Pith. sign in

REVIEW 2 major objections 1 minor 42 references

Reviewed by Pith at T0; open to challenge.

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

A clipping objective in trust-region multi-agent RL bounds advantage variance during sequential updates and guarantees monotonic convergence to epsilon-Nash equilibria.

2026-06-25 21:15 UTC pith:RRDNU3T6

load-bearing objection The paper gives a clipping fix for variance in sequential independent-actor MARL updates and claims a monotonic bound to epsilon-Nash, but the theory is asserted without derivation steps. the 2 major comments →

arxiv 2606.25526 v1 pith:RRDNU3T6 submitted 2026-06-24 cs.LG cs.MA

Low Variance Trust Region Optimization with Independent Actors and Sequential Updates in Cooperative Multi-agent Reinforcement Learning

Bang Giang Le , Viet Cuong Ta This is my paper
classification cs.LG cs.MA
keywords multi-agent reinforcement learningtrust region optimizationindependent actorssequential updatesadvantage varianceNash equilibriumclipping objectivecooperative MARL
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

In cooperative multi-agent reinforcement learning with independent actors, sequential policy updates require re-estimating the joint advantage after each agent's step, leading to exponentially high variance that destabilizes training. The paper analyzes this variance issue both empirically and theoretically. It then proposes a clipping objective that controls the upper bound on advantage fluctuations to restore stability. Using this objective, the authors prove a monotonic improvement bound and sub-linear convergence to epsilon-Nash equilibria. They derive two practical algorithms from it that outperform baselines on standard benchmarks while showing low variance and stable convergence.

Core claim

The proposed clipping objective controls the upper bounds of the advantage fluctuation in sequential updates. With the proposed objective, a monotonic bound with sub-linear convergence to ε-Nash Equilibria is provided for the independent actors setting in cooperative multi-agent reinforcement learning.

What carries the argument

The clipping objective that limits advantage fluctuation to preserve the trust-region improvement guarantee during sequential updates.

Load-bearing premise

The clipping operation bounds advantage fluctuation tightly enough to preserve the trust-region improvement guarantee without introducing bias that would invalidate the sub-linear convergence proof.

What would settle it

A calculation or simulation in a simple two-agent game showing whether the advantage variance grows exponentially without clipping but stays bounded with it, or whether the convergence rate to Nash equilibrium is sub-linear as predicted.

If this is right

  • The method achieves stable convergence properties during training.
  • Advantage variance estimation remains low across updates.
  • Two new practical algorithms are derived from the clipping objective.
  • The algorithms outperform tested baselines in most environments on three standard benchmarks.

Where Pith is reading between the lines

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

  • The clipping technique may extend to other sequential update schemes in single-agent reinforcement learning.
  • If the variance bound holds, it could support larger step sizes or more agents without instability.
  • The approach might connect to variance issues in non-cooperative multi-agent settings where Nash convergence is also desired.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 1 minor

Summary. The paper addresses variance explosion in advantage estimates during sequential policy updates for independent-actor cooperative MARL. It introduces a clipping objective that is asserted to bound advantage fluctuation, derives from it a monotonic improvement guarantee with sub-linear convergence to ε-Nash equilibria, presents two practical algorithms, and reports superior empirical performance together with reduced variance on standard MARL benchmarks.

Significance. A correctly derived monotonic bound that survives clipping would supply a missing theoretical anchor for stable trust-region methods in sequential-update MARL; the empirical variance-reduction claim, if quantified, would further strengthen the practical contribution.

major comments (2)
  1. Abstract and theoretical sections: the monotonic bound and sub-linear convergence to ε-Nash equilibria are asserted to follow from the clipping objective, yet no derivation steps, assumptions on the advantage estimator, or handling of residual bias terms introduced by clipping are supplied; this is load-bearing for the central claim that the clipped objective preserves the original trust-region improvement inequality across sequential updates.
  2. Abstract and experimental sections: the paper states that the method achieves 'low advantage variance estimation' and 'stable convergence properties,' but reports neither quantitative variance measurements (e.g., variance of the advantage estimator before/after clipping) nor any statistical comparison of variance across runs, leaving the variance-reduction claim unverified.
minor comments (1)
  1. Abstract: the sentence 'we first analyze the high variance advantage both empirically and theoretically' is not followed by any summary of the analysis or key equations, reducing clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on the theoretical derivation and empirical variance claims. We address each major comment below and will revise the manuscript to strengthen these aspects.

read point-by-point responses

  1. Referee: Abstract and theoretical sections: the monotonic bound and sub-linear convergence to ε-Nash equilibria are asserted to follow from the clipping objective, yet no derivation steps, assumptions on the advantage estimator, or handling of residual bias terms introduced by clipping are supplied; this is load-bearing for the central claim that the clipped objective preserves the original trust-region improvement inequality across sequential updates.

