This paper introduces ASCAI, a novel adaptive sampling methodology that can learn how to effectively compress Deep Neural Networks (DNNs) for accelerated inference on resource-constrained platforms. Modern DNN compression techniques comprise various hyperparameters that require per-layer customization to ensure high accuracy. Choosing such hyperparameters is cumbersome as the pertinent search space grows exponentially with the number of model layers. To effectively traverse this large space, we devise an intelligent sampling mechanism that adapts the sampling strategy using customized operations inspired by genetic algorithms. As a special case, we consider the space of model compression as a vector space. The adaptively selected samples enable ASCAI to automatically learn how to tune per-layer compression hyperparameters to optimize the accuracy/model-size trade-off. Our extensive evaluations show that ASCAI outperforms rule-based and reinforcement learning methods in terms of compression rate and/or accuracy