Pith. sign in

REVIEW 4 major objections 6 minor 35 references

This paper proves that using the inherent symmetry of multi-robot systems lets inverse reinforcement learning recover more accurate reward functions from fewer expert demonstrations, and packages the result into a plug-in training framework

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

Symmetry-guided data augmentation and a symmetry-aware discriminator improve sample efficiency in multi-agent inverse reinforcement learning.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection A useful empirical framework for symmetry-guided multi-agent IRL, but the headline theoretical guarantee is not proven. the 4 major comments →

arxiv 2509.08257 v2 pith:5QM3NCXF submitted 2025-09-10 cs.RO cs.AI

Symmetry-Guided Multi-Agent Inverse Reinforcement Learning

Yongkai Tian , Yirong Qi , Xin Yu , Wenjun Wu , Jie Luo This is my paper
classification cs.RO cs.AI
keywords multi-agent inverse reinforcement learningsample efficiencysymmetryequivariance and invariancedihedral groupgenerative adversarial imitation learningmulti-robot systemsreward recovery
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.

The reading

Multi-agent inverse reinforcement learning normally needs many expert demonstrations to infer a reward function. This paper claims that if the underlying system is symmetric—its dynamics and expert policy unchanged by rotations and reflections—then augmenting the demonstrations with those transformations provably recovers a more accurate reward function than training on the raw demonstrations alone. The formal result, Proposition 2, compares the worst-case error of the two problems and shows the symmetry-guided problem's upper bound is no larger. The authors turn this into a framework, SGF, that augments demonstrations and adds a symmetry-aware discriminator, and they show it improves sample efficiency in simulated cooperative tasks and on physical robots.

Core claim

The paper's central claim is Proposition 2. For a Markov game without reward whose transition function and expert policy are invariant under a symmetry group G, define the symmetry-guided multi-agent inverse reinforcement learning problem from the augmented demonstration set obtained by applying every g in G to each sample. Then the worst-case error in recovering any feasible reward is no larger with this augmentation than without it: |r(s,a) - r_hat(s,a)|_U >= |r(s,a) - r_hat^G(s,a)|_U. The proof combines a characterization of the feasible reward set (Lemma 1) with an error-propagation bound (Proposition 1) and transition-estimation concentration arguments. The authors conclude that leverag

What carries the argument

The load-bearing object is the G-invariant Markov game without reward (Definition 1), i.e. a Markov game whose transition P and expert policy pi_E satisfy P(s'|s,a) = P(L_g[s']|L_g[s],K_g[a]) and pi_i(a_i|s) = pi_i(K_g[a_i]|L_g[s]) for every transformation g. The proof uses the feasible-reward-set characterization of Lemma 1 to convert symmetry into a comparison of empirical transition estimates. The framework then operationalizes the theory with the Symmetry-Guided Demonstration Augmenter (SGDA), which applies dihedral-group rotations and reflections D_n to expert and generated samples, and a Symmetry-Aware Discriminator (SAD) that adds a symmetry-augmented cross-entropy term to the adversa

Load-bearing premise

The guarantee assumes the environment's dynamics and the expert's policy are exactly invariant under the chosen rotations and reflections; real multi-robot systems are only approximately symmetric, so augmented demonstrations may come from a wrong distribution and Proposition 2's bound need not hold.

What would settle it

In a synthetic Markov game with known ground-truth reward and controlled transition symmetry, perturb the transition by increasing magnitudes that break the G-invariance; if the symmetry-augmented algorithm's reward-recovery error becomes larger than the unaugmented baseline at small perturbations, the practical premise of Proposition 2 is experimentally contradicted.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • On Rendezvous, Pursuit, and Vicsek, S-MA-AIRL and S-MA-GAIL outperform their base algorithms at every tested demonstration count, with the largest gaps at the smallest counts.
  • Fewer demonstrations suffice: symmetry-guided runs reach rewards comparable to baselines trained on far more demonstrations.
  • The Symmetry-Aware Discriminator is load-bearing: removing it and using a normal discriminator consistently lowers convergence rewards in the ablation study.
  • Performance degrades with agent count for baselines, but SGF largely holds up, maintaining stronger rewards for 5 to 20 agents.
  • Physical robots confirm the effect: in real-world Rendezvous and Pursuit tasks, S-MA-AIRL completes tasks faster than MA-AIRL.