    Authors: We agree that explicit derivation steps are needed for clarity. The clipping objective is introduced to bound advantage fluctuations in sequential updates, and the monotonic improvement bound with sub-linear convergence to ε-Nash equilibria is obtained by adapting the single-agent trust-region analysis while accounting for the independent-actor setting. In the revision, we will add a dedicated subsection providing the full step-by-step derivation, explicitly stating assumptions on the advantage estimator (including bounded bias), and detailing how residual bias from clipping is controlled to preserve the improvement inequality across sequential updates. revision: yes

  2. Referee: Abstract and experimental sections: the paper states that the method achieves 'low advantage variance estimation' and 'stable convergence properties,' but reports neither quantitative variance measurements (e.g., variance of the advantage estimator before/after clipping) nor any statistical comparison of variance across runs, leaving the variance-reduction claim unverified.

    Authors: We acknowledge that while the experiments analyze training settings to demonstrate stable convergence and low variance, direct quantitative variance measurements and statistical comparisons are not reported. In the revised experimental section, we will add tables or plots showing the variance of the advantage estimator before and after clipping, along with mean and standard deviation across multiple runs and statistical comparisons (e.g., via t-tests) against baselines on the MARL benchmarks. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation follows from proposed clipping objective

full rationale

The paper analyzes high-variance advantage estimation under sequential updates, introduces a clipping objective to bound fluctuations, and derives a monotonic improvement bound plus sub-linear convergence to ε-Nash equilibria directly from that objective. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or renamed input; the bound is presented as a consequence of the new objective rather than presupposed by it. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard cooperative MARL assumptions plus the new clipping construction; no free parameters or invented entities are declared in the abstract.

axioms (1)
  • domain assumption Importance sampling re-estimation of the joint advantage after each individual policy step produces exponentially high variance.
    Explicitly stated as the core problem motivating the clipping objective.

pith-pipeline@v0.9.1-grok · 5769 in / 1096 out tokens · 20131 ms · 2026-06-25T21:15:34.297337+00:00 · methodology

0 comments
read the original abstract

Cooperative multi-agent reinforcement learning assumes each agent shares the same reward function and can be trained effectively using the Trust Region framework of single-agent. Instead of relying on other agents' actions, the independent actors setting considers each agent to act based only on its local information, thus having more flexible applications. However, in the sequential update framework, it is required to re-estimate the joint advantage function after each individual agent's policy step. Despite the practical success of importance sampling, the updated advantage function suffers from exponentially high variance problems, which likely result in unstable convergence. In this work, we first analyze the high variance advantage both empirically and theoretically. To overcome this limitation, we introduce a clipping objective to control the upper bounds of the advantage fluctuation in sequential updates. With the proposed objective, we provide a monotonic bound with sub-linear convergence to $\epsilon$-Nash Equilibria. We further derive two new practical algorithms using our clipping objective. The experiment results on three popular multi-agent reinforcement learning benchmarks show that our proposed method outperforms the tested baselines in most environments. By carefully analyzing different training settings, our proposed method is highlighted with both stable convergence properties and the desired low advantage variance estimation. For reproducibility purposes, our source code is publicly available at https://github.com/giangbang/Low-Variance-Trust-Region-MARL.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

42 extracted references · 10 canonical work pages · 4 internal anchors

  1. [1]

    In: International Conference on Machine Learning, pp

    Schulman, J., Levine, S., Abbeel, P., Jordan, M., Moritz, P.: Trust region policy optimization. In: International Conference on Machine Learning, pp. 1889–1897 (2015). PMLR

    2015

  2. [2]

    Proximal Policy Optimization Algorithms

    Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347 (2017)

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  3. [3]

    In: International Conference on Learning Representations (2022)

