Handling uncertainty is critical for ensuring reliable decision-making in intelligent systems. Modern neural networks are known to be poorly calibrated, resulting in predicted confidence scores that are difficult to use. This article explores improving confidence estimation and calibration through the application of bilevel optimization, a framework designed to solve hierarchical problems with interdependent optimization levels. A self-calibrating bilevel neural-network training approach is introduced to improve a model's predicted confidence scores. The effectiveness of the proposed framework is analyzed using toy datasets, such as Blobs and Spirals, as well as more practical simulated datasets, such as Blood Alcohol Concentration (BAC). It is compared with a well-known and widely used calibration strategy, isotonic regression. The reported experimental results reveal that the proposed bilevel optimization approach reduces the calibration error while preserving accuracy.

翻译：处理不确定性对于确保智能系统可靠决策至关重要。已知现代神经网络校准效果不佳，导致预测置信度得分难以实际应用。本文通过应用双层优化框架探索改进置信度估计与校准的方法，该框架专为求解具有相互依赖优化层次的层级问题而设计。我们提出一种自校准双层神经网络训练方法，以改进模型的预测置信度得分。通过玩具数据集（如Blobs和Spirals）以及更贴近实际的模拟数据集（如血液酒精浓度数据集），分析了所提框架的有效性。该方法与经典且广泛使用的校准策略——等渗回归进行了对比。实验结果表明，所提出的双层优化方法在保持准确性的同时有效降低了校准误差。