Folk Theorem-based Loss Function for Robust and Fair Learning under Class Imbalance

Class imbalance biases deep classifiers toward majority classes and away from under-represented ones. We propose a loss function inspired by the Folk theorem from repeated-game theory: each class is treated, loosely, as a player whose classification accuracy is its payoff, and classes that persistently over-perform are assigned a dynamic penalty at both the batch level and the epoch level, while under-performing classes retain full gradient influence. The penalty is folded directly into each class's effective loss weight rather than added to the scalar loss value, so that it provably reshapes gradients instead of merely shifting a number (sec:method). We further combine per-class gradients into a Pareto-Optimal Gradient (POG) and reconcile that direction with the overall classification gradient via a two-objective PCGrad projection. The method is loss-agnostic and is evaluated on top of SCCE, Focal, LDAM, and Class-Balanced losses, across seven CNN backbones and four benchmark datasets (CIFAR-10, CIFAR-100, Fashion-MNIST, Caltech-101) under a single, unified preprocessing and imbalance protocol. We report macro-averaged precision/recall/F1, worst-class accuracy, and class-wise F1 variance alongside accuracy, and ablate the batch-level penalty, the epoch-level penalty, and the POG+PCGrad gradient fusion independently. Evaluated across seven CNN backbones and four base losses, the proposed penalty improves accuracy and fairness metrics over the corresponding baseline loss on the large majority of backbone/dataset combinations, most consistently when combined with SCCE. All code, configuration files, and raw per-run logs are released at an anonymized repository link: https://anonymous.4open.science/r/Folk-Theorem-Loss-3D8E