Abstract: We present a novel Bayesian-based optimization framework that addresses the challenge of generalization in overparameterized models when dealing with imbalanced subgroups and limited samples per subgroup. Our proposed tri-level optimization framework utilizes \textit{local} predictors, which are trained on a small amount of data, as well as a fair and class-balanced predictor at the middle and lower levels. To effectively overcome saddle points for minority classes, our lower-level formulation incorporates sharpness-aware minimization. Meanwhile, at the upper level, the framework dynamically adjusts the loss function based on validation loss, ensuring a close alignment between the \textit{global} predictor and local predictors. Theoretical analysis demonstrates the framework's ability to enhance classification and fairness generalization, potentially resulting in improvements in the generalization bound. Empirical results validate the superior performance of our tri-level framework compared to existing state-of-the-art approaches. The source code can be found at https://github.com/PennShenLab/FACIMS .
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