Incentivizing Truthfulness and Collaborative Fairness in Bayesian Learning

Collaborative machine learning involves training high-quality models using datasets from a number of sources. To incentivize sources to share data, existing data valuation methods fairly reward each source based on its data submitted as is. However, as these methods do not verify nor incentivize data truthfulness, the sources can manipulate their data (e.g., by submitting duplicated or noisy data) to artificially increase their valuations and rewards or prevent others from benefiting. This paper presents the first mechanism that provably ensures (F) collaborative fairness and incentivizes (T) truthfulness at equilibrium for Bayesian models. Our mechanism combines semivalues (e.g., Shapley value), which ensure fairness, and a truthful data valuation function (DVF) based on a validation set that is unknown to the sources. As semivalues are influenced by others' data, we introduce an additional condition to prove that a source can maximize its expected data values in coalitions and semivalues by submitting a dataset that captures its true knowledge. Additionally, we discuss the implications and suitable relaxations of (F) and (T) when the mediator has a limited budget for rewards or lacks a validation set. Our theoretical findings are validated on synthetic and real-world datasets.

When several parties contribute data to train a machine learning model together, they need a fair way to decide how much each party should be rewarded. Existing methods usually reward contributors based on how useful their submitted data is. However, this can be problematic as contributors may game the system by submitting duplicated, noisy or fake data to increase their reward or prevent others from benefiting. This paper proposes a reward mechanism for Bayesian models that satisfies both goals at the same time. It rewards each contributor based on how much their data helps the model, while also encouraging them to submit their data truthfully. The key idea is to combine a fair reward-splitting rule with a hidden validation set, which acts like a secret test that contributors cannot directly optimize by manipulating their data. Each contributor believes that on average, their true data leads to the highest reward. Importantly, our mechanism comes with theoretical guarantees: every contributor is fairly rewarded and under some assumptions, truthful submission forms a stable equilibrium. This means that when everyone else is truthful, no contributor can improve their expected reward by changing their data. We also study harder cases and their implications, such as when the reward budget is limited or when no validation set is available.