Unveiling bootstrap uncertainty bias: understanding bagging efficiency over Gaussian processes in materials active learning

Abstract Bayesian optimization-based active learning has been widely used in materials design fields. Its core lies in the usage of Bagging or Gaussian Processes model-based Expected Improvement strategies. However, the former (BGEI) is significantly more efficient than the latter (GPEI) in the short term, which contradicts the common belief that Bayesian optimization requires long-term iterations to achieve optimal results but has not received sufficient attention in the field. We systematically investigate the fundamental mechanisms behind this efficiency paradox. We reveal that in small-sample datasets, Bagging models significantly overestimate uncertainty near peak samples due to undersampling of influential points during bootstrap resampling. This bias inadvertently triggers what we term an “attention shift mechanism” enabling BGEI to efficiently exploit multiple peaks within existing datasets without extensive exploration, explaining its remarkable effectiveness in short-term materials optimization—particularly on sparse, peak-concentrated datasets such as those collected from the literature. In contrast, Gaussian Process uncertainty maintains a strict correlation with distance, enabling GPEI to achieve global optimization, though its efficiency is often limited by extensive exploration space and finite experimental budgets. As a practical contribution, we propose a “feasibility of exploration” (FE) criterion and determine its threshold to select between BGEI or GPEI to maximize optimization efficiency with a given budget and initial training data. Our findings challenge traditional understanding of active learning mechanisms in materials design and provide both theoretical insights and practical guidance for selecting optimal strategies.