In this paper, we provide a new framework to obtain the generalization bounds of the learning process for domain adaptation, and then apply the derived bounds to analyze the asymptotical convergence of the learning process. Without loss of generality, we consider two kinds of representative domain adaptation: one is with multiple sources and the other is combining source and target data. In particular, we use the integral probability metric to measure the difference between two domains. For either kind of domain adaptation, we develop a related Hoeffding-type deviation inequality and a symmetrization inequality to achieve the corresponding generalization bound based on the uniform entropy number. We also generalized the classical McDiarmid's inequality to a more general setting where independent random variables can take values from different domains. By using this inequality, we then obtain generalization bounds based on the Rademacher complexity. Afterwards, we analyze the asymptotic convergence and the rate of convergence of the learning process for such kind of domain adaptation. Meanwhile, we discuss the factors that affect the asymptotic behavior of the learning process and the numerical experiments support our theoretical findings as well.

本文提出了一种新的框架，通过应用获得的领域自适应学习过程的泛化界，分析了学习过程的渐近收敛。为了测量两个领域之间的差异，使用积分概率度量。通过不同的不等式和复杂度测量，证明了领域自适性学习的一些性质，并用数值实验验证了理论结果的正确性。

领域自适应的泛化界限