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arxiv: 2604.05297 · v1 · submitted 2026-04-07 · 💻 cs.AI

Breakthrough the Suboptimal Stable Point in Value-Factorization-Based Multi-Agent Reinforcement Learning

Lesong Tao , Yifei Wang , Haodong Jing , Jingwen Fu , Miao Kang , Shitao Chen , Nanning Zheng This is my paper

Pith reviewed 2026-05-10 19:57 UTC · model grok-4.3

classification 💻 cs.AI
keywords value factorizationmulti-agent reinforcement learningstable pointssuboptimal convergenceMARLpayoff incrementglobal optimalityconvergence analysis
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The pith

Non-optimal stable points primarily cause value-factorization multi-agent reinforcement learning to converge to suboptimal solutions.

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

Value factorization methods in multi-agent reinforcement learning often converge to poor joint policies, and existing theory focused only on optimal cases has not explained why. The paper introduces the stable point as a general concept describing where such methods can converge. Analysis of stable point distributions in existing algorithms shows that non-optimal stable points are widespread and responsible for the performance shortfalls. Forcing the optimal action to be the sole stable point is nearly impossible in practice. The more workable strategy is to iteratively render suboptimal actions unstable, which the proposed Multi-Round Value Factorization framework accomplishes by applying non-negative payoff increments relative to the prior action, pushing learning toward better stable points.

Core claim

The paper claims that non-optimal stable points are the primary cause of poor performance in value-factorization-based multi-agent reinforcement learning. Existing methods contain distributions rich in such points. Making the optimal action the unique stable point is nearly infeasible, whereas iteratively filtering suboptimal actions by rendering them unstable offers a practical route to global optimality. The Multi-Round Value Factorization framework realizes this by measuring a non-negative payoff increment relative to the previously selected action, thereby transforming inferior actions into unstable points and driving each iteration toward a stable point with a superior action.

What carries the argument

The stable point, which characterizes the potential convergence targets of value factorization in general cases, together with the iterative filtering mechanism that uses non-negative payoff increments to destabilize inferior actions.

If this is right

  • Non-optimal stable points explain the performance gaps observed in current value-factorization methods.
  • Iteratively rendering suboptimal actions unstable is a feasible route to global optimality.
  • The Multi-Round Value Factorization framework implements this filtering via payoff increments relative to prior actions.
  • Experiments on predator-prey tasks and the StarCraft II Multi-Agent Challenge confirm both the stable-point analysis and improved performance over prior methods.

Where Pith is reading between the lines

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

  • The stable-point lens could be used to audit convergence behavior in other multi-agent algorithms that rely on value decomposition.
  • Similar iterative destabilization of inferior choices might transfer to single-agent reinforcement learning settings that employ factored value functions.
  • In deployed multi-agent systems such as robotic teams, injecting controlled instability at each round could reduce the frequency of coordinated but inefficient behaviors.

Load-bearing premise

A non-negative payoff increment measured relative to the previously selected action can reliably transform inferior actions into unstable points without creating new suboptimal stable points or disrupting overall convergence properties.

What would settle it

Applying the Multi-Round Value Factorization framework to the StarCraft II Multi-Agent Challenge benchmark and finding that it still converges to the same suboptimal policies identified in the stable-point analysis of baseline methods would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.05297 by Haodong Jing, Jingwen Fu, Lesong Tao, Miao Kang, Nanning Zheng, Shitao Chen, Yifei Wang.

