In the Machine-to-Machine (M2M) transmission context, there is a great need to reduce the amount of transmitted information using lossy compression. However, commonly used image compression methods are designed for human perception, not for Artificial Intelligence (AI) algorithms performances. It is known that these compression distortions affect many deep learning based architectures on several computer vision tasks. In this paper, we focus on the classification task and propose a new approach, named expert training, to enhance Convolutional Neural Networks (CNNs) resilience to compression distortions. We validated our approach using MnasNet and ResNet50 architectures, against image compression distortions introduced by three commonly used methods (JPEG, J2K and BPG), on the ImageNet dataset. The results showed a better robustness of these two architectures against the tested coding artifacts using the proposed expert training approach. Our code is publicly available at https://github.com/albmarie/expert_training.