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The extent of loss in a seismic hazard can be moderated with on-time allocation of funds and initiation of recovery tasks. Among various examinations conducted following the hazard, buildings damages are assessed as part of the reconnaissance survey to learn and document the impact of the earthquake on structures. The results of the survey are used in financial aid estimation, which is crucial for the community rapid recovery acts after the hazard. Due to the urgent need for this information, the amount of information gained per unit of time should be optimized. This article aims at answering the question of how to maximize the information gain in the presence of resource constraints by directing the efforts of a reconnaissance surveying team. A data-driven method is proposed that actively learns the patterns of damage and recommends the most informative buildings to be inspected while considering the resource limitations. The framework utilizes an efficient active learning method based on mutual information and developed for Gaussian process regression (GPR) to identify the information-rich cases. To assess the contribution of information gain and resource allocation in the overall outcome of the damage inference, two simulated earthquake testbeds are studied. It is shown that in a co-optimization approach, damage labels of the majority of buildings can be accurately predicted after 1 week of damage inspections.