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Auto-Unrolled Proximal Gradient Descent: An AutoML Approach to Interpretable Waveform Optimization

Ahmet Kaplan

Abstract

This study explores the combination of automated machine learning (AutoML) with model-based deep unfolding (DU) for optimizing wireless beamforming and waveforms. We convert the iterative proximal gradient descent (PGD) algorithm into a deep neural network, wherein the parameters of each layer are learned instead of being predetermined. Additionally, we enhance the architecture by incorporating a hybrid layer that performs a learnable linear gradient transformation prior to the proximal projection. By utilizing AutoGluon with a tree-structured parzen estimator (TPE) for hyperparameter optimization (HPO) across an expanded search space, which includes network depth, step-size initialization, optimizer, learning rate scheduler, layer type, and post-gradient activation, the proposed auto-unrolled PGD (Auto-PGD) achieves 98.8% of the spectral efficiency of a traditional 200-iteration PGD solver using only five unrolled layers, while requiring only 100 training samples. We also address a gradient normalization issue to ensure consistent performance during training and evaluation, and we illustrate per-layer sum-rate logging as a tool for transparency. These contributions highlight a notable reduction in the amount of training data and inference cost required, while maintaining high interpretability compared to conventional black-box architectures.

Auto-Unrolled Proximal Gradient Descent: An AutoML Approach to Interpretable Waveform Optimization

Abstract

This study explores the combination of automated machine learning (AutoML) with model-based deep unfolding (DU) for optimizing wireless beamforming and waveforms. We convert the iterative proximal gradient descent (PGD) algorithm into a deep neural network, wherein the parameters of each layer are learned instead of being predetermined. Additionally, we enhance the architecture by incorporating a hybrid layer that performs a learnable linear gradient transformation prior to the proximal projection. By utilizing AutoGluon with a tree-structured parzen estimator (TPE) for hyperparameter optimization (HPO) across an expanded search space, which includes network depth, step-size initialization, optimizer, learning rate scheduler, layer type, and post-gradient activation, the proposed auto-unrolled PGD (Auto-PGD) achieves 98.8% of the spectral efficiency of a traditional 200-iteration PGD solver using only five unrolled layers, while requiring only 100 training samples. We also address a gradient normalization issue to ensure consistent performance during training and evaluation, and we illustrate per-layer sum-rate logging as a tool for transparency. These contributions highlight a notable reduction in the amount of training data and inference cost required, while maintaining high interpretability compared to conventional black-box architectures.
Paper Structure (25 sections, 5 equations, 4 figures, 3 tables)

This paper contains 25 sections, 5 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background
  4. Proximal Gradient Descent
  5. Problem Formulation
  6. Optimization Objective
  7. PGD-Ready Decomposition
  8. Proposed Methodology
  9. Deep Unrolling of PGD
  10. AutoML Integration via AutoGluon
  11. Experimental Design
  12. Simulation Environment
  13. Dataset and Baselines
  14. AutoML Search via AutoGluon
  15. Reproducibility
  16. ...and 10 more sections

Figures (4)

  • Figure 1: Abstract workflow of Auto-Unrolled Proximal Gradient Descent: classical PGD is transformed into a deep-unfolded network, AutoGluon automates architecture search and hyperparameter optimization, and the system outputs optimized beamforming vectors for wireless waveform optimization.
  • Figure 2: Sum-rate vs. training set size for all methods. Auto-PGD peaks at $N=10^3$ ($14.63$ bits/s/Hz, within $1.2\%$ of Classical PGD) and maintains strong performance down to $N=10^2$, while black-box baselines plateau well below the PGD-based methods.
  • Figure 3: AutoGluon HPO search history across 50 trials for each training size. Each point represents a candidate architecture evaluated during the search; the best configuration per size is highlighted.
  • Figure 4: Training loss curves over 200 epochs for all learned methods at $N=100$ and $N=1000$. Auto-PGD converges faster and to a lower loss than PGD-Net and the black-box baselines in both data regimes.