Scalable Primal-Dual Actor-Critic Method for Safe Multi-Agent RL with General Utilities

We investigate safe multi-agent reinforcement learning, where agents seek to collectively maximize an aggregate sum of local objectives while satisfying their own safety constraints. The objective and constraints are described by {\it general utilities}, i.e., nonlinear functions of the long-term state-action occupancy measure, which encompass broader decision-making goals such as risk, exploration, or imitations. The exponential growth of the state-action space size with the number of agents presents challenges for global observability, further exacerbated by the global coupling arising from agents' safety constraints. To tackle this issue, we propose a primal-dual method utilizing shadow reward and $κ$-hop neighbor truncation under a form of correlation decay property, where $κ$ is the communication radius. In the exact setting, our algorithm converges to a first-order stationary point (FOSP) at the rate of $\mathcal{O}\left(T^{-2/3}\right)$. In the sample-based setting, we demonstrate that, with high probability, our algorithm requires $\widetilde{\mathcal{O}}\left(ε^{-3.5}\right)$ samples to achieve an $ε$-FOSP with an approximation error of $\mathcal{O}(ϕ_0^{2κ})$, where $ϕ_0\in (0,1)$. Finally, we demonstrate the effectiveness of our model through extensive numerical experiments.

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Peer review

Reviewer bKHc5/10 · confidence 3/52023-07-05

Summary

The work extends constrained single-agent general utilities RL (where the objective is a non-convex function of occupancy measure) to a constrained multi-agent setting. Naturally, similar to single-agent, the constraints are satisfied in expectations. They assume the combined (global) objective to be additive in terms of agents. The major novelty part of the paper is the handling of constraints (unconstrained multi-agent is a prior work). In a multi-agent setting, communication is a challenge, and to tackle this, authors utilise a k-hop type method under which agents can communicate with nearby agents.

Strengths

- Extension to multi-agent constrained setting (constrained are of general utility type) - k-hop policies (I am not sure if it is a novel contribution or from earlier work) - Convergence analysis for both exact and stochastic setting

Weaknesses

Objective: The considered global objective function is additive in agents. For a framework of general utilities RL, I would expect to consider general dependence between the agent, especially since they motivate the problem for exploration/imitation. If the objective is exploration, then the current multi-agent framework is still performing exploration individually only and it might perform differently on a combined exploration objective. Contributions: The contributions were not so clear from [72]. If a multi-agent extension with truncated PG utilizing shadow rewards was already done and if a constrained part for a single agent existed, then I am not sure if the paper has a novel contribution. Experiments: Since the proposed algorithm is PG type, I would expect authors to level PG tools and perform experiments with high dim state action space and complicated dynamics, e.g. car or Ant (may be continuous space, not sure if easily can be done). Since the motivation of the problem is done using exploration and imitation tasks, I think an essential component in the paper should be some experiments on these tasks and comparing performance with the case when the additivity of agents is relaxed.

Questions

- I would suggest authors to have a subsection on challenges, wrt to a single agent case. It might be worth mentioning here that are not trivial single-agent to multi-agent extensions. - Is K-hop strategy and analysis existing in prior work? - Maybe bring related works in the main paper - It will be good to have an algorithm block in the main paper as well.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

2 fair

Contribution

1 poor

Limitations

no potential negative impact

Reviewer pEsM7/10 · confidence 4/52023-07-06

Summary

This paper studies the safe MARL with general utilities and focuses on the setting of distributed training without global observability. The authors propose a primal-dual actor-critic method with shadow reward and \kappa-hop policy to tackle the problems of scalability and incorporating general utilities. They provide the theoretical analysis for the convergence rate and sampling complexity. In addition, they also demonstrate the effectiveness of their method via comprehensive experiment results.

