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

TL;DR

This paper introduces a novel graph neural network-based approach for resource allocation in wireless networks, improving training speed and performance by leveraging dual variable regression and state-augmentation techniques.

Contribution

It presents a new method combining state-augmented GNNs with dual variable regression to enhance resource allocation efficiency and convergence in wireless networks.

Findings

Achieves near-optimal dual multiplier initialization for faster inference.

Demonstrates superior performance in transmit power control case studies.

Provides convergence proof and probabilistic bounds on dual function gaps.

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.