Active Prediction-Powered E-Values with Efficiency Guarantees

Quality statistical inference requires large amounts of data, which can be prohibitively hard to obtain. To overcome this, recent works on active prediction-powered inference leverage powerful AI models to produce surrogate data, occasionally sampling true labels to debias the results. However, existing methods struggle when the predictive model is inaccurate, often producing worse results than standard non-prediction-powered inference. In this paper, we propose a new framework for active prediction-powered e-values that resolves this efficiency issue. The key idea is to combine both strategies -- the standard and the prediction-powered one -- and adaptively bet between the two via a multi-armed bandit algorithm that achieves sublinear regret on a log utility. Theory and experimental results confirm the efficiency of the proposed algorithm.