We study learning algorithms when there is a mismatch between the distributions of the training and test datasets of a learning algorithm. The effect of this mismatch on the generalization error and model misspecification are quantified. Moreover, we provide a connection between the generalization error and the rate-distortion theory, which allows one to utilize bounds from the rate-distortion theory to derive new bounds on the generalization error and vice versa. In particular, the rate-distortion based bound strictly improves over the earlier bound by Xu and Raginsky even when there is no mismatch. We also discuss how "auxiliary loss functions" can be utilized to obtain upper bounds on the generalization error.

翻译：当学习算法的培训分布和测试数据集的分布不匹配时,我们学习算法。这种不匹配对一般错误和模型区分错误的影响是量化的。此外,我们提供了一般错误和率扭曲理论之间的联系,允许人们利用率扭曲理论的界限来得出关于一般错误的新界限,反之亦然。特别是,基于费率扭曲的严格约束性改善了Xu和Raginsky先前约束的范围,即使没有不匹配的情况。我们还讨论了如何利用“辅助损失功能”来获得普遍错误的上限。