Domain Adaptation with Adaptive $f$-Divergence: Tighter Variational Representation and Generalization Bounds

We study unsupervised domain adaptation (UDA) where measuring cross-domain discrepancy is critical. Most UDA approaches fix a single $f$-divergence a priori, which can be suboptimal across heterogeneous shifts. We propose a framework that (i) tightens the variational lower bound of an $f$-divergence by inserting a learnable, monotone $L$-Lipschitz transform $\tau$ (Tighter-VR), and (ii) selects the divergence family adaptively from data via a likelihood-based criterion. The resulting estimator yields more informative and statistically efficient discrepancy estimates while recovering prior fixed-divergence methods as special cases. Theoretically, we derive a target-risk bound whose three components are a transformed source risk, a Tighter-VR discrepancy between domains, and an ideal-hypothesis residual; we further provide finite-sample guarantees using standard complexity measures. Empirically, on Office-31, Office-Home, Digits, and VisDA-2017, our method consistently improves accuracy over strong baselines, showing that coupling Tighter-VR with adaptive divergence selection is useful for UDA.

Machine learning models often work well on data similar to their training data, but their accuracy can drop when used in a new setting, such as moving from synthetic images to real camera images or from one image collection to another. A common way to handle this problem is to make the training and new data look more similar to the model, but existing methods usually rely on one fixed way of measuring the difference between the two datasets. Our work builds a method that can learn a better measure of this difference while training. It also adjusts the type of measure it uses based on the data, instead of choosing it in advance. We provide mathematical analysis showing when this approach should reduce the risk of errors on the new data. In experiments on standard image adaptation benchmarks, the method improved accuracy over several strong baselines. This can help reduce the need to label large amounts of new data whenever a model is deployed in a changed environment.