论文简报
cs.IT 2605.26163v1 值得读

Adversarial Water-Filling: Theory, Algorithms and Foundation Model

Xindi Tong, Chee Wei Tan, H. Vincent Poor

发布日期：2026-05-24 17:37 相关性：1.0000 价值：0.8000 分类：cs.IT cs.LG math.OC
arXiv 摘要 PDF 原文 网页正文

摘要

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.

相关性判断

high
相关方向
information_theory wireless_communications optimization machine_learning_for_communications
判断依据

Directly on water-filling, minimax power allocation, spectrum sharing, and wireless communications; clearly in cs.IT/coding-adjacent technical scope worth later review.

价值判断

High relevance to cs.IT via minimax water-filling, wireless spectrum sharing, and power allocation. Structure evidence shows substantial technical content: KKT analysis, minimax formulation, projected extragradient methods, I-MMSE, GNN architecture, and local convergence theory. Claims include both theory/algorithms and empirical speedups/generalization, making it worth deeper review for the workflow.

核心问题与主要方法

核心问题

Competitive wireless resource allocation under worst-case interference in multi-operator spectrum sharing

场景：LEO/NTN spectrum sharing with coupled frequency-space power allocation, Gaussian or discrete constellations, and optional linear spatial constraints

主要方法

Formulates transmit allocation and worst-case interference as a constrained max-min AWF game over frequency and space, with simplex budgets for p and n and optional spatial constraints Ap <= p_hat. Uses water-filling/KKT analysis to expose low-dimensional dual water levels: nu for transmit power, mu for interference, and theta-induced channel-wise shifts under spatial constraints. Extends Gaussian water-filling to mercury/water-filling via mutual-information objectives and I-MMSE-based gradients, acknowledging loss of closed-form proximal updates and possible nonconvexity. Interprets AWF through primal-dual and PDHG/extragradient dynamics, motivating a learned projected extragradient solver. Builds the foundation model from permutation-invariant set encoding for unordered channels, sparse constraint-graph message passing for A^T theta effects, distribution tokens for modulation curves, and simplex projections to enforce budgets.

关键贡献与后续阅读

关键贡献

Introduces AWF as a unified minimax framework for competitive wireless resource allocation over frequency and space, explicitly modeling worst-case interference in multi-operator LEO/NTN spectrum sharing. Separates the tractable Gaussian regime from the harder discrete-constellation mercury/water-filling regime, identifying convex-concave structure for Gaussian AWF and nonconvex behavior for mercury/water-filling. Derives KKT/water-level characterizations showing how transmit, interference, and spatial constraint dual variables coordinate high-dimensional channel allocations. Connects AWF to PDHG/proximal/extragradient optimization, using this structure to design learned projected extragradient iterations instead of a fixed-size direct regressor. Proposes a domain-structured wireless foundation model with permutation-invariant channel representations, sparse constraint-aware GNN message passing, modulation distribution tokens, and global latent variables for water-level dynamics. Provides conditional theoretical support: fixed points satisfying projected first-order conditions correspond to KKT points, and learned dynamics converge locally linearly under regularity and contractivity assumptions. Reports empirical generalization across unseen channel sizes, modulation formats including held-out 256QAM, and unseen constraint families, with more than one-order-of-magnitude runtime improvement over Mirror-Prox baselines.

研究启发

Do the reported tables show statistically robust comparisons across enough random AWF instances, especially for held-out 256QAM and dense correlated constraints? How sensitive is the learned extragradient model to the choice of unroll length T=64, stepsize clamping, and the residual-based training objective? Does the code reproduce the claimed 16x-18x speedups on hardware beyond the reported RTX 3050 setup? How realistic are the generated channel, noise, budget, and sparse constraint distributions for actual multi-operator LEO coexistence scenarios?

限制与不确定性

Learned dynamics have only local convergence guarantees under regularity and contractivity assumptions. Nonconvex mercury/water-filling setting lacks global convergence guarantees. Value depends on empirical validity of reported generalization and runtime gains, which is not verified from the full paper here.

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