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Authentication is the task of confirming the matching relationship between a data instance and a given identity. Typical examples of authentication problems include face recognition and person re-identification. Data-driven authentication could be affected by undesired biases, i.e., the models are often trained in one domain (e.g., for people wearing spring outfits) while applied in other domains (e.g., they change the clothes to summer outfits). Previous works have made efforts to eliminate domain-difference. They typically assume domain annotations are provided, and all the domains share classes. However, for authentication, there could be a large number of domains shared by different identities/classes, and it is impossible to annotate these domains exhaustively. It could make domain-difference challenging to model and eliminate. In this paper, we propose a domain-agnostic method that eliminates domain-difference without domain labels. We alternately perform latent domain discovery and domain-difference elimination until our model no longer detects domain-difference. In our approach, the latent domains are discovered by learning the heterogeneous predictive relationships between inputs and outputs. Then domain-difference is eliminated in both class-dependent and class-independent spaces to improve robustness of elimination. We further extend our method to a meta-learning framework to pursue more thorough domain-difference elimination. Comprehensive empirical evaluation results are provided to demonstrate the effectiveness and superiority of our proposed method.