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We reveal the incoherence between the widely-adopted empirical domainadversarial training and its generally-assumed theoretical counterpart based on$\mathcal{H}$-divergence. Concretely, we find that $\mathcal{H}$-divergence isnot equivalent to Jensen-Shannon divergence, the optimization objective indomain adversarial training. To this end, we establish a new theoreticalframework by directly proving the upper and lower target risk bounds based onjoint distributional Jensen-Shannon divergence. We further derivebi-directional upper bounds for marginal and conditional shifts. Our frameworkexhibits inherent flexibilities for different transfer learning problems, whichis usable for various scenarios where $\mathcal{H}$-divergence-based theoryfails to adapt. From an algorithmic perspective, our theory enables a genericguideline unifying principles of semantic conditional matching, featuremarginal matching, and label marginal shift correction. We employ algorithmsfor each principle and empirically validate the benefits of our framework onreal datasets.

Beyond $\mathcal{H}$-Divergence: Domain Adaptation Theory With Jensen-Shannon Divergence