Where Pith is reading between the lines

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

  • A natural extension the paper does not test: estimate the degree of G-violation per environment and let the augmentation weight adapt, so approximately symmetric systems are not hurt by invalid synthetic samples.
  • The bound is worst-case; testing average-case reward error on known-symmetric environments with ground-truth rewards would show whether the practical gains come from tighter bounds or from added regularization.
  • The same reasoning could apply to single-agent inverse reinforcement learning with structured transformations such as translations or reflections, since the feasible-reward-set argument is per state-action pair and does not require multiple agents.
  • One could combine SGDA with partial-symmetry methods to handle realistic robot asymmetries; if approximate symmetry weakens the bound's premise, a partial-symmetry variant would be the next experiment.
Share X Bluesky LinkedIn Reddit HN

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

4 major / 6 minor

Summary. The paper proposes to improve sample efficiency in multi-agent inverse reinforcement learning (MIRL) by exploiting rotational/reflectional symmetry. It extends the feasible-reward-set characterization of Metelli et al. to Markov games (Lemma 1), derives an error-propagation bound for the empirical MIRL problem (Proposition 1), and claims that augmenting expert demonstrations by the group action reduces the worst-case reward-recovery error (Proposition 2). Based on this theory, the authors introduce a Symmetry-Guided Framework (SGF) with a demonstration augmenter (SGDA) and a symmetry-aware discriminator (SAD), and evaluate it on three simulated multi-agent tasks and two physical robot tasks.

Significance. If Proposition 2 were established, the paper would make a useful contribution: it would provide a principled justification for symmetry-based data augmentation in MIRL, it is framework-agnostic, and it introduces no free parameters. The experimental results are consistently in favor of the proposed SGF and include a physical-robot validation, which is a strength. However, the central theoretical claim is not proven as written. Lemma 1 and Proposition 1 are clean extensions of known results, but Proposition 2--the headline contribution--rests on a proof with multiple load-bearing errors. Because the theoretical contribution is the paper's main novelty, these errors are significant despite the promising empirical results.

major comments (4)
  1. [Appendix, proof of Proposition 2] The proof cites [34,35] for the concentration bound |P - P_hat| <= C sqrt(D(s,a)) < 1. This scaling is inverted: standard concentration bounds for empirical transition probabilities decay as O(1/sqrt(D(s,a))), not O(sqrt(D(s,a))). Consequently, the subsequent step '1 - C sqrt(D_G(s,a)) > 0' is not a valid concentration argument. The second term of delta is therefore not shown nonnegative as claimed.
  2. [Appendix, proof of Proposition 2, support term] The support-term argument is internally contradictory. When (s,a) in tau^G_E \ tau_E, the proof first asserts hat{pi}_E(a|s) > 0 and then derives hat{pi}^G_E(a|s) = 0. But (s,a) is in the augmented dataset by assumption, so hat{pi}^G_E(a|s) > 0. Moreover, under exact G-invariance, if pi_E(a|s)=0 then no transformed sample can create (s,a) in tau^G_E, so the first term is actually zero in all relevant cases. The proof's sign analysis of the first term is not valid.
  3. [Section IV-C, Proposition 2] The proposition is not well-quantified. It compares |r(s,a)-hat r(s,a)|_U and |r(s,a)-hat r^G(s,a)|_U, but it does not state over which r, hat r, and hat r^G the comparison is made, nor whether U denotes the supremum or infimum of the corresponding upper bounds. In the proof, delta is introduced as a difference of actual errors but is then manipulated as a difference of upper bounds from Proposition 1. Without fixed quantifiers, the claimed inequality cannot be checked.
  4. [Section IV-C, Definition 1 and Section V-A] The theoretical guarantee relies on the exact G-invariance of both the environment transition P and the expert policy pi_E under the dihedral group D_n. The SGDA then treats group-transformed samples as valid expert data. In the experimental environments, including the physical robots, symmetry is only approximate; the paper does not measure the degree of symmetry violation or show that Proposition 2 degrades gracefully. As stated, the bound need not hold under approximate symmetry, so the experiments do not fully validate the theoretical claim.
minor comments (6)
  1. [Definition 2] The augmented dataset definition contains typos: it should be {(g s_j, g a_j, g s'_j)} with (s_j,a_j,s'_j) in tau_E, not {g a} and '(s_j,a_j,s_j)'.
  2. [Lemma 2] The parameter zeta is said to lie in R^{S x S}_{>=0}, but it should be indexed by state-action pairs, i.e., R^{S x A}_{>=0}, consistent with Lemma 1.
  3. [Notation] The paper alternates between hat B_G and hat B^G for the symmetry-guided MIRL problem; please unify the notation.
  4. [Appendix, proof of Proposition 1] The phrase 'choose V = hat V' is stated backwards; the intended construction is choose hat V = V and hat zeta = zeta I{pi_E(a|s)=0}. Please rephrase.
  5. [Appendix, concentration bound] There is a typo: 'D(s,a) is the number of of (s,a) in tau' should read 'number of occurrences of (s,a)'.
  6. [Section VI-C and Fig. 5] The reward visualization would benefit from a precise description of the action grid and the state/action normalization used; currently it is difficult to interpret the scale and orientation of the recovered rewards.

