FACMAC: Factored Multi-Agent Centralised Policy Gradients
Authors: Bei Peng
Tabish Rashid
Christian Schroeder de Witt
Pierre-Alexandre Kamienny
Philip Torr
Wendelin Boehmer
Shimon Whiteson
Venue: NeurIPS 2021 Poster (2021)
Keywords: multi-agent reinforcement learning
multi-agent policy gradients

Abstract: We propose FACtored Multi-Agent Centralised policy gradients (FACMAC), a new method for cooperative multi-agent reinforcement learning in both discrete and continuous action spaces. Like MADDPG, a popular multi-agent actor-critic method, our approach uses deep deterministic policy gradients to learn policies. However, FACMAC learns a centralised but factored critic, which combines per-agent utilities into the joint action-value function via a non-linear monotonic function, as in QMIX, a popular multi-agent $Q$-learning algorithm. However, unlike QMIX, there are no inherent constraints on factoring the critic. We thus also employ a nonmonotonic factorisation and empirically demonstrate that its increased representational capacity allows it to solve some tasks that cannot be solved with monolithic, or monotonically factored critics. In addition, FACMAC uses a centralised policy gradient estimator that optimises over the entire joint action space, rather than optimising over each agent's action space separately as in MADDPG. This allows for more coordinated policy changes and fully reaps the benefits of a centralised critic. We evaluate FACMAC on variants of the multi-agent particle environments, a novel multi-agent MuJoCo benchmark, and a challenging set of StarCraft II micromanagement tasks. Empirical results demonstrate FACMAC's superior performance over MADDPG and other baselines on all three domains.

FACMAC: Factored Multi-Agent Centralised
Policy Gradients
Bei Peng" University of Liverpool
Tabish Rashid" University of Oxford
Christian A. Schroeder de Witt" University of Oxford
Pierre-Alexande Kamienny
Philip H. S. Torr University Oxford
Wendelin Böhmer Delft University of Technology
Facebook Al Research
Shimon Whiteson University of Oxford
Abstract
We propose FACtored Multi-Agen Centralised policy gradients (FACMAC), method for cooperative multi-agent reinforcement learning in both discrete and con- tinuous action spaces. Like MADDPG, popular multi-agent actor-critic method, our approach uses deep deterministic policy gradients to learn policies. However, FACMAC learns centralised but factored critic, which combines per-agent util- ities into the joint action-value function via non-linear monotonic function, as in QMIX, popular multi-agent Q-learning algorithm. However, unlike QMIX, there are no inherent constraints on factoring the critic. We thus also employ a nonmonotonic factorisation and empirically demonstrate that its increased rep- resentational capacity allows it to solve some tasks that cannot be solved with monolithie, or monotonically factored critics. In addition, FACMAC uses a cen- tralised policy gradient estimator that optimises over the entire joint action space, rather than optimising over each agent's action space separately as in MADDPG. This allows for more coordinated policy changes and fully reaps the benefits of a centralised critic. We evaluate FACMAC on variants of the multi-agent particle environments, a novel multi-agent MuJoCo benchmark, and a challenging set of StarCraft II micromanagement tasks. Empirical results demonstrate FACMAC's superior performance over MADDPG and other baselines all three domains.
Introduction
Significant progress has been made in cooperative multi-agent reinforcement learning (MARL) under the paradigm of centralised training with decentralised execution (CTDE) 27 18 in recent years, both value-based [41 31 37 32 44, 30) and actor-critic [23] 9 36 13 approaches. Most popular multi-agent actor-critic methods such as COMA [9] and MADDPG 23 learn centralised critic with decentralised actors. The critic centralised to make use of all available information (i.e., it can condition the global state and the joint action) to estimate the joint action-value function Qiot, unlike a decentralised critic that estimates the local action-value function Qa based only on individual observations and actions for each agent Even though the joint action-value function
* 'Equal contribution. Correspondence to: Bei Peng <bei. wiwerpeoleep.c....o
1 Work done while the authors were at the University of Oxford.
'COMA learns single centralised critic for all cooperative agents due parameter sharing. For each agent the critic has different inputs can thus output different values for the same state and joint action.
