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Speed-vs-Accuracy Tradeoff in Collective Estimation: An Adaptive Exploration-Exploitation Case

The tradeoff between accuracy and speed is considered fundamental to individual and collective decision-making. In this paper, we focus on collective estimation as an example of collective decision-making. The task is to estimate the average scalar intensity of a desired feature in the environment. The solution we propose consists of exploration and exploitation phases, where the switching time is a factor dictating the balance between the two phases. By decomposing the total accuracy into bias and variance, we explain that diversity and social interactions could promote the accuracy of the collective decision. We also show how the exploration-vs-exploitation tradeoff relates to the speed-vs-accuracy tradeoff. One significant finding of our work is that there is an optimal duration for exploration to compromise between speed and accuracy. This duration cannot be determined offline for an unknown environment. Hence, we propose an adaptive, distributed mechanism enabling individual agents to decide in a decentralized manner when to switch. Moreover, the spatial consequence of the exploitation phase is an emergent collective movement, leading to the aggregation of the collective at the iso-contours of the mean intensity of the environmental field in the spatial domain. Examples of potential applications for such a fully distributed collective estimation model are spillage capturing and source localization.