Strengths

(1) Novel formulation: This paper provides a clear mathematical formulation for the MARL with general utility problems. This formulation will help the real-world multi-agent problem modeling in the general case, and encourage more discussion on the intersected domain of Safe RL and MARL. (2) Solid theoretical analysis: This work provides solid mathematical analysis for the convergence guarantee in general-utilities settings. The analysis is rigorous as well as easy to follow. In addition, they provide a detailed discussion of the properties and show how the convergence can be guaranteed in common multi-agent scenarios. (3) Comprehensive experimental results: The authors validate their proposed method using three experiment tasks of different categories. It is a pleasure to see the detailed task description, code implementation, and results corresponding to different settings (e.g. number of neighbors, constraint thresholds) in the submission.

Weaknesses

(1) Lack of baseline comparison in the main context: I understand that the authors want to display more theoretical analysis so they may move the baseline comparison into the appendix. However, I would suggest adding this section back to the main content as it is one of the most convincing parts to show the strengths of this work.

Questions

(1) Experiment settings: I am wondering how you design the experiment settings. Based on your description in section H.4, (1.1) what is the motivation to set an upper bound for the cumulative reward in the Pistonball task? (1.2) Do you mean additional cost u_i in line 1287, or this term is directly added to the reward as the penalization?

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

4 excellent

Presentation

4 excellent

Contribution

4 excellent

Limitations

The authors adequately addressed the limitations.

Reviewer Vbe76/10 · confidence 4/52023-07-07

Summary

This paper considers the safe multi-agent rl in the fully-decentralized setting. In the system, agents need to satisfy local safety constraints, and they also have to maximize the joint objectives. Moreover, the objectives are general utilities, which have broader applications than common discounted reward. Authors utilize shadow reward and kappa-hop neighbor truncation to limit the communication to be only among neighboring agents, which removes the need of global state and global Q function when updating each local agent. Both convergence and the sample complexity are analyzed. The experiment results also validate the effectiveness of the proposed algorithm.

Strengths

This paper has the following merits. 1. The paper is well-written generally and easy to follow. 2. The kappa-hop truncation is intuitive and interesting for many real-world applications, and it also successfully eliminates the need of global state and global Q of all agents. 3. Authors establish detailed convergence and sample complexity analysis, with thorough proofs and discussions.

Weaknesses

While promising, I have some concerns on the proposed algorithm. See Questions part for more details.

Questions

I have the following concerns on the paper. 1. The potential scope and real-world applications for such fully-distributed MARL are not clear. As we all know, rl usually requires heavy exploration of the environment, and it also needs lots of samples to converge. Thus, it becomes adventurous and high-cost to deploy these policies directly to the environment, and let them train in a distributed way. 2. The communication protocol for two unconnected but neighboring agents is not clear. They can communicate directly through P2P, or they can only transmit the data agent-by-agent if the communication is limited to connected agents. Such difference is essential for the algorithm design, as the former one may generate high-cost for communication, while the latter one may bring data latency to each agent. 3. Assumption 3.2 is too strong, as it involves the summation over all agents. The system that satisfies the assumption is nearly independent, as each agent's action has little influence on other's state transition. 4. The algorithm has 3 major steps but relies heavily on communication. The communication complexity is not analyzed in the work, which is in fact a major metric for decentralized optimization algorithms [1,2]. Further, the scalability is not experimented/discussed in detail in the paper. In fact, I have doubts on the scalability of the algorithm, especially for dense agents, as the communication overhead becomes extremely heavy. One related work is missing [3]. [1]. Optimal and Practical Algorithms for Smooth and Strongly Convex Decentralized Optimization, NIPS, 2020 [2]. Lower Bounds and Optimal Algorithms for Smooth and Strongly Convex Decentralized Optimization Over Time-Varying Networks, NIPS, 2021 [3]. Decom: decomposed policy for constrained cooperative multi-agent reinforcement learning, AAAI, 2023

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

4 excellent

Presentation

4 excellent

Contribution

4 excellent

Limitations

Authors discussed the future works on the scalable safe MARL algorithms with adaptive communication of agents’ state/action information and intelligent sampling of agents’ trajectories. I personally prefer to focus more on the time-varying networks [2], where the connection is unstable and the communication has some unignored latency.

