Valuing Updates, Not Rounds, in Fully Asynchronous Federated Learning

Contribution evaluation assigns credit to clients in federated learning and underpins incentives and participation. Existing methods rely on synchronous rounds, which supply fixed participants, a common reference model, and a well-defined aggregate for every subset of updates. Fully asynchronous training removes all three. Replayed on the same training traces, eight published evaluators rank clients in conflicting ways, so it is unclear what quantity their scores estimate. We introduce FedACE, which values each asynchronous update through its own cooperative game. The players are the update itself and the updates applied between its dispatch and its arrival, the reference is the global model from which it was computed, and every coalition is composed in the recorded arrival order. All three are read from the execution record rather than chosen by the evaluator. We prove that this game is well-posed, that the recorded sequence of global models identifies its composition order under an explicit non-degeneracy condition, and that it coincides with the classical round game when coalitions are composed by a synchronous batch rule. FedACE solves small games exactly by enumeration, estimates larger ones with score-blind random permutation rings, credits each update exactly once, and never alters the training trajectory. Because the game admits exact evaluation, we score every estimator against the same exact Shapley value rather than a proxy. Across 27,000 updates on CIFAR-10, CIFAR-100, and Tiny-ImageNet, FedACE solves 73.4% of the games exactly. On all 681 nine-update games, it uses 23% of the utility queries required by exhaustive enumeration and is closer to the exact value than every compared estimator in each of the nine training runs. At the same query budget, Monte Carlo sampling incurs 1.7 to 1.9 $\times$ the error of FedACE.