Federated Learning is increasingly used so that multiple data owners can learn a joint model without revealing their data. We consider in particular how to provide incentives so that the effort to contribute accurate data is appropriately rewarded. This is particularly challenging as the contributed data remains private and cannot be inspected directly. Known game-theoretic schemes for rewarding truthful data do not take into account novelty of data. This creates arbitrage opportunities where participants can gain rewards for redundant data, and the federation may be forced to pay out more incentives than justified by the value of the FL model. We show how a scheme based on influence can both guarantee that the incentive budget is bounded in proportion to the value of the resulting FL model, and that reporting data as accurately as possible is the dominant strategy of the participants.

We show how influence computation can be carried out while ensuring differential privacy guarantees to data owners. The privacy guarantee can be adjusted to achieve a tradeoff between privacy and reward. We next investigate what happens when the test data used for computing the influence is also elicited from participants. We show that if a portion of the testing data is of low quality, the incentive scheme will induce data collection with exactly the same proportion of low quality data, and thus in general it cannot be used to improve data quality over that of the test data. However, when the difference between corrupted and uncorrupted data is unbiased noise, incentives based on influence do incite higher payment for data with less noise. This corresponds in particular to the tradeoff when noise is added to obfuscate data and ensure privacy.