Edge offloading for deep neural networks (DNNs) can be adaptive to the input's complexity by using earlyexit DNNs. These DNNs have side branches throughout their architecture, allowing the inference to end earlier in the edge. The branches estimate the accuracy for a given input. If this estimated accuracy reaches a threshold, the inference ends on the edge. Otherwise, the edge offloads the inference to the cloud to process the remaining DNN layers. However, DNNs for image classification deals with distorted images, which negatively impact the branches' estimated accuracy. Consequently, the edge offloads more inferences to the cloud. This work introduces expert side branches trained on a particular distortion type to improve robustness against image distortion. The edge detects the distortion type and selects appropriate expert branches to perform the inference. This approach increases the estimated accuracy on the edge, improving the offloading decisions. We validate our proposal in a realistic scenario, in which the edge offloads DNN inference to Amazon EC2 instances. 1