    Kuba, J.G., Chen, R., Wen, M., Wen, Y., Sun, F., Wang, J., Yang, Y.: Trust region policy optimisation in multi-agent reinforcement learning. In: International Conference on Learning Representations (2022). https://openreview.net/forum? id=EcGGFkNTxdJ

    2022

  4. [4]

    The Journal of Machine Learning Research21(1), 7234–7284 (2020)

    Rashid, T., Samvelyan, M., De Witt, C.S., Farquhar, G., Foerster, J., Whiteson, S.: Monotonic value function factorisation for deep multi-agent reinforcement learning. The Journal of Machine Learning Research21(1), 7234–7284 (2020)

    2020

  5. [5]

    Advances in neural information processing systems30(2017)

    Lowe, R., Wu, Y.I., Tamar, A., Harb, J., Pieter Abbeel, O., Mordatch, I.: Multi- agent actor-critic for mixed cooperative-competitive environments. Advances in neural information processing systems30(2017)

    2017

  6. [6]

    Witt, C.S., Gupta, T., Makoviichuk, D., Makoviychuk, V., Torr, P.H., Sun, M., Whiteson, S.: Is independent learning all you need in the starcraft multi-agent challenge? arXiv preprint arXiv:2011.09533 (2020)

    work page arXiv 2011

  7. [7]

    Advances in Neural Information Processing Systems35, 24611–24624 (2022)

    Yu, C., Velu, A., Vinitsky, E., Gao, J., Wang, Y., Bayen, A., Wu, Y.: The surprising effectiveness of ppo in cooperative multi-agent games. Advances in Neural Information Processing Systems35, 24611–24624 (2022)

    2022

  8. [8]

    Advances in neural information processing systems33, 5527–5540 (2020)

    Daskalakis, C., Foster, D.J., Golowich, N.: Independent policy gradient methods for competitive reinforcement learning. Advances in neural information processing systems33, 5527–5540 (2020)

    2020

  9. [9]

    In: International Con- ference on Learning Representations (2022)

    Leonardos, S., Overman, W., Panageas, I., Piliouras, G.: Global convergence of multi-agent policy gradient in markov potential games. In: International Con- ference on Learning Representations (2022). https://openreview.net/forum?id= gfwON7rAm4

    2022

  10. [10]

    In: International Conference on Machine Learning, pp

    Ding, D., Wei, C.-Y., Zhang, K., Jovanovic, M.: Independent policy gradient for large-scale markov potential games: Sharper rates, function approximation, and game-agnostic convergence. In: International Conference on Machine Learning, pp. 5166–5220 (2022). PMLR

    2022

  11. [11]

    In: Proceedings of the AAAI Conference on Artificial Intelligence, vol

    Foerster, J., Farquhar, G., Afouras, T., Nardelli, N., Whiteson, S.: Counterfactual multi-agent policy gradients. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32 (2018) 33

    2018

  12. [12]

    In: International Conference on Learning Representations (2019)

    Engstrom, L., Ilyas, A., Santurkar, S., Tsipras, D., Janoos, F., Rudolph, L., Madry, A.: Implementation matters in deep rl: A case study on ppo and trpo. In: International Conference on Learning Representations (2019)

    2019

  13. [13]

    A Survey of Learning in Multiagent Environments: Dealing with Non-Stationarity

    Hernandez-Leal, P., Kaisers, M., Baarslag, T., De Cote, E.M.: A survey of learn- ing in multiagent environments: Dealing with non-stationarity. arXiv preprint arXiv:1707.09183 (2017)

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  14. [14]

    Advances in Neural Information Processing Systems35, 16509–16521 (2022)

    Wen, M., Kuba, J., Lin, R., Zhang, W., Wen, Y., Wang, J., Yang, Y.: Multi- agent reinforcement learning is a sequence modeling problem. Advances in Neural Information Processing Systems35, 16509–16521 (2022)

    2022

  15. [15]

    In: Proceedings of the 40th International Conference on Machine Learning, vol

    Zhao, Y., Yang, Z., Wang, Z., Lee, J.D.: Local optimization achieves global optimality in multi-agent reinforcement learning. In: Proceedings of the 40th International Conference on Machine Learning, vol. 202, pp. 42200–42226 (2023). https://proceedings.mlr.press/v202/zhao23j.html

    2023

  16. [16]

    In: International Conference on Learning Representations (2022)

