As Machine Learning (ML) is increasingly used in solving various tasks in real-world applications, it is crucial to ensure that ML algorithms are robust to any potential worst-case noises, adversarial attacks, and highly unusual situations when they are designed. Studying ML robustness will significantly help in the design of ML algorithms. In this paper, we investigate ML robustness using adversarial training in centralized and decentralized environments, where ML training and testing are conducted in one or multiple computers. In the centralized environment, we achieve a test accuracy of 65.41% and 83.0% when classifying adversarial examples generated by Fast Gradient Sign Method and DeepFool, respectively. Comparing to existing studies, these results demonstrate an improvement of 18.41% for FGSM and 47% for DeepFool. In the decentralized environment, we study Federated learning (FL) robustness by using adversarial training with independent and identically distributed (IID) and non-IID data, respectively, where CIFAR-10 is used in this research. In the IID data case, our experimental results demonstrate that we can achieve such a robust accuracy that it is comparable to the one obtained in the centralized environment. Moreover, in the non-IID data case, the natural accuracy drops from 66.23% to 57.82%, and the robust accuracy decreases by 25% and 23.4% in C&W and Projected Gradient Descent (PGD) attacks, compared to the IID data case, respectively. We further propose an IID data-sharing approach, which allows for increasing the natural accuracy to 85.04% and the robust accuracy from 57% to 72% in C&W attacks and from 59% to 67% in PGD attacks.