Guaranteed Environment-Action Regularization for Feature-Level Federated Domain Generalization

Federated domain generalization (FDG) trains on isolated source clients but must predict on an unseen domain without target data. Existing feature-statistic augmentation interpolates observed styles or heuristically explores feature statistics, but does not certify that the feature actually consumed by the loss lies outside the observed environment hull. We propose FedGEAR (Guaranteed Environment-Action Regularization), a target-blind architecture that certifies this realized training action. Clients compute shared, class-balanced translation/log-scale sketches; the server learns an effective-rank environment basis, and a step-compensated endpoint makes the re-sketched acted coordinate cross a supporting hyperplane by a positive margin. Clients mine the hardest certified action and directly train the deployed semantic predictor, while a normalized witness is used only during training. We prove the exterior certificate and derive a structural target-risk decomposition that exposes action approximation, candidate coverage, bank drift, predictor consistency, and uncontrolled target mismatch. Across 294 controlled feature-level runs on OfficeHome-65, CIFAR-10C/100C, and a missing-combination benchmark, FedGEAR has the highest mean accuracy in all seven protocols under a controlled common-interface comparison with thirteen baseline adaptations. Its 0.28-point gain over FedWon is small but consistent: all seven protocol means are positive and a hierarchical bootstrap gives [0.08, 0.53]. A matched control keeps every component but omits step compensation: endpoints remain 100% exterior, acted exteriority falls to 2–12%, yet mean accuracy changes by only 0.03 points. The certificate is therefore a verifiable exposure property, not an accuracy guarantee. A separate all-65-class, four-target, three-seed short-budget trainable-ResNet audit finds comparable performance to FedWon (28.08% versus 28.12%; paired 95% CI [−0.20, 0.13]), showing end-to-end competitiveness rather than superiority.