# Adversarial Water-Filling: Theory, Algorithms, and a Domain-Specific Wireless Foundation Model

arXiv: https://arxiv.org/abs/2605.26163 · HTML: https://mlsanity.com/paper/2605.26163/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 24 May 2026.

## Builds on (most cited first, 18 of 18)

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- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Graph Neural Networks for Scalable Radio Resource Management: Architecture Design and Theoretical Analysis](https://mlsanity.com/paper/2007.07632/) (2020)
- [On the Road to 6G: Visions, Requirements, Key Technologies and Testbeds](https://mlsanity.com/paper/2302.14536/) (2023)
- [Multi-Agent Deep Reinforcement Learning for Dynamic Power Allocation in Wireless Networks](https://mlsanity.com/paper/1808.00490/) (2018)
- [WirelessLLM: Empowering Large Language Models Towards Wireless Intelligence](https://mlsanity.com/paper/2405.17053/) (2024)
- [ColO-RAN: Developing Machine Learning-based xApps for Open RAN Closed-loop Control on Programmable Experimental Platforms](https://mlsanity.com/paper/2112.09559/) (2021)
- [Learning to Continuously Optimize Wireless Resource in a Dynamic Environment: A Bilevel Optimization Perspective](https://mlsanity.com/paper/2105.01696/) (2021)
- [A Survey on Non-Geostationary Satellite Systems: The Communication Perspective](https://mlsanity.com/paper/2107.05312/) (2021)
- [Dynamic Task Offloading and Resource Allocation for Ultra-Reliable Low-Latency Edge Computing](https://mlsanity.com/paper/1812.08076/) (2018)
- [OrchestRAN: Network Automation through Orchestrated Intelligence in the Open RAN](https://mlsanity.com/paper/2201.05632/) (2022)
- [OpenRAN Gym: AI/ML Development, Data Collection, and Testing for O-RAN on PAWR Platforms](https://mlsanity.com/paper/2207.12362/) (2022)
- [Adversarial Machine Learning Threat Analysis and Remediation in Open Radio Access Network (O-RAN)](https://mlsanity.com/paper/2201.06093/) (2022)
- [A Graph Foundation Model for Wireless Resource Allocation](https://mlsanity.com/paper/2604.07390/) (2026)
- [OpenRANet: Neuralized Spectrum Access by Joint Subcarrier and Power Allocation with Optimization-based Deep Learning](https://mlsanity.com/paper/2409.12964/) (2024)

## Abstract (arXiv)

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, the corresponding power-allocation problem admits a convex-concave formulation with a unique saddle point. 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 settings. In addition, we develop a domain-specific 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 establish projected-stationarity/Karush-Kuhn-Tucker consistency and conditional local convergence of the learned AWF dynamics under local regularity and stability conditions. Experiments demonstrate empirical generalization across unseen problem sizes, constraint structures, discrete constellations, and channel-weighted objectives, while achieving a median speedup exceeding one order of magnitude over Mirror-Prox on matched instances at comparable first-order solution quality. The related code can be found at https://github.com/convexsoft/AWF.