Deep Distributional Learning with Non-crossing Quantile Network

Guohao Shen; Runpeng Dai; Guojun Wu; Shikai Luo; Chengchun Shi; Hongtu Zhu

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arXiv · 2504.08215

Deep Distributional Learning with Non-crossing Quantile Network

Guohao Shen·Runpeng Dai·Guojun Wu·Shikai Luo·Chengchun Shi·Hongtu Zhu

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Abstract

In this paper, we introduce a non-crossing quantile (NQ) network for conditional distribution learning. By leveraging non-negative activation functions, the NQ network ensures that the learned distributions remain monotonic, effectively addressing the issue of quantile crossing. Furthermore, the NQ network-based deep distributional learning framework is highly adaptable, applicable to a wide range of applications, from classical non-parametric quantile regression to more advanced tasks such as causal effect estimation and distributional reinforcement learning (RL). We also develop a comprehensive theoretical foundation for the deep NQ estimator and its application to distributional RL, providing an in-depth analysis that demonstrates its effectiveness across these domains. Our experimental results further highlight the robustness and versatility of the NQ network.

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BibTeX RIS

Guohao Shen, Runpeng Dai, Guojun Wu, Shikai Luo, Chengchun Shi, Hongtu Zhu. 2025-04-11. Deep Distributional Learning with Non-crossing Quantile Network. https://arxiv.org/abs/2504.08215

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