Controlled Sequential Information Fusion With Social Sensors
Sujay Bhatt, Vikram Krishnamurthy · IEEE Transactions on Automatic Control · 2020
A sequence of social sensors estimates an unknown parameter (modeled as a state of nature) by performing Bayesian social learning, and myopically optimizes 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 information about the underlying state? This article presents five 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 a closed form, and is such that it switches between two exactly specified incentive policies at the threshold. Second, it is shown that the optimal incentive sequence is asubmartingale, 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 suboptimal policy; in other words, controlled information fusion with social sensors can be consistent. Fourth, uniform bounds on the average additional cost incurred by the fusion center for employing a suboptimal policy are provided. This characterizes the tradeoff between the cost of information acquisition and consistency for the fusion center. Finally, uniform bounds on the budget saved by employing policies that guarantee state estimation in finite time are provided.