Title: A General Upper Bound for Unsupervised Domain Adaptation. Abstract: In this work, we present a novel upper bound of target error to address the problem for unsupervised domain adaptation. Recent studies reveal that a deep neural network can learn transferable features which generalize well to novel tasks. Furthermore,  Ben-David et al. (2010) provide an upper bound for target error when transferring the knowledge, which can be summarized as minimizing the source error and  distance between marginal distributions simultaneously. However, common methods based on the theory usually ignore the joint error such that samples from different classes might be mixed together when matching marginal distribution. And in such case, no matter how we minimize the marginal discrepancy, the target error is not bounded due to an increasing joint error. To address this problem, we propose a general upper bound taking joint error into account, such that the undesirable case can be properly penalized. In addition, we utilize constrained hypothesis space to further formalize a tighter bound as well as a novel cross margin discrepancy to measure the dissimilarity between hypotheses which alleviates instability during adversarial learning. Extensive empirical evidence shows that our proposal outperforms related approaches in image classification error rates on standard domain adaptation benchmarks.