35th Conference on Neural Information Processing Systems (NcurIPS 2021).

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these actor-critic methods can represent is not restricted, in practice they significantly underperform value-based methods like QMIX [31] on the challenging StarCraft Multi-Agent Challenge (SMAC)
K5
benchmark
R3 32
In this paper, propose novel approach called FACtored Multi-Agent Centralised policy gradients (FACMAC), which works for both discrete and continuous cooperative multi-agent tasks, Like MADDPG, our approach uses deep deterministic policy gradients [20] to learn decentralised policies. However, FACMAC learns a single centralised but factored critic, which factors the joint action-value function Qio into per-agent utilities Qu that are combined via a non-linear monotonic function, as in the popular Q Q-learning algorithm QMIX [3I]. While the critic used in COMA and MADDPG is also centralised, it monolithic rather than factored Compared to learning a monolithic critic, our factored critic can potentially scale better to tasks with larger number of agents and/or actions. In addition, in contrast to other value-based approaches such as QMIX, there are no inherent constraints on factoring the critic. This allows us to employ rich value factorisations, including nonmonotonic ones, that value-based methods cannot directly use without forfeiting decentralisability or introducing other significant algorithmic changes. We thus also employ a nonmonotonic factorisation and empirically demonstrate that its increased representational capacity allows it to solve some tasks that cannot be solved with monolithic, or monotonically factored critics.
In MADDPG, a separate policy gradient derived for each agent individually, which optimises its policy assuming all other agents' actions are fixed. This could cause the agents to converge to sub-optimal policies in which no single agent wishes to change its action unilaterally. In FACMAC, we use a new centralised gradient estimator that optimises over the entire joint action space, rather than optimising over each agent's ss action space separately as in MADDPG. The agents' policies are thus trained as single joint-action policy, which can enable learning of more coordinated behaviour, as well as the ability to escape sub-optimal solutions. The centralised gradient estimator fully reaps the benefits of learning centralised critic, by not implicitly marginalising over the actions of the other agents in the policy-gradient update. The gradient estimator used in MADDPG is also known to be vulnerable to relative overgeneralisation [7). To overcome this issue, in our centralised gradient estimator, we sample all actions from all agents' current policies when evaluating the joint action-value function. We empirically show that MADDPG can quickly get stuck in local optima in simple continuous matrix game, whereas our centralised gradient estimator finds the optimal policy. While Lyu et al. [24] recently show that merely using centralised critic (with per-agent gradients that optimise over each agent's 's actions separately) does not necessarily lead to better coordination between agents, centralised gradient estimator re-establishes the value of using centralised critics.
Most recent works on continuous MARL focus on evaluating their algorithms on the multi-agent particle environments [23] which feature simple two-dimensional world with some basic simulated physics. To demonstrate FACMAC's s scalability to more complex continuous domains and to stimulate more progress in continuous MARL, introduce Multi-Agent MuJoCo (MAMuJoCo), a new, comprehensive benchmark suite that allows the study of decentralised continuous control. Based on the popular single-agent MuJoCo benchmark [5], MAMuJoCo features a wide variety of novel robotic control tasks in which multiple agents within a single robot have to solve a task cooperatively.
We evaluate FACMAC on variants of the multi-agent particle environments 23 and our novel MAMuJoCo benchmark, which both feature continuous action spaces, and the challenging SMAC benchmark (35), which features discrete action spaces. Empirical results demonstrate FACMAC's superior performance over MADDPG and other baselines on all three domains. In particular, FACMAC scales better when the number of agents (and/or actions) and the complexity of the task increases. Results on SMAC show that FACMAC significantly outperforms stochastic DOP (46), which recently claimed to be the first multi-agent actor-critic method to outperform state-of- -het-rt valued-based methods on SMAC, in all scenarios we tested. Moreover, our ablations and additional experiments demonstrate the advantages of both factoring the critic and using our centralised gradient estimator. We show that, compared to learning a monolithic critic, learning a factored critic can: 1) better take advantage of the centralised gradient estimator to optimise the agent policies when the
In MADDPG, each agent learns its own centralised critic, as it is designed for general multi- learning problems, including cooperative, competitive, and mixed settings.
