Minimax Generalized Cross-Entropy

TL;DR

This paper introduces a convex minimax formulation of generalized cross-entropy (MGCE) for supervised classification, improving robustness, convergence speed, and calibration, especially with noisy labels.

Contribution

The paper proposes a novel convex minimax formulation of GCE, enabling efficient optimization and better performance over existing non-convex approaches.

Findings

MGCE achieves higher accuracy on benchmark datasets.

MGCE converges faster than traditional GCE.

MGCE provides better calibration, especially with label noise.

Abstract

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.