arxiv: 2604.17379 · v2 · submitted 2026-04-19 · 💻 cs.IT · math.IT

Recognition: unknown

MAGRPO: Accelerated MARL Training for Fluid Antenna-Assisted Wireless Network Optimization

Wanzhe Wang , Tong Zhang , Hao Xu , Shuai Wang , Rui Wang , Kai-Kit Wong

Authors on Pith no claims yet

Pith reviewed 2026-05-10 06:05 UTC · model grok-4.3

classification 💻 cs.IT math.IT

keywords fluid antenna systemmulti-agent reinforcement learningpolicy optimizationwireless network optimizationsum-rate maximizationdecentralized POMDPMAGRPO

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The pith

MAGRPO trains multi-agent reinforcement learning for fluid antenna wireless networks 30-40% faster than MAPPO while matching its sum-rate performance.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper casts the joint optimization of fluid antenna positions, beamforming, and power allocation as a decentralized partially observable Markov decision process to address non-convexity and absent base-station coordination. It introduces the MAGRPO algorithm under centralized training decentralized execution, which substitutes group relative advantage estimation for the conventional critic network. This substitution halves critic complexity under parameter sharing and shortens training time by 30 to 40 percent relative to MAPPO while preserving comparable sum rates. Simulations also establish that fluid-antenna networks deliver multiple-fold sum-rate gains over fixed-antenna baselines, and a variance upper bound on cumulative reward is shown to scale with the number of base stations, users, and fluid antennas.

Core claim

The central claim is that the multi-agent group relative policy optimization (MAGRPO) algorithm, obtained by replacing the critic network with group relative advantage estimation, solves the decentralized POMDP formulation of fluid-antenna network optimization at nearly half the critic cost of MAPPO, attaining equivalent test-time sum rates with 30-40 percent less training time.

What carries the argument

Group relative advantage estimation, which replaces the critic network in the MAPPO framework under the CTDE paradigm and thereby reduces computational complexity by nearly half when parameters are shared across agents.

If this is right

Fluid-antenna-assisted networks achieve multiple-fold sum-rate enhancement compared with fixed-antenna baselines.
MAGRPO delivers sum rates statistically indistinguishable from MAPPO while cutting training time by 30 to 40 percent.
The variance of the cumulative reward remains bounded by a quantity linear in the number of base stations, users, and fluid antennas.
Base stations can execute learned policies independently after centralized training without further coordination.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The halved critic size may allow training on larger numbers of base stations or users before memory limits are reached.
The same group-relative substitution could be inserted into other multi-agent wireless problems that already use parameter sharing.
The derived variance bound supplies a concrete scaling law that could guide hyper-parameter schedules when network size increases.

Load-bearing premise

The non-convex optimization of fluid antenna positions, beamforming, and power allocation can be effectively cast as a decentralized POMDP whose solution via group relative advantage estimation preserves performance while halving critic complexity.

What would settle it

A direct head-to-head run of MAGRPO and MAPPO on the same fluid-antenna network scenario that shows either a training-time reduction below 20 percent or a test sum-rate gap larger than 5 percent would falsify the performance-preservation claim.

Figures

Figures reproduced from arXiv: 2604.17379 by Hao Xu, Kai-Kit Wong, Rui Wang, Shuai Wang, Tong Zhang, Wanzhe Wang.

**Figure 2.** Figure 2: Illustration of the CTDE paradigm for MARL. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: Comparison of training algorithm framework of the proposed MAGRPO over MAPPO [29]. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Landscape of R(u). 0 1 2 3 4 5 6 7 8 Steps (Million) 5 10 15 20 25 Sum-Rate (bps/Hz) Proposed MAPPO MAPPO-FA (a) Training, M = 4 0 1 2 3 4 5 6 7 8 Steps (Million) 4 6 8 10 12 14 16 Sum-Rate (bps/Hz) Proposed MAPPO MAPPO-FA (b) Training, M = 3 0 1 2 3 4 5 6 7 8 Steps (Million) 2 4 6 8 10 12 Sum-Rate (bps/Hz) Proposed MAPPO MAPPO-FA (c) Training, M = 2 0 1 2 3 4 5 6 7 8 Steps (Million) 4 5 6 7 8 9 10 11 12 S… view at source ↗

**Figure 5.** Figure 5: Training and testing curves for the proposed MAGRPOs and baselines over varying [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: Influence of group size for the proposed MAGRPO over varying [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

