Paper:
Existing works in deep Multi-Agent Reinforcement Learning (MARL) mainly focus on coordinating cooperative agents to complete certain tasks jointly. However, in many cases of the real world, agents are self-interested such as employees in a company and clubs in a league. Therefore, the leader, i.e., the manager of the company or the league, needs to provide bonuses to followers for efficient coordination, which we call expensive coordination. The main difficulties of expensive coordination are that i) the leader has to consider the long-term effect and predict the followers' behaviors when assigning bonuses and ii) the complex interactions between followers make the training process hard to converge, especially when the leader's policy changes with time. In this work, we address this problem through an event-based deep RL approach. Our main contributions are threefold.
(1) We model the leader's decision-making process as a semi-Markov Decision Process and propose a novel multi-agent event-based policy gradient to learn the leader's long-term policy. (2) We exploit the leader-follower consistency scheme to design a follower-aware module and a follower-specific attention module to predict the followers' behaviors and make accurate response to their behaviors. (3) We propose an action abstraction-based policy gradient algorithm to reduce the followers' decision space and thus accelerate the training process of followers. Experiments in resource collections, navigation, and the predator-prey game reveal that our approach outperforms the state-of-the-art methods dramatically.

Review:
This paper proposes an interesting event-based policy gradient algorithm for single-leader multi-follower Stackelberg Markov Games (SMG). The authors claimed 3 contributions on their work: model the leader's decision-making process as a semi-MDP and proposed an event-based policy gradient algorithm for the leader to consider long-term effect; exploit a leader-follower consistency scheme with a follower-aware module and a follower-specific attention module to better predict the follower's behaviors; and propose an action-abstraction policy gradient algorithm in order to make SMG easier to converge.
The proposed model is interesting and the authors have done sufficient empirical studies to show the success of their method, as well as some necessary theoretical derivations. My major concern about this work is whether the task that this paper follows is widely studied in the reinforcement learning community, as the authors mentioned that only [1] can be used as baseline methods since the other methods can not be applied in their problem. But in general I think this is an interesting paper. Some detailed comments and suggestions:
1. This paper proposed 3 major contributions: event-based policy gradient, leader-follower consistency scheme and action abstraction policy gradient. The authors show the empirical performance comparison for the case with and without each of these techniques in the experiments. It can be seen that all of the 3 techniques help the proposed method perform better. In addition, the proposed method performs better compared to the state-of-the-art method (in [1]). Hence the authors have shown the success of their algorithm empirically. One thing that can be done to improve this paper is to show a joint comparison for the 2 ^ 3 = 8 cases of with / without any of the 3 techniques so that we can gain a better understanding about the effect of these 3 techniques.
2. The authors provide some necessary theoretical derivations to compute the policy gradients. But there are some typos in the equations. For example, the numerator of the equation of the case e_i^k\not\in A_T in I(e_i^k) at the bottom of page 4 is incorrect. In addition, the equation on the second last line of page 3 should be P_\gamma(s_{t+1}, \omega_t, a_t | s_t, \omega_{t-1}), not P_\gamma(s_{t+1}, \omega_t | s_t, \omega_{t-1}, a_t).  Please check the details and solve these typos.
3. It will be better if the authors can provide more theoretical analysis or quantitative explanation about the proposed method. For example, why a dense EBPG better than a sparse one? Why the equations in the attention mechanism appear in their form, not some similar forms (e.g. scale the values from the function A before putting them into the softmax function)? Intuitively the proposed techniques make sense, but it will be great if more insights are provided.
4. As I mentioned, I am concerned if the proposed problem is widely studied in the reinforcement learning community. Also, since the authors mentioned in the appendix that two of the tasks are original from [2], but we can not apply the method in [2] as a baseline method. It is possible to modify the method in [2] to fit with the setting and compare with them?
5. It will be better if the authors can rearrange the paper for a little bit, since there are too many important details (e.g. experiment settings, assumptions in the theorems) are in appendix.
Questions:
1. Can the authors try to modify the method in [2] and compare with it (details in my comment 4)?
Reference:
[1] Tianmin Shu and Yuandong Tian. M3RL: Mind-aware multi-agent management reinforcement learning. In ICLR, 2019.
[2] Ryan Lowe, Yi Wu, Aviv Tamar, Jean Harb, OpenAI Pieter Abbeel, and Igor Mordatch. Multi-agent actor-critic for mixed cooperative-competitive environments. In NeurIPS, pp. 6379–6390, 2017.