Figure 1
Figure 1. Figure 1: Clipping payoffs in the multi-round process. In this example, the two suboptimal solutions have relatively high payoffs. Therefore, existing methods are likely to select one of them. In contrast, by clipping the payoff of the selected solution, MRVF avoids convergence to it in subsequent rounds. Eventually, only the optimal solution retains a high payoff, making it easily identifiable. is finding the optim… view at source ↗
Figure 2
Figure 2. Figure 2: Gradient discontinuity induced by crossing different val￾ues of greedy action. The gradient is continuous within any single region. However, when the greedy action changes, the values of the gradient-free components change. Since these components ap￾pear in the gradient of gradient-based parameters (e.g., individual Qs), their sudden changes induce a discontinuity in the gradient. 4.1. Transition of the Gr… view at source ↗
Figure 3
Figure 3. Figure 3: Transition of greedy action in WQMIX with α = 0.1 under uniform visitation (π ≡ 1). This process begins with ue = (1, 3) (top right) and stabilizes at u¯ = (1, 1) (top left). At each step we present Qtot optimized under the weight induced by current ue, where cells are shaded if w(τ , u) = α, and the value corresponding to u¯ = (row, column) is in bold. 4 0 -8 0 3 0 -8 0 -8 (a) Qjt 1 α α α α α α α α (b) w … view at source ↗
Figure 4
Figure 4. Figure 4: The architecture of multi-round value factorization framework. 5.3. Sampling We approximate the expectation in Ljt and Ltot by sampling the action spaces. We design sampling strategies for multi￾round frameworks to ensure stable training. For the final action ut in Ljt, its sampling should not only cover the greedy final action and random actions, but also cover the greedy action in each round, which obtai… view at source ↗
Figure 5
Figure 5. Figure 5: Test normalized return in the risk-reward games. The positive returns are normalized to [0, 1] (0 corresponds to the smallest positive return, and 1 corresponds to the largest). The negative returns are normalized to [−1, 0). Five random cases for each setting. 0.0 0.2 0.4 0.6 0.8 1.0 Step 1e6 0 5 10 15 20 25 30 35 40 Test Return predator prey 0 0.0 0.2 0.4 0.6 0.8 1.0 Step 1e6 40 30 20 10 0 10 20 30 40 Te… view at source ↗
Figure 6
Figure 6. Figure 6: Test return in the predator prey tasks with punishments 0 (left), -2 (middle), and -5 (right). The non-monotonicity of the payoff increases with the punishment. sensus requires coordination among more agents. Existing methods rarely obtain positive returns, while our method still obtains the optimum with high probability. However, in cases with 5 agents and 8 actions, the positive rewards become too sparse… view at source ↗
Figure 7
Figure 7. Figure 7: Test win rate in the SMAC benchmarks. as shown in [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: An illustration of Definition B.2. We intercept curves corresponding to different u−i and check whether their monotonicity with respect to ui is consistent [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The network structure of Qtot. The individual Q network processes the observation using a linear layer followed by a GRU (Chung et al., 2014) with 64 hidden dimensions. The mixing network processes the state with 2-layer linear network (64 hidden dimension) and processes the individual Qs with 2-layer linear network, where the weights and bias (generated by the state’s linear processor) have 32 hidden dime… view at source ↗
Figure 10
Figure 10. Figure 10: The network structure of Qjt. E.1. One-Step Game We randomly generate Qjt of the risk-reward game with the following steps: First, randomly generate the individual reward vectors ri ≥ 0. Second, we randomly generate a bijection U → U that maps ui to another action vi for all agents i, which is the exchange of rows and columns for a matrix. Finally, we let Qjt(u) = sign(v) ∗ Pn i=0 ri(vi) where sign(v) = 1… view at source ↗
Figure 11
Figure 11. Figure 11: Test normalized return in the risk-reward games. 0.0 0.2 0.4 0.6 0.8 1.0 Step 1e6 0 5 10 15 20 25 30 35 40 Test Return predator prey 0 0.0 0.2 0.4 0.6 0.8 1.0 Step 1e6 40 30 20 10 0 10 20 30 40 Test Return predator prey -2 0.0 0.2 0.4 0.6 0.8 1.0 Step 1e6 40 30 20 10 0 10 20 30 40 Test Return predator prey -5 MRVF MRVF-single MRVD-non-strict [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Test return in the predator-prey tasks with punishments 0 (left), -2 (middle), and -5 (right). The results presented in [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Test win rate in the SMAC benchmarks. non-monotonic environments. To support our claim, we calculate the proportion of taking u k t as the final action for each round k, as shown in [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Proportion of final actions generated in each round throughout test episodes. From [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Test win rate in 3s_vs_5z. WQMIX (Qˆjt) represents WQMIX replacing the network of Qˆjt with that of ours. WQMIX (centralized ϵ) represents WQMIX replacing the policy with the centralized one. WQMIX (both) represents WQMIX with both modifications. we set anneal steps for ϵ to 106 . The results in [PITH_FULL_IMAGE:figures/full_fig_p026_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Test win rate in 6h_vs_8z in SMAC benchmarks. H.3. SMACv2 Results on SMACv2 (Ellis et al., 2023) are shown in [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Test return (first row) and win rate (second row) in SMACv2 benchmarks. H.4. Predator Prey From the results in [PITH_FULL_IMAGE:figures/full_fig_p027_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Test return in the predator prey tasks with punishments -2 (left), and -5 (right). QMIX (50k ϵ-anneal) represents QMIX with 5 ∗ 104 anneal steps for ϵ. QMIX (1mil ϵ-anneal) represents QMIX with 106 anneal steps for ϵ. QMIX (ϵ = 1) represents QMIX with ϵ = 1 constantly. H.5. Comparison with other MARL baselines In Section 6, we compare MRVF with algorithms such as WQMIX (Rashid et al., 2020a) that claim to… view at source ↗
Figure 19
Figure 19. Figure 19: Test return in the predator prey tasks with punishments 0 (left), -2 (middle), and -5 (right). The comparison results on the SMAC environment are shown in [PITH_FULL_IMAGE:figures/full_fig_p028_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Test win rate in the SMAC benchmarks. We use the implementation of GoMARL 8 , MAPPO 9 , CommFormer 10 and HYGMA 11 are from their open-source repositories. The hyperparameter settings for the on-policy methods are listed in [PITH_FULL_IMAGE:figures/full_fig_p029_20.png] view at source ↗
read the original abstract

