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We consider a crowdsourcing data acquisition scenario, such as federatedlearning, where a Center collects data points from a set of rational Agents,with the aim of training a model. For linear regression models, we show how apayment structure can be designed to incentivize the agents to providehigh-quality data as early as possible, based on a characterization of theinfluence that data points have on the loss function of the model. Ourcontributions can be summarized as follows: (a) we prove theoretically thatthis scheme ensures truthful data reporting as a game-theoretic equilibrium andfurther demonstrate its robustness against mixtures of truthful and heuristicdata reports, (b) we design a procedure according to which the influencecomputation can be efficiently approximated and processed sequentially inbatches over time, (c) we develop a theory that allows correcting thedifference between the influence and the overall change in loss and (d) weevaluate our approach on real datasets, confirming our theoretical findings.

Rewarding High-Quality Data via Influence Functions