'We use "centralised and monolithic critic" and "monolithic critic" interchangeably to refer to the centralised critic used in COMA and MADDPG, and "centralised but factored critic" and "factored critic" interchangeably refer to the critic used in approach.
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number of agents and/or actions is large, and 2) leverage a nonmonotonic factorisation to solve tasks that cannot be solved with monolithic or monotonically factored critics.
2 Background
We consider a fully cooperative multi-agent lask in which a team of agents interacts with the same environment to achieve some common goal. It can be modeled as a decentralised partially observable Markov decision process (Dec-POMDPP) [28] consisting of tuple G = (N,, S, U, P. S2 7) Here N = [l..................... n denotes the finite set of agents and E S describes the true state of the environment. At each time step, each agent E N selects discrete or continuous action u. E U, forming a joint action u E U = U This results in a transition to the next state according to the state transition function P(s'|s, u) S x U x 5 - [0, 1] and team reward r(s. u). [0, 1) is discount factor. Due to the partial observability, each agent a E W draws an individual partial observation Og E Q from the observation kernel ((s.ol a). Each agent learns stochastic policy Ta (Ma (Mal or deterministic policy (a (Ta), conditioned only on its local action-observation history Ta E 7 (9t x U)" The joint stochastic policy π induces a joint action-value function: QT (st, Ut) 1 1 [Re|st, Uz),
where R2 = -i= T'T++ is the discounted return. Similarly, the joint deterministic policy μ induces a joint action-value function denoted (st, Uz). We adopt the centralised training with decentralised execution (CTDE) paradigm 27 [8] where policy training can exploit extra global information that might be available and has the freedom to share information between agents during training. However, during execution, each agent must act with only access to its own oostrv-observttion history.
VDN and QMIX. VDN [4]] and QMIX 33 are Q-lcarning algorithms for cooperative MARL tasks with discrete actions. They both aim efficiently learn a centralised but factored action-value function Q using CTDE. To ensure consistency between the centralised and decentralised policies, VDN and QMIX factor Th assuming additivity and monotonicity, respectively. More specifically, VDN factors Qto into sum of the per-agent utilities: Q (T, u: Φ) = Σ ===1 QT (Ta: Na: Φa). QMIX, however, represents Quo as a continuous monotonic mixing function of each agent's 's utilities:
(T, u, Φ v)) = f (s, Q (T1, "1: i1)....,,.9 (Tn, Un; 2n)). where afc 2 V, E N. This TQ. is sufficient to ensure that the global arg max performed on Quo yields the same result as a set of individual arg max performed on each 05e Here f is approximated by monotonic mixing network, parameterised by sb. Monotonicity can be guaranteed by non non-negative mixing weights. These weights are generated by separate hypernetworks [[2) which condition on the full state s. QMIX is trained end-to-end to minimise the following loss:
C(d, ()) = ED (1000
u, u, 11))
(1)
where the bootstrapping target yu = r + 7 maxu' u', (To ,' Here r is the global reward, and o= and v/- are parameters of the target Q and mixing network, respectively, as in DQN (26.. The expectation is estimated with a minibatch of transitions sampled from an experience replay buffer D (1I. During execution, each agent selects actions greedily with respect to its own Q
(T',
23 is an extension of DDPG (00 to multi-agent settings. It is an actor- critic, off-policy method that uses the paradigm of CTDE learn deterministic policies in continuous action spaces. In MADDPG, a separate actor and critic is learned for each agent, such that each agent can have its own arbitrary reward function. It therefore applicable either cooperative, competitive, or mixed settings. We assume each agent has a deterministic policy Ma (Ta: fa), parameterised by 0, (abbreviated as pa), and let μ = (Ta: 0=) be the set of all agent policies. In MADDPG, centralised and monolithic critic that estimates the joint valuue function Q! (s. ui...., . Uy 6g) learned for each agent a separately. The critic is said to be centralised as it utilises information only available to it during the centralised training phase, the global state and the actions of all agents, U1, "1...., Un, to estimate the joint action-value function Qu, which is parameterised by Qa- This joint action-valus function is trained by minimising the following loss:
MADDPG. MADDPG
[(da)= = ED (
Qu ui, Uni oo))
'If the global state is not available, the centralised and monolithic critic can condition on the joint observations or ocserniobservation histories.
