Minimax Generalized Cross-Entropy
This work addresses a specific issue in supervised classification for machine learning practitioners, offering an incremental improvement over existing loss functions.
The paper tackles the problem of balancing optimization difficulty and robustness in classification by proposing a minimax formulation of generalized cross-entropy (MGCE), which results in convex optimization and achieves strong accuracy, faster convergence, and better calibration, especially with label noise.
Loss functions play a central role in supervised classification. Cross-entropy (CE) is widely used, whereas the mean absolute error (MAE) loss can offer robustness but is difficult to optimize. Interpolating between the CE and MAE losses, generalized cross-entropy (GCE) has recently been introduced to provide a trade-off between optimization difficulty and robustness. Existing formulations of GCE result in a non-convex optimization over classification margins that is prone to underfitting, leading to poor performances with complex datasets. In this paper, we propose a minimax formulation of generalized cross-entropy (MGCE) that results in a convex optimization over classification margins. Moreover, we show that MGCEs can provide an upper bound on the classification error. The proposed bilevel convex optimization can be efficiently implemented using stochastic gradient computed via implicit differentiation. Using benchmark datasets, we show that MGCE achieves strong accuracy, faster convergence, and better calibration, especially in the presence of label noise.