Competitive resource allocation problems over frequency and space can be formulated as minimax interaction between transmit power and worst-case interference. This formulation naturally arises in multi-operator low Earth orbit (LEO) satellite spectrum sharing, where transmissions from competing constellations interfere in real-time. Under Gaussian channels, AWF is strongly convex--concave on nondegenerate active channels, whereas discrete constellations yield generally nonconvex mercury/water-filling formulations. In this paper we propose the Adversarial Water-Filling (AWF) problem with corresponding theory and algorithms for these real situations. In addition, we develop a wireless foundation model for AWF to learn the AWF search dynamics. The architecture incorporates permutation-invariant channel representations, a constraint-aware graph neural network (GNN) with sparse message passing, and global latent variables capturing the low-dimensional water level implied by the AWF optimality. Through learned projected extragradient iterations, the model approximates stationary solutions of the constrained minimax problem arising under mercury/water-filling. We further show that, under local regularity and contractivity conditions, the learned AWF dynamics converge locally linearly around regular stationary points. Experiments demonstrate empirical generalization across unseen problem sizes, different constraints, and multiple discrete constellations, while achieving more than one-order-of-magnitude runtime improvements over iterative baselines. The related code can be found at https://github.com/convexsoft/AWF.

翻译：频率与空间上的竞争性资源分配问题可建模为发射功率与最坏情况干扰之间的极小极大交互。该模型自然出现在多运营商低地球轨道（LEO）卫星频谱共享场景中，其中竞争星座的传输信号会实时产生干扰。在高斯信道下，AWF在非退化活跃信道上呈现强凸-凹特性，而离散星座则导致一般的非凸水银/注水公式。本文针对这些实际场景提出对抗性注水（AWF）问题，并建立相应的理论与算法。此外，我们开发了一种用于AWF的无线基础模型，以学习AWF搜索动态。该架构融合了排列不变信道表示、具有稀疏消息传递的约束感知图神经网络（GNN），以及捕捉由AWF最优性隐含的低维水位线的全局潜变量。通过学习的投影外梯度迭代，该模型逼近水银/注水框架下约束极小极大问题的平稳解。我们进一步证明，在局部正则性与收缩性条件下，学习得到的AWF动态在正则平稳点附近具有局部线性收敛性。实验表明，该模型在未见过的不同问题规模、约束类型及多种离散星座上均展现出经验泛化能力，同时相比迭代基线方法实现了超过一个数量级的运行时间提升。相关代码可见于https://github.com/convexsoft/AWF。