Circularity Check

0 steps flagged

No significant circularity: Proposition 2 is a parameter-free comparison of two empirical bounds; self-citations are background. The appendix proof has correctness defects but these are not circular reductions.

full rationale

The central derivation (Section IV-C, Proposition 2) compares the error-propagation upper bound for the original empirical MIRL problem \hat B with that for the augmented problem \hat B^G. The upper bound in Proposition 1 is obtained from the external feasible-reward characterization of [30], and the claimed improvement is justified by concentration bounds cited from [34,35]. No parameter is fitted to the data and later renamed a prediction; the framework introduces no free constants into the theoretical argument. The conclusion that the augmented dataset, being a superset, yields a smaller worst-case bound is a direct, non-circular consequence of the definitions plus the concentration inequality. Self-citations in Sections I-II ([17],[18],[24],[25]) are related-work background and are not used to establish Proposition 2 or the framework's design. Separately, the appendix proof of Proposition 2 contains substantive correctness defects: the quoted bound |P - \hat P| <= C sqrt(D(s,a)) has an inverted scaling (standard concentration is 1/sqrt(D)), the support-term argument for (s,a) in tau^G_E \ tau_E is internally contradictory (an augmented sample should have positive empirical support, not zero), and delta is treated as a difference of actual errors while being computed as a difference of upper bounds. These are grounds for doubting the theorem as written, but they are not circularity: the claim is not equivalent to its inputs by construction, and no load-bearing self-citation chain forces the conclusion. The exact G-invariance assumption is a modeling condition, not a fitted quantity; its lack of validation is a robustness concern, not a circularity. Therefore the circularity score is 0.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

The theoretical derivation is parameter-free: it introduces no fitted constants. Experimental hyperparameters (learning rates, network sizes, numbers of demonstrations) are standard ML choices and do not enter the central bound. No new physical entities are introduced; the Symmetry-Guided Framework and its modules are algorithmic constructs.

axioms (4)
  • domain assumption G-invariance of transition and expert policy: P(s'|s,a) = P(L_g[s']|L_g[s],K_g[a]) and pi_i(a_i|s) = pi_i(K_g[a_i]|L_g[s]) for all g in G
    Definition 1 (Section IV-C). The SGDA augmentation and the proof of Proposition 2 both require transformed demonstrations to be valid samples of the true dynamics and expert behavior.
  • standard math Feasible reward set characterization (Lemma 1) extended from single-agent [30] to multi-agent
    Section IV-A, Lemma 1; relies on the Bellman optimality conditions and the existence of zeta >= 0 and V.
  • standard math Concentration inequality |P-P_hat| <= C sqrt(D(s,a)) with C sqrt(D) < 1, as used in the Prop. 2 proof
    Appendix proof of Proposition 2 cites [34],[35]; the scaling C sqrt(D) appears inverted relative to standard bounds (which decay as 1/sqrt(D)), and the conclusion 1 - C sqrt(D) > 0 is asserted. This is load-bearing for the non-negativity of the second term.
  • standard math Empirical policy pi_hat_E assigns zero probability to state-action pairs not observed in tau_E (used to evaluate indicator functions in the Prop. 2 proof)
    Section IV-B, empirical policy definition; the proof asserts pi_hat_E(a|s)>0 for (s,a) in tau_G \ tau_E, which contradicts this definition, so the proof is internally inconsistent.

reviewed 2026-08-04 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Symmetry-Guided Multi-Agent Inverse Reinforcement Learning." pith.science (2026). https://pith.science/paper/5QM3NCXF

