Modern semi-supervised learning (SSL) methods rely on pseudolabeling and consistency regularization. Pseudolabeling is typically performed by comparing the model’s confidence scores and a predefined threshold. While several heuristics have been proposed to improve threshold selection, the underlying issues of overconfidence and miscalibration in confidence scores remain largely unaddressed, leading to inaccurate pseudolabels, degraded test accuracy, and prolonged training. We take a first-principles approach to learn confidence scores and thresholds with an explicit knob for error. This flexible framework addresses the fundamental question of optimal scores and threshold selection in pseudolabeling. Moreover, it gives practitioners a principled way to control the quality and quantity of pseudolabels. Such control is vital in SSL, where balancing pseudolabel quality and quantity directly affects model performance and training efficiency. Our experiments show that, by integrating this framework with modern SSL methods, we achieve significant improvements in accuracy and training efficiency. In addition, we provide novel insights on the trade-offs between the choices of the error parameter and the end model’s performance.

Auto-labeling is an important family of techniques that produce labeled training sets with minimum manual annotation. A prominent variant, threshold-based auto-labeling (TBAL), works by finding thresholds on a model's confidence scores above which it can accurately automatically label unlabeled data. However, many models are known to produce overconfident scores, leading to poor TBAL performance. While a natural idea is to apply off-the-shelf calibration methods to alleviate the overconfidence issue, we show that such methods fall short. Rather than experimenting with ad-hoc choices of confidence functions, we propose a framework for studying the optimal TBAL confidence function. We develop a tractable version of the framework to obtain Colander (Confidence functions for Efficient and Reliable Auto-labeling), a new post-hoc method specifically designed to maximize performance in TBAL systems. We perform an extensive empirical evaluation of Colander and compare it against methods designed for calibration. Colander achieves up to 60% improvement on coverage over the baselines while maintaining error level below 5% and using the same amount of labeled data.