# A Particle-Swarm-Assisted Gradient Meta-Learning Algorithm for Joint Transmit Precoding and STAR-RIS Coefficient Optimization

arXiv: https://arxiv.org/abs/2609.29150 · HTML: https://mlsanity.com/paper/2609.29150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
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- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [On the Road to 6G: Visions, Requirements, Key Technologies and Testbeds](https://mlsanity.com/paper/2302.14536/) (2023)
- [Intelligent Reflecting Surface Enhanced Wireless Network via Joint Active and Passive Beamforming](https://mlsanity.com/paper/1810.03961/) (2018)
- [Wireless Networks Design in the Era of Deep Learning: Model-Based, AI-Based, or Both?](https://mlsanity.com/paper/1902.02647/) (2019)
- [Wireless Communications Through Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/1906.09490/) (2019)
- [Reconfigurable Intelligent Surfaces: Principles and Opportunities](https://mlsanity.com/paper/2007.03435/) (2020)
- [Weighted Sum-Rate Maximization for Reconfigurable Intelligent Surface Aided Wireless Networks](https://mlsanity.com/paper/1912.11999/) (2019)
- [Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface with Discrete Phase Shifts](https://mlsanity.com/paper/1906.03165/) (2019)
- [Intelligent Reflecting Surfaces: Physics, Propagation, and Pathloss Modeling](https://mlsanity.com/paper/1911.03359/) (2019)
- [Joint Design for Simultaneously Transmitting And Reflecting (STAR) RIS Assisted NOMA Systems](https://mlsanity.com/paper/2106.03001/) (2021)
- [Coverage Characterization of STAR-RIS Networks: NOMA and OMA](https://mlsanity.com/paper/2104.10006/) (2021)
- [A Gradient Meta-Learning Joint Optimization for Beamforming and Antenna Position in Pinching-Antenna Systems](https://mlsanity.com/paper/2506.12583/) (2025)

## Abstract (arXiv)

This paper investigates the joint optimization of the transmit precoder and the transmission/reflection coefficients of a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) to maximize the weighted sum rate (WSR) in a multi-user downlink. We propose a particle-swarm-assisted gradient meta-learning (PSA-GML) algorithm for this non-convex problem. The original problem is first equivalently transformed via an amplitude-split parameterization and a collapsed precoder representation, which automatically satisfy the energy-conservation constraint and reduce the search dimension. Particle swarm optimization (PSO) then performs a global search over the STAR-RIS coefficients to yield a high-quality, initialization-robust warm start, with the transmit precoder obtained in closed form. Departing from conventional alternating optimization (AO), a coordinate-wise long short-term memory (LSTM) meta-optimizer trained by first-order gradient meta-learning further refines the coefficients and precoder jointly, learning per-coordinate adaptive update rules from data. The meta-optimizer is trained offline and applied to unseen channels without further adaptation. Numerical results show that PSA-GML attains an 11.06 bits/s/Hz WSR at 10 dB with N=32 elements and K=4 users, exceeding AO by 13.1% (and by 6.2% even with multiple random restarts) and the random-phase scheme by 35.1%. In the interference-limited regime it reaches 83.9% of the hand-designed Adam refinement without manual hyper-parameter tuning, and it transfers zero-shot across regimes, indicating that the learned update rule captures the intrinsic WSR landscape structure.