[Submitted on 17 May 2025 (v1), last revised 14 Oct 2026 (this version, v5)]
Abstract:In federated learning (FL), a center trains a shared model from updates that clients compute on their private data. Collecting and training on data is costly, so a strategic client may contribute little data and free-ride on the model trained by the others. We study mechanisms that incentivize data contribution and learn the model at the same time. Our first mechanism, UPBReD, updates the clients ‘ contributions and the model jointly, and converges at a geometric rate to a Nash equilibrium of the contribution game together with the welfare-maximizing model for those contributions. This equilibrium can involve under-contribution, so our second mechanism, 2P-UPBReD, adds budget-balanced transfers that make full contribution a dominant strategy, after which training converges to the optimal model; we also give conditions under which every client prefers to participate. Both mechanisms trust what clients report about the data they use and the gradients they compute. We show that no payment rule can reward unverifiable contributions unless something the center observes depends on the data actually used. Building on this, T-2P-UPBReD checks each client’s reported contribution against the other clients ‘ realized valuations of the trained model, and prices gradient reports with a budget-balanced charge. It elicits truthful contribution reports, makes gradient reports approximately truthful, still reaches full contribution and the optimal model, and never runs a deficit. Experiments on CIFAR-10, FEMNIST, and Twitter show that 2P-UPBReD matches the welfare of FedAvg trained on all data, while strategic clients without incentives lower the welfare of the learned model.
Submission history
From: Swaprava Nath [view email]
[v1] Sat, 17 May 2025 14:04:20 UTC (141 KB)
[v2] Thu, 19 Jun 2025 14:06:03 UTC (140 KB)
[v3] Mon, 13 Oct 2025 10:24:17 UTC (151 KB)
[v4] Mon, 16 Mar 2026 01:56:51 UTC (197 KB)
[v5] Wed, 14 Oct 2026 09:30:50 UTC (247 KB)