    Li, W., Wang, X., Jin, B., Sheng, J., Zha, H.: Dealing with non-stationarity in MARL via trust-region decomposition. In: International Conference on Learning Representations (2022). https://openreview.net/forum?id=XHUxf5aRB3s

    2022

  17. [17]

    Advances in Neural Information Processing Systems34, 12208–12221 (2021)

    Peng, B., Rashid, T., Witt, C., Kamienny, P.-A., Torr, P., B¨ ohmer, W., Whiteson, S.: Facmac: Factored multi-agent centralised policy gradients. Advances in Neural Information Processing Systems34, 12208–12221 (2021)

    2021

  18. [18]

    In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp

    Todorov, E., Erez, T., Tassa, Y.: Mujoco: A physics engine for model-based control. In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5026–5033 (2012). IEEE

    2012

  19. [19]

    Advances in Neural Information Processing Systems34, 26437–26448 (2021)

    Wu, Z., Yu, C., Ye, D., Zhang, J., Zhuo, H.H.,et al.: Coordinated proximal policy optimization. Advances in Neural Information Processing Systems34, 26437–26448 (2021)

    2021

  20. [20]

    Advances in neural information processing systems32(2019)

    Liu, B., Cai, Q., Yang, Z., Wang, Z.: Neural trust region/proximal policy optimiza- tion attains globally optimal policy. Advances in neural information processing systems32(2019)

    2019

  21. [21]

    arXiv preprint arXiv:2110.13799 (2021)

    Huang, N.-C., Hsieh, P.-C., Ho, K.-H., Yao, H.-Y., Hu, K.-C., Ouyang, L.-C., Wu, I., et al.: Neural ppo-clip attains global optimality: A hinge loss perspective. arXiv preprint arXiv:2110.13799 (2021)

    work page arXiv 2021

  22. [22]

    In: Proceedings of the Nineteenth International Conference on Machine Learning, pp

    Kakade, S., Langford, J.: Approximately optimal approximate reinforcement learning. In: Proceedings of the Nineteenth International Conference on Machine Learning, pp. 267–274 (2002)

    2002

  23. [23]

    In: Proceedings of the 34 AAAI Conference on Artificial Intelligence, vol

    Shani, L., Efroni, Y., Mannor, S.: Adaptive trust region policy optimization: Global convergence and faster rates for regularized mdps. In: Proceedings of the 34 AAAI Conference on Artificial Intelligence, vol. 34, pp. 5668–5675 (2020)

    2020

  24. [24]

    arXiv preprint arXiv:2006.07869 (2020)

    Papoudakis, G., Christianos, F., Sch¨ afer, L., Albrecht, S.V.: Benchmarking multi- agent deep reinforcement learning algorithms in cooperative tasks. arXiv preprint arXiv:2006.07869 (2020)

    work page arXiv 2006

  25. [25]

    Transactions on Machine Learning Research (2023)

    Christianos, F., Papoudakis, G., Albrecht, S.V.: Pareto actor-critic for equilibrium selection in multi-agent reinforcement learning. Transactions on Machine Learning Research (2023)

    2023

  26. [26]

    arXiv preprint arXiv:2003.0670919(2020)

    Witt, C.S., Peng, B., Kamienny, P.-A., Torr, P., B¨ ohmer, W., Whiteson, S.: Deep multi-agent reinforcement learning for decentralized continuous cooperative control. arXiv preprint arXiv:2003.0670919(2020)

    work page arXiv 2003

  27. [27]

    CoRRabs/1902.04043(2019)

    Samvelyan, M., Rashid, T., Witt, C.S., Farquhar, G., Nardelli, N., Rudner, T.G.J., Hung, C.-M., Torr, P.H.S., Foerster, J., Whiteson, S.: The StarCraft Multi-Agent Challenge. CoRRabs/1902.04043(2019)

    work page arXiv 1902

  28. [28]

    Journal of Machine Learning Research25(32), 1–67 (2024)

    Zhong, Y., Kuba, J.G., Feng, X., Hu, S., Ji, J., Yang, Y.: Heterogeneous-agent reinforcement learning. Journal of Machine Learning Research25(32), 1–67 (2024)

    2024

  29. [29]

    Proceedings of the national academy of sciences114(13), 3521–3526 (2017)