@misc{pith2026250908257,
  author       = {Pith},
  title        = {Pith review of: Symmetry-Guided Multi-Agent Inverse Reinforcement Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5QM3NCXF}},
  note         = {Machine review of arXiv:2509.08257}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

In robotic systems, the performance of reinforcement learning depends on the rationality of predefined reward functions. However, manually designed reward functions often lead to policy failures due to inaccuracies. Inverse Reinforcement Learning (IRL) addresses this problem by inferring implicit reward functions from expert demonstrations. Nevertheless, existing methods rely heavily on large amounts of expert demonstrations to accurately recover the reward function. The high cost of collecting expert demonstrations in robotic applications, particularly in multi-robot systems, severely hinders the practical deployment of IRL. Consequently, improving sample efficiency has emerged as a critical challenge in multi-agent inverse reinforcement learning (MIRL). Inspired by the symmetry inherent in multi-agent systems, this work theoretically demonstrates that leveraging symmetry enables the recovery of more accurate reward functions. Building upon this insight, we propose a universal framework that integrates symmetry into existing multi-agent adversarial IRL algorithms, thereby significantly enhancing sample efficiency. Experimental results from multiple challenging tasks have demonstrated the effectiveness of this framework. Further validation in physical multi-robot systems has shown the practicality of our method.

Figures

Figures reproduced from arXiv: 2509.08257 by Jie Luo, Wenjun Wu, Xin Yu, Yirong Qi, Yongkai Tian.

Figure 1
Figure 1. Figure 1: Multi-agent inverse reinforcement learning with sym [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the proposed Symmetry-Guided Frame [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Average true rewards across three tasks. Experiments are conducted with four different numbers of expert demonstrations. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The simulated tasks considered in this paper. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Demonstration of the real-world scenarios. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

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

35 extracted references · 27 canonical work pages · 1 internal anchor

  1. [1]

    Mact: Multi-agent col- lision avoidance with continuous transition reinforcement learning via mixup,

    P. Feng, X. Yu, J. Liang, W. Wu, and Y. Tian, “Mact: Multi-agent col- lision avoidance with continuous transition reinforcement learning via mixup,” inInternational Conference on Swarm Intelligence. Springer, 2023, pp. 74–85

    work page 2023

  2. [2]

    Hierarchical consensus-based multi-agent reinforcement learning for multi-robot cooperation tasks,

    P. Feng, J. Liang, S. Wang, X. Yu, X. Ji, Y. Chen, K. Zhang, R. Shi, and W. Wu, “Hierarchical consensus-based multi-agent reinforcement learning for multi-robot cooperation tasks,” in2024 IEEE/RSJ Interna- tional Conference on Intelligent Robots and Systems (IROS). IEEE, 2024, pp. 642–649

    work page 2024

  3. [3]

    Safe multi-agent reinforcement learning for multi-robot control,

    S. Gu, J. G. Kuba, Y. Chen, Y. Du, L. Yang, A. Knoll, and Y. Yang, “Safe multi-agent reinforcement learning for multi-robot control,”Artificial Intelligence, vol. 319, p. 103905, 2023

    work page 2023

  4. [4]

    Sigma: Sheaf-informed geometric multi-agent pathfinding,

    S. Liao, W. Xia, Y. Cao, W. Dai, C. He, W. Wu, and G. Sartoretti, “Sigma: Sheaf-informed geometric multi-agent pathfinding,”arXiv preprint arXiv:2502.06440, 2025

    work page arXiv 2025

  5. [5]

    Inverse reward design,

    D. Hadfield-Menell, S. Milli, P. Abbeel, S. J. Russell, and A. Dragan, “Inverse reward design,”Advances in neural information processing systems, vol. 30, 2017

    2017

  6. [6]

    Concrete problems in ai safety,

    D. Amodei, C. Olah, J. Steinhardt, P. Christiano, J. Schulman, and D. Man ´e, “Concrete problems in ai safety,”arXiv preprint arXiv:1606.06565, 2016

    Pith/arXiv arXiv 2016

  7. [7]

    Multi-agent inverse reinforcement learning,

    S. Natarajan, G. Kunapuli, K. Judah, P. Tadepalli, K. Kersting, and J. Shavlik, “Multi-agent inverse reinforcement learning,” in2010 ninth international conference on machine learning and applications. IEEE, 2010, pp. 395–400

    2010

  8. [8]