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where y" = + QQth u4y ui....,, (P Here Ta is the reward received by each agent a, u4..... uf, is the set of target policies with delayed parameters 07 and 05 are the parameters of the target critic. The replay buffer DD contains the transition tuples (s, M,,...,, Uny .i...., Tn).
The following policy gradient can be calculated individually to update the policy of each agent at
Vo ((u)) = ED (a. V.. Qa Ma,...,, ", (x))
where the current agent a' 's action ua is sampled from its current policy Hı when evaluating the joint action-value function Qhe while all other agents' actions are sampled from the replay buffer D.
3 FACMAC
In this section, we propose a new approach called FACtored Multi-Agent Centralised policy gradients (FACMAC) that uses centralised but factored critic and a centralised gradient estimator to learn continuous cooperative tasks. We start by describing the idea of learning a centralised but factored critic. We then discuss our new centralised gradient estimator and demonstrate its benefit in simple continuous matrix game. Finally, we discuss how we adapt our method to discrete cooperative tasks.
3.1 Learning a Centralised but Factored Critic
Learning centralised and monolithic critic conditioning on the global state and the joint action can be difficult and/or impractical when the number of agents and/or actions large [33. We thus employ value function factorisation in the multi-agent actor-critic framework to enable scalable learning of a centralised critic Dec-POMDPs. Another key advantage of adopting value factorisation in an actor-critic framework is that, compared to value-based methods, it allows for more flexible factorisation as the critic's ' design not constrained. One can employ any type of factorisation, including nonmonotonic factorisations that value-based methods cannot directly use without forfeiting decentralisability or introducing other significant algorithmic changes.
Specifically, in FACMAC, all agents share centralised critic Q that is factored as:
(ha u, 9; Φ v²) = go (s, 1Q (Tas Uai & )=)))=
(4)
where & and o. are parameters of the joint action-valt value function Q and agent-wise utilities QK- respectively. our canonical implementation which we refer to as FACMAC, Dr a non-linear monotonic function parametrised as mixing network with parameters 1h, in QMIX (31. To evaluate the policy, the centralised but factored critie is trained by minimising the following loss:
[(d, 1b) ED (1V Qloer (T, 8; Φb 15)
(5)
where fot = +or+-Q4 ( u(T;: 0 5'; &f ..). Here the replay buffer, and 0_, "T and 2b are parameters of the target actors, critic, and mixing network, respectively.
Leveraging the flexibility of our approach, namely the lack of restrictions the form of the critic, we also explore a new nonmonotonic factorisation with full representational capacity. The joint action-value function Q is represented utilities Q#a This nonmonotonic mixing function is parameterised as a mixing network, with a similar architecture G in FACMAC, but without the constraint of monotonicity enforced by using non-negative weights. We refer to this method as D.CMMAC-nommoootonicccc Additionally, to better understand the advantages of factoring a centralised critic, we also explore two additional simpler factorisation schemes. These include factoring the centralised critic Q into a sum of per-agent utilities Qu in VDN (FACMAC-vdn), and as a sum of Q!- and a state-dependent bias (FACMAC-vdn-s) Our value factorisation technique is general and can be readily applied to any multi-agent actor-critic algorithms that learn centralised and monolithic critics 23
non-linear nonmonotonic mixing function of per-agent
3.2 Centralised Policy Gradients
To update the decentralised policy of each agent, a naive adaptation of the deterministic policy gradient used by MADDPG (shown in 3s)
Jo ED Vo, (Ta) nn Qua (T, un, ..., Un. 8) (u. (Ta)
(6)

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Computing centralised gradient
Quo (T, u)
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Figure 1:
The overall FACMAC architecture. (a) The decentralised policy networks. There is a sampling step since we sample from the categorical distribution when using discrete actions. (b) The centralised but factored critic. (c) The non-linear monotonic mixing function.
