Safe and Carefree Prediction-Powered Mean Estimation with Provable Cost Saving

The growing power of modern computing has enabled remarkable advances in digital models that mimic/predict the real world surprisingly well. However, depending on use cases, deficiencies of digital models would vary and may bring a critically wrong conclusion about the real world. In this work, we propose a new mean estimation framework that utilizes both real-world data and digital (synthetic) data. Despite widely reported challenges, the proposed framework strictly maintains the same guarantee as that of the pure real-world data case while provably reducing (at least no harm) the asymptotic cost using any arbitrary digital models. The key idea is to exploit the power of e-values, which allows us to safely identify the best way of incorporating digital data via e-merging with the universal portfolio algorithm. Experimental results on telecommunication engineering and AI intelligence evaluation confirm the theory.