FedTau: Correcting Observation-Induced Target Mismatch in Federated Learning

Federated learning (FL) trains a shared predictor from heterogeneous client data, but existing methods mainly address heterogeneity after local objectives have already been defined. We identify an earlier source of discrepancy: clients may observe the same underlying prediction task through different sampling or recording mechanisms, causing their local supervision to encode different prediction targets. We refer to this phenomenon as observation-induced target mismatch. To address this, we formulate FL as learning a shared reference response distribution through client-specific observation mechanisms and propose FedTau, a unified $\tau$-correction that corrects local supervision where the mismatch first occurs. For each observed record, FedTau evaluates the shared predictor through the corresponding observation mechanism and defines $\tau$ as the difference between the observed-data negative log-likelihood and the conventional supervised loss. Theoretically, we show that the corrected client objectives can achieve a common predictive optimum and analyze the effect of observation-mechanism estimation errors on local updates and aggregation. Experiments on nine datasets against twenty-three distinct baselines demonstrate consistent improvements across all three tasks. In particular, FedTau improves CIFAR-10 accuracy by $12.32\%$ over the second-best under severe class-prior heterogeneity, reduces RMSE by $6.67\%$–$37.61\%$ across three right-censored regression datasets, and improves both token likelihood and token accuracy on all three sequence-prediction datasets.