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In non-stationary environments, learning machines usually confront the domain adaptation scenario where the data distribution does change over time. Previous domain adaptation works have achieved great success in theory and practice. However, they always lose robustness in noisy environments where the labels and features of examples from the source domain become corrupted. In this paper, we report our attempt towards achieving accurate noise-robust domain adaptation. We first give a theoretical analysis that reveals how harmful noises influence unsupervised domain adaptation. To eliminate the effect of label noise, we propose an offline curriculum learning for minimizing a newly-defined empirical source risk. To reduce the impact of feature noise, we propose a proxy distribution based margin discrepancy. We seamlessly transform our methods into an adversarial network that performs efficient joint optimization for them, successfully mitigating the negative influence from both data corruption and distribution shift. A series of empirical studies show that our algorithm remarkably outperforms state of the art, over 10% accuracy improvements in some domain adaptation tasks under noisy environments.