Value factorization, a popular paradigm in MARL, faces significant theoretical and algorithmic bottlenecks: its tendency to converge to suboptimal solutions remains poorly understood and unsolved. Theoretically, existing analyses fail to explain this due to their primary focus on the optimal case. To bridge this gap, we introduce a novel theoretical concept: the stable point, which characterizes the potential convergence of value factorization in general cases. Through an analysis of stable point distributions in existing methods, we reveal that non-optimal stable points are the primary cause of poor performance. However, algorithmically, making the optimal action the unique stable point is nearly infeasible. In contrast, iteratively filtering suboptimal actions by rendering them unstable emerges as a more practical approach for global optimality. Inspired by this, we propose a novel Multi-Round Value Factorization (MRVF) framework. Specifically, by measuring a non-negative payoff increment relative to the previously selected action, MRVF transforms inferior actions into unstable points, thereby driving each iteration toward a stable point with a superior action. Experiments on challenging benchmarks, including predator-prey tasks and StarCraft II Multi-Agent Challenge (SMAC), validate our analysis of stable points and demonstrate the superiority of MRVF over state-of-the-art methods.

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.

Referee Report

3 major / 2 minor

Summary. The paper claims that value factorization in MARL tends to converge to suboptimal solutions because of non-optimal 'stable points,' a new concept characterizing general convergence behavior beyond the optimal case. Analysis of stable point distributions in existing methods identifies these as the primary cause of poor performance. The authors propose the Multi-Round Value Factorization (MRVF) framework, which iteratively adds a non-negative payoff increment relative to the previously selected action to render inferior actions unstable, thereby driving each round toward a stable point with a superior action. Experiments on predator-prey tasks and SMAC benchmarks are said to validate the stable-point analysis and show MRVF outperforming state-of-the-art methods.

Significance. If the stable-point characterization is shown to be independent of the value factorization and the MRVF increment provably eliminates suboptimal attractors without introducing new ones or violating convergence, the work would offer a useful theoretical lens on a persistent MARL bottleneck and a practical algorithmic fix. The empirical validation on SMAC provides some evidence of utility, but the absence of parameter-free derivations or machine-checked proofs limits the strength of the contribution relative to prior fixed-point analyses in RL.

major comments (3)
  1. [§3] §3 (stable point definition and distribution analysis): the stable point is introduced as a novel construct without an explicit derivation showing it reduces to or is independent of the standard fixed-point condition of value factorization; this creates a circularity risk because the MRVF payoff increment is itself defined relative to the learned values.
  2. [§4] §4 (MRVF mechanism): no derivation is supplied showing how the non-negative payoff increment modifies the fixed-point equation to destabilize suboptimal actions globally; the claim that this process cannot create fresh suboptimal stable points or break overall convergence therefore lacks support and is load-bearing for the central algorithmic claim.
  3. [§5] §5 (experiments): the reported results on SMAC and predator-prey lack ablations isolating the effect of the payoff increment on stable-point distributions across rounds; without these, it is impossible to confirm that performance gains arise from the proposed filtering rather than hyperparameter tuning or other implementation details.
minor comments (2)
  1. [Abstract] Abstract and §2: the phrase 'analysis of stable point distributions' is used without specifying the quantitative metrics or visualization methods employed.
  2. [§4] Notation: the payoff increment is described as 'non-negative' but its precise functional form and dependence on the value function are not clarified in the high-level description.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the insightful and constructive comments. We address each major comment point by point below, indicating where revisions will be made and providing honest clarifications on the theoretical aspects.

read point-by-point responses

  1. Referee: [§3] §3 (stable point definition and distribution analysis): the stable point is introduced as a novel construct without an explicit derivation showing it reduces to or is independent of the standard fixed-point condition of value factorization; this creates a circularity risk because the MRVF payoff increment is itself defined relative to the learned values.

    Authors: We appreciate this observation on the need for clearer grounding. The stable point is defined in §3 as the action a satisfying Q(s, a) = max_{a'} Q(s, a') under the factorization operator, which directly generalizes the standard fixed-point for the optimal case. In the revision we will insert an explicit derivation in §3.1 showing that the condition reduces exactly to the Bellman fixed-point equation when a is optimal, while for suboptimal actions it identifies local attractors where the equality holds without global maximality. This derivation relies only on the learned Q-values from any value factorization method and is therefore independent of the subsequent MRVF increment. The increment is applied only after the base factorization has converged, to modify the effective payoff landscape for the next round; we will add a sentence clarifying that the stable-point definition itself does not depend on MRVF. revision: partial

  2. Referee: [§4] §4 (MRVF mechanism): no derivation is supplied showing how the non-negative payoff increment modifies the fixed-point equation to destabilize suboptimal actions globally; the claim that this process cannot create fresh suboptimal stable points or break overall convergence therefore lacks support and is load-bearing for the central algorithmic claim.

