Fast State-Augmented Learning for Wireless Resource Allocation with Dual Variable Regression

2025-06-23

AI Summary

This paper addresses the resource allocation problem in multi-user wireless networks under average performance constraints, aiming to maximize global utility. We propose a state-augmented graph neural network (GNN) to jointly model network topology and channel state information, treating Lagrange dual variables as graph signals for end-to-end optimization. A novel two-stage dual-variable regression mechanism is introduced: an auxiliary GNN provides near-optimal initialization of dual multipliers, while dynamic sampling-based dual descent accelerates Lagrangian function optimization. We develop an offline-online learning framework integrating graph signal processing with convex optimization theory. Theoretical analysis establishes algorithmic convergence and derives an exponential-probability bound on the duality gap. Experiments on transmit power control demonstrate substantial improvements over conventional dual subgradient methods—achieving higher efficiency, faster convergence, and enhanced robustness to channel dynamics and topology variations.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Graph-based Machine Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We consider resource allocation problems in multi-user wireless networks, where the goal is to optimize a network-wide utility function subject to constraints on the ergodic average performance of users. We demonstrate how a state-augmented graph neural network (GNN) parametrization for the resource allocation policy circumvents the drawbacks of the ubiquitous dual subgradient methods by representing the network configurations (or states) as graphs and viewing dual variables as dynamic inputs to the model, viewed as graph signals supported over the graphs. Lagrangian maximizing state-augmented policies are learned during the offline training phase, and the dual variables evolve through gradient updates while executing the learned state-augmented policies during the inference phase. Our main contributions are to illustrate how near-optimal initialization of dual multipliers for faster inference can be accomplished with dual variable regression, leveraging a secondary GNN parametrization, and how maximization of the Lagrangian over the multipliers sampled from the dual descent dynamics substantially improves the training of state-augmented models. We demonstrate the superior performance of the proposed algorithm with extensive numerical experiments in a case study of transmit power control. Finally, we prove a convergence result and an exponential probability bound on the excursions of the dual function (iterate) optimality gaps.

Problem

• Optimize wireless network resource allocation under ergodic constraints
• Overcome dual subgradient drawbacks with state-augmented GNN policies
• Enhance training via dual variable regression and Lagrangian maximization

Innovation

• State-augmented GNN for resource allocation
• Dual variable regression for faster inference
• Lagrangian maximization over sampled multipliers