提出平滑版分位数激活函数，提升分位数神经网络的训练效率和精度。
ConquerNet: Convolution-Smoothed Quantile ReLU Neural Networks with Minimax Guarantees
- 用卷积平滑替代传统非光滑激活，使损失函数更易优化。
- 在多个分位点上优于标准方法，尤其在高低分位点表现突出。
- 理论证明具有极小最大风险保证，适合对鲁棒性要求高的场景。
分位数回归是分布学习的基础工具，但深层模型因pinball损失的非光滑性面临重大优化挑战。本文提出ConquerNet，一种卷积平滑的分位数ReLU神经网络，能在保持分位数结构的同时生成光滑目标函数。在温和条件下，我们建立了ConquerNet的一般非渐近风险界，提供了在Besov函数类上的极小最大保证。数值实验表明，该方法在多个分位点上均优于标准分位数神经网络，整体提升了估计精度与训练效率，尤其在高、低分位点优势显著。
原文摘要 · Abstract (English)
Quantile regression is a fundamental tool for distributional learning but poses significant optimization challenges for deep models due to the non-smoothness of the pinball loss. We propose ConquerNet, a class of \textbf{con}volution-smoothed \textbf{qu}antil\textbf{e} \textbf{R}eLU neural \textbf{net}works, which yield smooth objectives while preserving the underlying quantile structure. We establish general nonasymptotic risk bounds for ConquerNet under mild conditions, providing minimax guarantees over Besov function classes. In numerical studies, we demonstrate that the proposed approach outperforms standard quantile neural networks at multiple quantile levels, showing improved estimation accuracy and training efficiency across the board, with particularly pronounced advantages at high and low quantiles.
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