Online Missing-Update Correction under Informative Client Participation

Cross-device federated learning relies on partial participation, yet client availability can depend on prior activity, staleness, and optimization state. The returned updates can therefore be an informative rather than representative subset, causing standard averaging to favor repeatedly available clients. Existing methods typically correct participation probabilities or reconstruct missing updates; either correction can become misspecified as availability and client trajectories drift. We introduce FedDORA, a server-side framework that treats participation as sequential missingness and combines leakage-free online propensity estimation with vector-valued update prediction. A population-normalized orthogonal aggregate couples these two nuisance models: under history-conditional ignorability and overlap, either a correct propensity or update model removes conditional aggregation bias, while joint misspecification enters through a product remainder. We establish an exact bias identity, an explicit variance formula under conditional client independence, and a general non-convex convergence bound. Across CIFAR-10, CIFAR-100, and OfficeHome, controlled observable and latent participation mechanisms, residual adaptation, and oracle interventions, FedDORA achieves competitive endpoint performance while providing strong tail and mechanism-level evidence for informative-participation correction. Ablations and hidden-driver tests further delineate its identification boundary.