Exploring the Potential of Bilevel Optimization for Calibrating Neural Networks

2025-03-17

AI Summary

Neural network prediction confidence often deviates from true posterior probabilities, undermining decision reliability. To address this, we propose the first self-calibrating bilevel optimization framework explicitly designed for confidence calibration: the inner-level optimizes classification performance, while the outer-level directly minimizes calibration metrics—such as the Expected Calibration Error (ECE)—enabling end-to-end joint training and calibration. Our method leverages implicit function differentiation and gradient expansion to compute exact outer-level gradients, eliminating the need for post-hoc calibration and preserving classification accuracy. Evaluations on synthetic benchmarks—including Blobs, Spirals, and BAC simulation datasets—demonstrate significant ECE reduction compared to isotropic regression and other baselines. These results validate the effectiveness and generalizability of bilevel optimization for confidence calibration across diverse data geometries.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• Improving neural network confidence estimation and calibration
• Applying bilevel optimization to enhance model reliability
• Reducing calibration error without sacrificing accuracy

Innovation

• Bilevel optimization for neural network calibration
• Self-calibrating training approach improves confidence scores
• Reduces calibration error while maintaining model accuracy