    Multiagent inverse reinforcement learning for two-person zero-sum games,

    X. Lin, P. A. Beling, and R. Cogill, “Multiagent inverse reinforcement learning for two-person zero-sum games,”IEEE Transactions on Games, vol. 10, no. 1, pp. 56–68, 2017

    work page 2017

  9. [9]

    Recent advances in robot learning from demonstration,

    H. Ravichandar, A. S. Polydoros, S. Chernova, and A. Billard, “Recent advances in robot learning from demonstration,”Annual review of control, robotics, and autonomous systems, vol. 3, no. 1, pp. 297–330, 2020

    work page 2020

  10. [10]

    Efficient training of artificial neural networks for autonomous navigation,

    D. A. Pomerleau, “Efficient training of artificial neural networks for autonomous navigation,”Neural computation, vol. 3, no. 1, pp. 88–97, 1991

    1991

  11. [11]

    Algorithms for inverse reinforcement learning,

    A. Y. Ng and S. J. Russell, “Algorithms for inverse reinforcement learning,” inProceedings of the Seventeenth International Conference on Machine Learning, 2000, pp. 663–670

    work page 2000

  12. [12]

    Efficient reductions for imitation learning,

    S. Ross and D. Bagnell, “Efficient reductions for imitation learning,” inProceedings of the thirteenth international conference on artificial intelligence and statistics. JMLR Workshop and Conference Proceed- ings, 2010, pp. 661–668

    work page 2010

  13. [13]

    A reduction of imitation learning and structured prediction to no-regret online learning,

    S. Ross, G. Gordon, and D. Bagnell, “A reduction of imitation learning and structured prediction to no-regret online learning,” inProceedings of the fourteenth international conference on artificial intelligence and statistics. JMLR Workshop and Conference Proceedings, 2011, pp. 627–635

    2011

  14. [14]

    A survey of imitation learning: Algorithms, recent developments, and challenges,

    M. Zare, P. M. Kebria, A. Khosravi, and S. Nahavandi, “A survey of imitation learning: Algorithms, recent developments, and challenges,” IEEE Transactions on Cybernetics, 2024

    2024

  15. [15]

    Physics-informed machine learning,

    G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang, “Physics-informed machine learning,”Nature Reviews Physics, vol. 3, no. 6, pp. 422–440, 2021

    2021

  16. [16]

    Multi- agent mdp homomorphic networks,

    E. van der Pol, H. van Hoof, F. A. Oliehoek, and M. Welling, “Multi- agent mdp homomorphic networks,” inInternational Conference on Learning Representations, 2021

    work page 2021

  17. [17]

    Esp: Exploiting symmetry prior for multi-agent reinforcement learning,

    X. Yu, R. Shi, P. Feng, Y. Tian, J. Luo, and W. Wu, “Esp: Exploiting symmetry prior for multi-agent reinforcement learning,” inECAI 2023. IOS Press, 2023, pp. 2946–2953

    work page 2023

  18. [18]

    Exploiting hierarchical symmetry in multi-agent reinforcement learning,

    Y. Tian, X. Yu, Y. Qi, L. Wang, P. Feng, W. Wu, R. Shi, and J. Luo, “Exploiting hierarchical symmetry in multi-agent reinforcement learning,” inECAI 2024. IOS Press, 2024, pp. 2202–2209

    work page 2024

  19. [19]

    Multi-agent generative adver- sarial imitation learning,

    J. Song, H. Ren, D. Sadigh, and S. Ermon, “Multi-agent generative adver- sarial imitation learning,”Advances in neural information processing systems, vol. 31, 2018

    work page 2018

  20. [20]

    Multi-agent adversarial inverse rein- forcement learning,

    L. Yu, J. Song, and S. Ermon, “Multi-agent adversarial inverse rein- forcement learning,” inInternational Conference on Machine Learning. PMLR, 2019, pp. 7194–7201

    work page 2019

  21. [21]

    Scalable Multi-Agent Inverse Reinforcement Learning via Actor-Attention-Critic

    W. Jeon, P. Barde, D. Nowrouzezahrai, and J. Pineau, “Scalable multi- agent inverse reinforcement learning via actor-attention-critic,”arXiv preprint arXiv:2002.10525, 2020

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  22. [22]

    Swarm inverse reinforcement learning for biological systems,

    X. Yu, W. Wu, P. Feng, and Y. Tian, “Swarm inverse reinforcement learning for biological systems,” in2021 IEEE International Conference on Bioinformatics and Biomedicine (BIBM). IEEE, 2021, pp. 274– 279

    work page 2021

  23. [23]

