Fairness of Shapley Approximation
In any distributed setting with a single common product, such as in Federated Learning (where multiple participants train a Machine Learning model together in a privacy-friendly way), the contribution of the individuals is a crucial question. For instance, when several pharmaceutical companies train a model together, which leads to a huge breakthrough, how should they split the pay-off corresponding to the model?
Equal distribution is as unfair as the one based on the dataset sizes, as neither considers the data quality. What does fair mean in the first place? Shapley defined four fundamental fairness properties and proved that his reward allocation scheme is the only one that satisfies all. On the other hand, it is exponentially hard to compute, so it is standard practice to approximate it in real life.
The student's task is to study existing approximation methods and verify (theoretically or empirically) to what extent these methods respect the four desired properties.
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