the trade-off between the cost of information acquisition and consistency, for the fusion center.