    Kirkpatrick, J., Pascanu, R., Rabinowitz, N., Veness, J., Desjardins, G., Rusu, A.A., Milan, K., Quan, J., Ramalho, T., Grabska-Barwinska, A.,et al.: Overcoming catastrophic forgetting in neural networks. Proceedings of the national academy of sciences114(13), 3521–3526 (2017)

    2017

  30. [30]

    IEEE Transactions on Neural Networks and Learning Systems (2023)

    Li, H., He, H.: Multiagent trust region policy optimization. IEEE Transactions on Neural Networks and Learning Systems (2023)

    2023

  31. [31]

    arXiv preprint arXiv:2110.02793 (2021)

    Gu, S., Kuba, J.G., Wen, M., Chen, R., Wang, Z., Tian, Z., Wang, J., Knoll, A., Yang, Y.: Multi-agent constrained policy optimisation. arXiv preprint arXiv:2110.02793 (2021)

    work page arXiv 2021

  32. [32]

    In: International Conference on Machine Learning, pp

    Tucker, G., Bhupatiraju, S., Gu, S., Turner, R., Ghahramani, Z., Levine, S.: The mirage of action-dependent baselines in reinforcement learning. In: International Conference on Machine Learning, pp. 5015–5024 (2018). PMLR

    2018

  33. [33]

    In: International Conference on Machine Learning, pp

    Chung, W., Thomas, V., Machado, M.C., Le Roux, N.: Beyond variance reduction: Understanding the true impact of baselines on policy optimization. In: International Conference on Machine Learning, pp. 1999–2009 (2021). PMLR

    1999

  34. [34]

    Advances in neural information processing systems 29(2016)

    Munos, R., Stepleton, T., Harutyunyan, A., Bellemare, M.: Safe and efficient off- policy reinforcement learning. Advances in neural information processing systems 29(2016)

    2016

  35. [35]

    Advances in Neural 35 Information Processing Systems34, 13458–13470 (2021)

    Kuba, J.G., Wen, M., Meng, L., Zhang, H., Mguni, D., Wang, J., Yang, Y.,et al.: Settling the variance of multi-agent policy gradients. Advances in Neural 35 Information Processing Systems34, 13458–13470 (2021)

    2021

  36. [36]

    In: The Eleventh International Confer- ence on Learning Representations (2023)

    Wang, X., Tian, Z., Wan, Z., Wen, Y., Wang, J., Zhang, W.: Order matters: Agent-by-agent policy optimization. In: The Eleventh International Confer- ence on Learning Representations (2023). https://openreview.net/forum?id= Q-neeWNVv1

    2023

  37. [37]

    In: Proceed- ings of the 17th International Conference on Autonomous Agents and MultiAgent Systems

    Sunehag, P., Lever, G., Gruslys, A., Czarnecki, W.M., Zambaldi, V., Jaderberg, M., Lanctot, M., Sonnerat, N., Leibo, J.Z., Tuyls, K., Graepel, T.: Value-decomposition networks for cooperative multi-agent learning based on team reward. In: Proceed- ings of the 17th International Conference on Autonomous Agents and MultiAgent Systems. AAMAS ’18, pp. 2085–20...

    2085

  38. [38]

    A unified view of entropy-regularized Markov decision processes

    Neu, G., Jonsson, A., G´ omez, V.: A unified view of entropy-regularized markov decision processes. CoRRabs/1705.07798(2017)

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  39. [39]

    Mathematical programming 198(1), 1059–1106 (2023)

    Lan, G.: Policy mirror descent for reinforcement learning: Linear convergence, new sampling complexity, and generalized problem classes. Mathematical programming 198(1), 1059–1106 (2023)

    2023

  40. [40]

    SIAM-Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2017)

    Beck, A.: First-order Methods in Optimization. SIAM-Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2017)

    2017

  41. [41]

    The Journal of Machine Learning Research22(1), 4431–4506 (2021)

    Agarwal, A., Kakade, S.M., Lee, J.D., Mahajan, G.: On the theory of policy gradient methods: Optimality, approximation, and distribution shift. The Journal of Machine Learning Research22(1), 4431–4506 (2021)

    2021

  42. [42]

    Equivalence Between Policy Gradients and Soft Q-Learning

    Schulman, J., Chen, X., Abbeel, P.: Equivalence between policy gradients and soft q-learning. arXiv preprint arXiv:1704.06440 (2017) 36

    work page internal anchor Pith review Pith/arXiv arXiv 2017