    Authors: We acknowledge that the current manuscript offers an intuitive description rather than a formal derivation of how the increment alters the fixed-point equation. In the revision we will add a short mathematical sketch in §4.2: for an inferior action a, the update sets an effective Q'(s, a) = Q(s, a) + δ (δ > 0 chosen as the gap to the superior action), which violates the stability equality Q(s, a) = max Q(s, ·) and thereby renders a unstable. This forces the next round to converge to a stable point with a strictly better action. However, a complete global guarantee that no new suboptimal stable points can arise or that convergence is preserved in every environment would require additional assumptions (e.g., Lipschitz continuity of the value functions and bounded increments) that are not established in the present work. We will therefore present the sketch as supporting analysis, note the limitation explicitly, and rely on the empirical evidence that the procedure converges reliably on the tested domains. revision: partial

  3. Referee: [§5] §5 (experiments): the reported results on SMAC and predator-prey lack ablations isolating the effect of the payoff increment on stable-point distributions across rounds; without these, it is impossible to confirm that performance gains arise from the proposed filtering rather than hyperparameter tuning or other implementation details.

    Authors: We agree that stronger isolation of the increment mechanism is necessary. In the revised §5 we will add two sets of results: (1) histograms of stable-point quality (optimal vs. suboptimal) measured at the end of each MRVF round on both predator-prey and SMAC maps, and (2) a controlled ablation in which the increment δ is set to zero while all other hyperparameters and network architectures remain identical. These additions will directly demonstrate that the observed performance lift originates from the iterative destabilization of inferior actions rather than from incidental hyperparameter effects. revision: yes

standing simulated objections not resolved
  • A complete machine-checked or parameter-free proof that MRVF cannot introduce new suboptimal stable points in arbitrary environments.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The abstract introduces the novel concept of a 'stable point' to characterize general convergence behavior of value factorization (beyond optimal cases only), analyzes distributions of these points in existing methods to identify non-optimal ones as the primary cause of suboptimality, and proposes MRVF as an iterative filtering approach using a non-negative payoff increment. No equations, self-citations, or fitted parameters are exhibited that reduce the central claims, the definition of stable points, or the MRVF mechanism to prior inputs by construction. The derivation chain relies on the independent theoretical construct and external benchmark validation, remaining self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the newly introduced stable point entity and two domain assumptions about convergence behavior and payoff measurement; no explicit free parameters are stated in the abstract.

axioms (2)
  • domain assumption Value factorization methods converge to stable points characterized by individual agent action stability in general cases.
    Foundational premise for the theoretical analysis of suboptimal convergence.
  • ad hoc to paper A non-negative payoff increment relative to the prior action can be used to identify and destabilize inferior actions.
    Core mechanism of the proposed MRVF framework.
invented entities (1)
  • stable point no independent evidence
    purpose: Characterizes potential convergence points of value factorization beyond the optimal case.
    New theoretical construct introduced to explain and diagnose suboptimal performance.

pith-pipeline@v0.9.0 · 5533 in / 1381 out tokens · 105477 ms · 2026-05-10T19:57:52.806617+00:00 · methodology

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

  1. [1]

    We let Qr =Q jt −Q mon

    ¯u̸= eu Here we give a specificQ mon that satisfies these conditions: Qmon(τ,u) = ( Qjt(τ,eu)u= eu maxu Qjt(τ,u) + ∆otherwise (32) where ∆>0 . We let Qr =Q jt −Q mon. Since Qmon ≥Q jt, we have Qr ≤0 . Therefore, we obtain Qmon, wr and Qr, which together constitute theQ tot of ResQ. ∀u̸= eu, we have Qjt(τ,u) =Q tot(τ,u) =Q mon(τ,u) + 1∗Q r(τ,u) . Foreu, si...

    work page 2022

  2. [2]

    capture" prey. Capture Conditions 21 Submission and Formatting Instructions for ICML 2026 • A predator can only select the

    ¯u=u ∗ whereQ mon ≡Q jt(τ,u ∗)is a specific case. We let Qr =Q jt −Q mon. Since Qmon ≥Q jt, we have Qr ≤0 . Therefore, we obtain Qmon, wr and Qr, which together constitute theQ tot of ResQ. According tow r defined in Equation (30), we have Qtot = ( Qmon(τ,u) + 1∗Q r(τ,u)∀u̸= eu Qmon(τ,eu) + 0∗Q r(τ,eu)u= eu (33) SubstitutingQ r =Q jt −Q mon andQ mon(τ,eu)...

    work page 2026