Title: Self-Adaptive Perturbation Radii for Adversarial Training. Abstract: Adversarial training has been shown to be the most popular and effective  technique to protect models from imperceptible adversarial samples. Despite its success, it also accompanies the significant performance degeneration to clean data. To achieve a good performance on both clean and adversarial samples, the main effort  is searching for an adaptive perturbation radius for each training sample, which essentially suffers from a  conflict between exact searching  and  computational overhead. To address this conflict, in this paper, firstly we show the superiority of adaptive perturbation radii intuitively and theoretically regarding the   accuracy and robustness respectively. Then we propose our novel self-adaptive adjustment framework for perturbation radii without tedious searching. We also discuss this framework on both deep neural networks (DNNs) and kernel support vector machines (SVMs).  Finally, extensive experimental results show that our framework can improve not only natural generalization performance but also adversarial robustness. It is also competitive with existing searching strategies in terms of running time.