FedCoin: A Peer-to-Peer Payment System for Federated Learning

1 Introduction

• FL keeps sensitive data with distributed owners, addressing privacy constraints that make centralized storage problematic.Local model updates, rather than raw data, are transmitted, and local data do not leave the owners.Source: §1 · p. 1
• Shapley values are widely used to assess FL-client contributions fairly, but their computation remains costly even with approximation methods.The cited complexity for exact SV-based distribution is O(n!), where n is the number of data items.Source: §1 · p. 1
• FedCoin uses Proof of Shapley (PoSap) consensus to calculate clients’ Shapley values and records incentive payments immutably, without relying on a central FL server.The blockchain-based peer-to-peer payment scheme is intended to provide nonrepudiation and tamper-resistance.Source: §1 · p. 1
• Experiments on real-world data report that FedCoin determines Shapley-value contributions with an upper bound on the computational resources required for consensus.The work also presents FedCoin as an opportunity for entities with computational resources but no local data to contribute to FL.Source: §1 · pp. 1–2

2 Related Work

• Existing incentive mechanisms optimize rewards for self-interested FL clients and customers, whereas FedCoin is compatible with them in determining the customer payment budget.Examples described include contract theory and Stackelberg-game-based mechanisms.Source: §2 · p. 2
• Prior Shapley-value work includes polynomial-time and group-sampling approximations, while FedCoin aims to leverage otherwise-wasted distributed computation rather than reduce computational complexity.The passage cites Ancona et al. (2019) and Jia et al. (2019) for these approximation approaches.Source: §2 · p. 2
• Earlier FL blockchain systems use immutable ledgers to record local gradients or updates and aggregate them in a trusted manner; FedCoin uses the network as a computational engine and payment ledger.The cited systems include FLChain, BlockFL, blockchain-based server removal, and trust management.Source: §2 · p. 2

3 Preliminaries

• The overall dataset D consists of the local datasets D1 through DK, with total size n equal to the sum of their client dataset sizes.Each client k has a local dataset Dk of size nk.Source: §3 · p. 2
• The optimization objective is expressed using F(w), the aggregate loss over the dataset.The supplied passage introduces the objective function after defining the per-sample loss Fi(w) for model parameters at round t.Source: §3 · p. 2
• SGD-based methods, including federated averaging, compute local gradients; clients update their models and the server aggregates the local models into the global model.The aggregation step uses an aggregation function A.Source: §3 · p. 2

4 FedCoin

• The FL server publishes training tasks, aggregates client updates for ComPrice, and pays SapPrice for blockchain valuation, while total task payments stay within requester budget V.The system has an FL network and a peer-to-peer blockchain network; the server coordinates training and receives V from the requester.Source: §4 · pp. 2–3

4.1 Shapley Value Based Blockchain Consensus

• PoSap miners estimate client Shapley values by averaging marginal contributions over random client rankings; a result within difficulty D lets a miner append a block to the longest chain.Miners broadcast estimates, and block verification checks that the winner’s result is sufficiently close to the local aggregate.Source: §4.1 · pp. 3–4

4.2 Dynamic Mining Difficulty

• Mining difficulty decreases as block-generation speed increases and increases with mining power when block-generation speed is held constant.The paper describes difficulty updates as a way to adapt block mining to these two factors.Source: §4.2 · p. 4

4.3 The Payment Scheme

• A pre-agreed contract splits V into TrainPrice, ComPrice, and SapPrice; the block winner receives TrainPrice+SapPrice and allocates TrainPrice to clients with positive Shapley values.Transactions recording these transfers are stored in the new block.Source: §4.3 · pp. 4–5

5 Analysis

• PoSap incentivizes miners to contribute resources: miners applying more mining power have higher chances of winning a block.A successful winner can record transactions and receive payment from the FL server.Source: §5 · p. 5
• FedCoin can resist collusion by up to 50% of miners, but not beyond that stated threshold.The paper compares this limit with Bitcoin’s vulnerability to mining pools attracting more than 50% of miners.Source: §5 · p. 5
• Sequential task processing makes selfish mining irrational because withholding a winning block prevents the miner from receiving its reward and mining the next task.The next Shapley-value task waits for payment completion in the current block.Source: §5 · p. 5
• With parallel tasks and equal propagation delays, selfish miners earn more than honest miners when their pool exceeds 25% of mining power.The paper therefore does not recommend processing training requests in parallel.Source: §5 · p. 5

6.1 Experiment Settings

• The experiment uses MNIST’s 70,000 images, divided among 100 clients in ten groups with different data-quality types.Each client trains a classical neural network for 20 iterations, with FedAvg aggregating local model parameters.Source: §6.1 · p. 5

6.3 Results and Discussion

• Only types T0–T4 have positive Shapley values; values decline from T0 to T9 as client data quality decreases.The authors interpret negative values for T5–T9 as indicating that those clients can mislead model training.Source: Figure 4 · p. 6, §6.3 · p. 6

6.2 Data Quality Evaluation

• Data quality, measured by EMD against the full MNIST distribution, declines linearly from type T0 to T9.A higher EMD indicates lower data quality.Source: §6.2 · p. 6

6.3 Results and Discussion

• About 2,500 Shapley calculation iterations suffice for block generation once difficulty exceeds 1e−3 (D < 1e−3).The reported generation time converges at about 2,500 iterations, indicating an upper bound on consensus computational cost.Source: Figure 6 · p. 6, §6.3 · p. 6
• Models trained using clients with negative Shapley values have lower testing accuracy than the model trained using all 100 clients.FedCoin does not reward clients with negative Shapley values.Source: §6.3 · p. 6

• FedCoin is a blockchain-based FL payment system where PoSap computes client Shapley values, payments are immutably recorded, and payouts need no central FL server.Source: §7 · p. 6
• Experiments show FedCoin properly determines FL clients’ Shapley Value-based contributions with an upper bound on computational resources required for consensus.Source: §7 · p. 6
• FedCoin is described as the first attempt to leverage blockchain in FL incentive schemes, opening opportunities for non-data owners to contribute to FL.Source: §7 · p. 6