Reviewer fkzS7/10 · confidence 3/52023-07-11

Summary

This paper considers the problem of safe/constrained multi-agent reinforcement learning (MARL) with general utilities and constraints, which could be generic functions of agents' occupancy measures. A distributed method is proposed for solving the constrained MARL problem with local constraints, where each agent can communicate to its few-hop neighbors in the underlying network graph topology. The proposed algorithm is theoretically analyzed in terms of convergence behavior and sample complexity, and numerical results are provided to demonstrate the efficacy of the proposed method in multiple constrained MARL environments.

Strengths

- The problem of constrained/safe MARL is of great practical interest and importance, so the paper focuses on a timely topic of interest to the NeurIPS audience. - Distributed training of safe RL policies in multi-agent settings is of significance, and the paper makes important contributions in this direction. - Extensive theoretical and numerical analysis is provided to showcase the benefits of the proposed approach.

Weaknesses

- The presentation and structure of the paper could be improved, especially since many of the important parts of the paper (especially the algorithm pseudo-code, flowchart, and numerical results) are deferred to the appendix. Mindful of the space limitations, it would be great if the authors could shuffle the contents in their revision to include the pseudo-code/flowchart and more numerical results in the main body of the paper, with at least one result for each environment introduced in Section 5. - The authors mention [25] (Lu et al., AAAI'21) in their discussion of related work, but I would have liked a more extensive discussion on the similarities and differences between this work and [25], especially since they both consider an underlying graph topology, as well as numerical comparisons with [25] in addition to MAPPO-Lagrangian. - The paper mostly focuses on tabular MARL settings with a finite state space. It is unclear how the proposed method generalizes to continuous state spaces.

Questions

- I believe the Transition decomposition assumption in lines 106-108 is very strong. Could you please comment on how you justify this assumption in practical settings and whether it could be relaxed to a weaker assumption? - How does the proposed method extend to the case where the objective in Eq. (5) is not separable? - Intuitively, the upper bound in Eq. (13) should depend on $\omega$ and $\chi$ in Assumption 3.2, so please discuss why they do not appear here. - In Eq. (15), could $1/n$ be replaced with $1/|\mathcal{N}_i^{\kappa}|$? I understand that this is simply a scaling factor, but truncating the policies to $\kappa$-hop neighbors could also justify the aforementioned replacement, where the Lagrangian is always *averaged* over the $\kappa$-hop neighborhood of each agent. - Does Fig. 1-d show that the constraints are always violated? Does this mean that no feasible policy in this environment might exist? - In the Appendix, it is shown that MAPPO-L performs worse than the proposed method. Could you provide a more in-depth discussion of why this happens? As the authors allude to, MAPPO-L has access to the global state during the centralized training phase, so it is okay (and probably expected) if the proposed method (which is fully distributed) underperforms MAPPO-L. - Since a graph structure and distributed implementation are the underpinnings of the proposed method, how does the proposed method related to graph neural networks (GNNs)? The agents could perform message passing to their neighbors through a GNN architecture, so it would be helpful if the authors could discuss potential connections of their method to MARL methods based on GNNs, such as the following reference [A]: [A] Jiang, Jiechuan, Chen Dun, Tiejun Huang, and Zongqing Lu. "Graph Convolutional Reinforcement Learning." In International Conference on Learning Representations. 2019.

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

As mentioned under **Weaknesses**, the extension to non-tabular MARL settings is unclear. Furthermore, the robustness of the proposed method to imperfect communication among agents (e.g., noise perturbations, random communication link drops, delays, time/frequency resource constraints, etc.) needs to be studied.

Reviewer fkzS2023-08-14

Thank you!

Thank you very much for the responses to my comments, which have resolved my concerns to a great extent. I have updated my score accordingly.

Authorsrebuttal2023-08-14

Thank you very much for appreciating our work and raising the score!

Program Chairsdecision2023-09-21

Decision

Accept (poster)

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