Learning the Robustness Mechanism with Bilevel Optimization

2026-09-28

AI Summary

This study addresses the reliance on manual hyperparameter tuning and low computational efficiency in distributionally robust optimization (DRO) by proposing an automated learning framework based on bilevel optimization. This approach pioneers the parameterization of robustness mechanisms, leveraging minimax modeling to automatically learn optimal parameters from held-out data. It accommodates scenarios both with and without group labels, thereby eliminating extensive manual tuning. Theoretically, we establish that the proposed method achieves generalization bounds comparable to grid search while significantly reducing sample complexity. Empirical evaluations demonstrate its effectiveness and scalability under complex distribution shifts, substantially improving the computational efficiency of DRO.

Abstract

We propose a distributionally robust learning framework where parameters defining the robustness mechanism are learned from held-out data instead of extensively tuned. Using bilevel optimization with both upper and lower level minimax problems, we create two instances of our framework to tackle setups with and without group labels in the training set. Theoretically, we provide sample complexity analysis for our robustness mechanism learning paradigm, showing that it achieves generalization guarantees comparable to exhaustive grid search while being more computationally efficient. Empirically, we evaluate our framework under a challenging setup when both intra-group and inter-group test distribution shifts occur at the same time, thereby demonstrating the efficacy and scalability of our method.

Problem

• distributionally robust learning
• bilevel optimization
• robustness mechanism
• distribution shift
• sample complexity

Innovation

• Bilevel Optimization
• Distributionally Robust Learning
• Sample Complexity
• Minimax Problems
• Distribution Shift