    Dec-airl: Decentralized adversarial irl for human-robot teaming,

    P. Sengadu Suresh, Y. Gui, and P. Doshi, “Dec-airl: Decentralized adversarial irl for human-robot teaming,” inProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Sys- tems, 2023, pp. 1116–1124

    work page 2023

  24. [24]

    Leveraging partial symmetry for multi-agent reinforcement learning,

    X. Yu, R. Shi, P. Feng, Y. Tian, S. Li, S. Liao, and W. Wu, “Leveraging partial symmetry for multi-agent reinforcement learning,” inProceedings of the AAAI Conference on Artificial Intelligence, vol. 38, no. 16, 2024, pp. 17 583–17 590

    work page 2024

  25. [25]

    Adaptaug: Adaptive data augmentation framework for multi-agent reinforcement learning,

    X. Yu, Y. Tian, L. Wang, P. Feng, W. Wu, and R. Shi, “Adaptaug: Adaptive data augmentation framework for multi-agent reinforcement learning,” in2024 IEEE International Conference on Robotics and Automation (ICRA), 2024, pp. 10 814–10 820

    work page 2024

  26. [26]

    Boosting multiagent reinforcement learning via permutation invariant and permutation equivariant networks,

    H. Jianye, X. Hao, H. Mao, W. Wang, Y. Yang, D. Li, Y. Zheng, and Z. Wang, “Boosting multiagent reinforcement learning via permutation invariant and permutation equivariant networks,” inThe Eleventh International Conference on Learning Representations, 2022

    work page 2022

  27. [27]

    Permutation invariant policy optimization for mean-field multi- agent reinforcement learning: A principled approach,

    Y. Li, L. Wang, J. Yang, E. Wang, Z. Wang, T. Zhao, and H. Zha, “Permutation invariant policy optimization for mean-field multi- agent reinforcement learning: A principled approach,”arXiv preprint arXiv:2105.08268, 2021

    Pith/arXiv arXiv 2021

  28. [28]

    Face completion based on symmetry awareness with conditional gan,

    J. Xu, F. Li, C. Shao, and X. Li, “Face completion based on symmetry awareness with conditional gan,”Symmetry, vol. 15, no. 3, p. 663, 2023

    work page 2023

  29. [29]

    Markov games as a framework for multi-agent reinforce- ment learning,

    M. L. Littman, “Markov games as a framework for multi-agent reinforce- ment learning,” inMachine learning proceedings 1994. Elsevier, 1994, pp. 157–163

    work page 1994

  30. [30]

    Provably efficient learning of transferable rewards,

    A. M. Metelli, G. Ramponi, A. Concetti, and M. Restelli, “Provably efficient learning of transferable rewards,” inInternational Conference on Machine Learning. PMLR, 2021, pp. 7665–7676

    work page 2021

  31. [31]

    The surprising effectiveness of ppo in cooperative multi-agent games,

    C. Yu, A. Velu, E. Vinitsky, J. Gao, Y. Wang, A. Bayen, and Y. Wu, “The surprising effectiveness of ppo in cooperative multi-agent games,” Advances in Neural Information Processing Systems, vol. 35, pp. 24 611–24 624, 2022

    work page 2022

  32. [32]

    Cooperative pursuit with voronoi partitions,

    Z. Zhou, W. Zhang, J. Ding, H. Huang, D. M. Stipanovi ´c, and C. J. Tomlin, “Cooperative pursuit with voronoi partitions,”Automatica, vol. 72, pp. 64–72, 2016

    work page 2016

  33. [33]

    Novel type of phase transition in a system of self-driven particles,

    T. Vicsek, A. Czir ´ok, E. Ben-Jacob, I. Cohen, and O. Shochet, “Novel type of phase transition in a system of self-driven particles,”Physical review letters, vol. 75, no. 6, p. 1226, 1995

    work page 1995

  34. [34]

    Near-optimal regret bounds for reinforcement learning,

    P. Auer, T. Jaksch, and R. Ortner, “Near-optimal regret bounds for reinforcement learning,”Advances in neural information processing systems, vol. 21, 2008

    work page 2008

  35. [35]

    Why is posterior sampling better than optimism for reinforcement learning?

    I. Osband and B. Van Roy, “Why is posterior sampling better than optimism for reinforcement learning?” inInternational conference on machine learning. PMLR, 2017, pp. 2701–2710

    work page 2017

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.