Performance-Based Pricing for Federated Learning via Auction

Many machine learning techniques rely on plenty of training data. However, data are often possessed unequally by different entities, with a large proportion of data being held by a small number of data-rich entities. It can be challenging to incentivize data-rich entities to help train models with others via federated learning (FL) if there are no additional benefits. This difficulty arises because these data-rich entities cannot enjoy the revenue increment generated from the improved performances on tasks controlled by data-limited entities. In this paper, we investigate pricing mechanisms through auctions for FL, focusing on auction scenarios with one data seller and some data-limited entities as buyers. The mechanisms aim to account for buyers' performance gains from the FL and provide equitable monetary compensation to the data seller. We first formulate the task as a performance-based auction mechanism design problem and offer a template that can accommodate multiple kinds of auctions with different desiderata. Utilizing this template, we instantiate different truthful strategies with different goals, including maximizing social welfare and maximizing the seller's profit in auctions. In addition, considering the randomness between the model test performance used in the auction and the actual performance in a production environment, we provide theoretical analyses to quantify the impact of the uncertainty on the social welfare or the seller's profit of auction mechanisms. We provide experimental results based on two datasets with synthetic buyers' valuation to illustrate the truthfulness, social welfare, and data sellers' profit.