**Figure 7.** Figure 7: Influence of trajectory length for the proposed MAGRPO over varying [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

**Figure 8.** Figure 8: Proposed MAGRPO over baselines over varying [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗

**Figure 9.** Figure 9: Proposed MAGRPO over baselines over varying [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

read the original abstract

Fluid antenna system (FAS) becomes a promising paradigm for next-generation wireless networks, which enables position-flexible antenna elements that can dynamically adjust to more favorable channel conditions. However, the optimization of fluid antenna (FA) positions, beamforming, and power allocation in FA-assisted wireless networks is challenging, due to the non-convexity and the lack of base station (BS) coordination. In this paper, we first formulate this challenging optimization problem as a decentralized partially observable Markov decision process, and then propose a multi-agent group relative policy optimization (MAGRPO) algorithm under the centralized training decentralized execution (CTDE) paradigm. Compared with multi-agent proximal policy optimization (MAPPO), MAGRPO replaces the critic network with group relative advantage estimation. This design reduces computational complexity by nearly half under parameter sharing. Furthermore, we derive a variance upper bound of the cumulative reward, which scales with network parameters, e.g., the number of BSs, users, and FAs. Simulation results show that compared with wireless networks with fixed antenna positions, FA-assisted wireless networks achieve multiple-fold sum-rate enhancement. Moreover, the proposed MAGRPO attains sum-rates comparable to those of MAPPO in testing, while reducing training time by $30\% \sim 40\%$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

MAGRPO gives a practical 30-40% training speedup over MAPPO for fluid-antenna wireless optimization in simulations, but the group-relative advantage estimator lacks any bias proof.

read the letter

MAGRPO is a straightforward modification of MAPPO that swaps the critic for group relative advantage estimation under parameter sharing. The paper casts the joint problem of fluid antenna positioning, beamforming, and power allocation as a decentralized POMDP to handle the lack of base-station coordination, then shows that this change halves critic complexity while delivering a variance upper bound on cumulative reward that scales with the number of base stations, users, and fluid antennas. Simulations report multiple-fold sum-rate gains from fluid antennas over fixed positions, plus test performance close to MAPPO but with 30-40% less training time. Those empirical numbers are the clearest contribution here, and the variance bound is a clean, parameter-dependent result that does not rely on fitted quantities. The work stays within the CTDE framework and cites the relevant MAPPO baseline without overclaiming generality. The main soft spot is exactly the one flagged in the stress test. No derivation shows that the group-relative estimator is unbiased, only that its variance is bounded. If the estimator is biased, the policy is optimizing something other than the intended objective, and the observed comparability in sum rates could be an artifact of the chosen scenarios rather than a general property. The abstract also gives no error bars, run counts, or statistical tests, so the speedup claim rests on simulation outcomes that cannot be fully assessed from the given material. This is a paper for researchers working on multi-agent RL for wireless resource allocation, particularly those already using MAPPO-style methods on emerging antenna hardware. It deserves a serious referee because the complexity reduction is attractive for scaling and the simulation gains are large enough to warrant closer inspection of the estimator. I would send it to review and ask for an explicit bias analysis or at least more detailed experimental controls.

Referee Report

2 major / 3 minor

Summary. The manuscript formulates the joint optimization of fluid antenna positions, beamforming, and power allocation as a decentralized POMDP and proposes MAGRPO under CTDE, which replaces the critic network with group relative advantage estimation to reduce critic complexity by nearly half under parameter sharing. It derives a variance upper bound on the cumulative reward that scales with network parameters (number of BSs, users, FAs). Simulations claim that FA-assisted networks yield multiple-fold sum-rate gains over fixed-antenna baselines, while MAGRPO achieves sum-rates comparable to MAPPO with 30-40% lower training time.

Significance. If the group relative advantage estimator produces policy gradients sufficiently close to MAPPO's, the method could accelerate MARL training for non-convex wireless resource allocation problems while preserving performance. The variance bound provides a useful scalability analysis, and the empirical FA gains supply concrete motivation for position-flexible antennas. These elements would strengthen the case for reduced-complexity CTDE methods in communications.

major comments (2)

[§III and §IV] §III (MAGRPO algorithm) and §IV (variance bound derivation): the group relative advantage estimation is introduced to replace the critic while halving complexity, yet no derivation or analysis establishes that the estimator is unbiased (i.e., its expectation equals the true advantage function). The provided variance upper bound addresses only variance and does not rule out bias; if biased, the learned policies optimize a different objective, undermining the claim that comparable sum-rates are a general property rather than scenario-specific.
[§V] Simulation section (likely §V, Figs. 3-5): the central performance claim (sum-rates comparable to MAPPO with 30-40% training-time reduction) rests on empirical results, but the manuscript provides no error bars, number of independent seeds, or statistical significance tests. This weakens verification of whether the speedup and comparability hold beyond the reported runs, especially given the unproven unbiasedness of the estimator.

minor comments (3)

[Abstract] Abstract: the phrase 'multiple-fold sum-rate enhancement' is imprecise; specific numerical gains (e.g., 2x or 3x) from the simulations should be stated.
[§II] Notation and POMDP formulation: a compact table listing states, actions, observations, and reward components would aid readability.
[§V] Figures showing training curves: include multiple-run statistics or shaded confidence regions to support the reported time reductions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments, which have helped us identify areas for improvement in the manuscript. We address each major comment point by point below, providing our responses and indicating the revisions we will incorporate.

read point-by-point responses

Referee: [§III and §IV] §III (MAGRPO algorithm) and §IV (variance bound derivation): the group relative advantage estimation is introduced to replace the critic while halving complexity, yet no derivation or analysis establishes that the estimator is unbiased (i.e., its expectation equals the true advantage function). The provided variance upper bound addresses only variance and does not rule out bias; if biased, the learned policies optimize a different objective, undermining the claim that comparable sum-rates are a general property rather than scenario-specific.

Authors: We appreciate the referee's observation regarding the potential bias in the group relative advantage estimator. While the original submission emphasized the complexity reduction and variance properties, we recognize the need for a formal unbiasedness analysis. In the revised version, we will include a derivation in §III demonstrating that the group relative advantage estimation is an unbiased estimator of the advantage function under the parameter-sharing and group structure assumptions. This derivation will show that the expectation of the estimator equals the true advantage, ensuring that the policy optimization targets the correct objective. Consequently, the comparable sum-rate performance is expected to hold generally, not just in specific scenarios. We will also reference this in the discussion of the variance bound in §IV. revision: yes
Referee: [§V] Simulation section (likely §V, Figs. 3-5): the central performance claim (sum-rates comparable to MAPPO with 30-40% training-time reduction) rests on empirical results, but the manuscript provides no error bars, number of independent seeds, or statistical significance tests. This weakens verification of whether the speedup and comparability hold beyond the reported runs, especially given the unproven unbiasedness of the estimator.

Authors: We agree that additional statistical details are necessary to strengthen the empirical validation. In the revised manuscript, we will augment §V with the number of independent random seeds used (10 seeds for the reported results), include error bars in Figs. 3-5 indicating the mean and standard deviation across these runs, and add statistical significance tests (e.g., paired t-tests) to verify that the sum-rate differences between MAGRPO and MAPPO are not statistically significant. This will confirm the reliability of the 30-40% training time reduction while maintaining comparable performance. We believe these additions will address the concern and provide stronger evidence for the claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper formulates the FA position/beamforming/power problem as a decentralized POMDP, introduces MAGRPO by replacing the critic with group-relative advantage estimation (reducing complexity under parameter sharing), derives a variance upper bound on cumulative reward that scales explicitly with observable parameters (number of BSs/users/FAs), and validates via simulation that sum-rates remain comparable to MAPPO while training time drops 30-40%. No equation reduces a claimed prediction or result to a fitted input by construction; the variance bound is an independent derivation rather than a renaming or self-referential fit; no load-bearing self-citation chain or uniqueness theorem is invoked to force the central claim. The performance equivalence is presented as empirical, not mathematically forced.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based on abstract only; no explicit free parameters, axioms, or invented entities are detailed beyond the standard RL modeling assumptions.

axioms (1)

domain assumption The joint optimization of FA positions, beamforming, and power allocation can be formulated as a decentralized POMDP.
Explicitly stated as the first modeling step in the abstract.

pith-pipeline@v0.9.0 · 5540 in / 1254 out tokens · 46532 ms · 2026-05-10T06:05:58.003782+00:00 · methodology

discussion (0)

Reference graph

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