Compared to the policy gradient used in MADDPG, the updates of all agents' individual deterministic policies now depend on the single shared factored critic Q as opposed to learning and utilising a monolithic critic Q! for each agent. However, there two main problems in both policy gradients. First, each agent optimises its own policy assuming all other agents' actions are fixed, which could cause the agents to converge to sub-optimal policies in which no single agent wishes to change its action unilaterally. Second, both policy gradients make the corresponding methods vulnerable to relative overgeneralisation [47] as, when agent a ascends the policy gradient based on Q or Q only its own action UA is sampled from its current policy Ha. while all other agents' actions are sampled from the replay buffer D. The other agents' actions thus might be drastically different from the actions their current policies would choose. This could cause the agents to converge to sub-optimal actions that appear to be better choice when considering the effect of potentially arbitrary actions from the other collaborating agents.
In FACMAC, action space, rather than optimising over each agent's 's actions separately as in both (3) and (6). to achieve better coordination among agents. In addition, overcome relative overgeneralisation, when calculating the policy gradient we sample all actions from all agents' current policies when evaluating Qte Our centralised policy gradient can thus be estimated
new centralised gradient estimator that optimises over the entire joint
VOJ(H) - ED Vou Qtior (T, (T) (T))
where μa (Mi(T); ............. nn (Tn; 0n)) is the set of all agents' current policies and all agents share the same actor network parameterised by 0. However, it is not a requirement of our method for all agents to share parameters in this manner.
the critic factorisation is linear, as in FACMAC-vdn, then the centralised gradient is equivalent to the per-agent gradients that optimise over each agent's 's actions separately. This is explored in more detail by DOP [46], which restricts the factored critic to be linear to exploit this equivalence. A major benefit of our method then, is that it does not place any such restrictions on the critic. As remarked by Lyu et al. [24], merely using a centralised critic with per-agent gradients does not necessarily lead to better coordination between agents due to the two problems outlined above. Even with factored critic, methods that use stochastic policy gradients can still suffer from the problems caused by the per-agent gradients if a fully factored stochastic policy is used. Our centralised gradient estimator, which uses deterministic policies and optimises over the entire joint action space, is required in order fully take advantage of a centralised critic.
Figure Dillustrates the overall FACMAC architecture. For each agent a, there is one policy network that decides which individual action (discrete or continuous) to take. There is also one critic network for each agent a that estimates the individual agent utilities Qa, which are then combined into the joint action-valle value function Qtoe via non-linear monotonic mixing function as in QMIX. Qios is then used by our centralised gradient estimator to help the actor update its policy parameters.
To show the benefits of our new centralised gradient estimator, we compare MADDPG with the centralised policy gradient (CPG) against the original MADDPG on a simple continuous cooperative matrix game with two agents. Figure 10 in Appendix D.I illustrates this matrix game. There is
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MADDPG [10]
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Figure 2: (a) Mean test return on Continuous Matrix Game (b) Left: Per-agent policy gradient at the origin. For agent (similarly for agent it since the gradient term assumes the other agent's action to be fixed and thus it only considers the relative improvements along the dotted line (agent I's own action space). Right: Our centralised policy gradient correctly determines the gradient for improving the joint action.
narrow path (shown in red) starting from the origin (0,0) to (1, 1), in which the reward gradually increases. Everywhere else there is small punishment moving away from the origin, increasing in magnitude further from the origin. Experimental results are shown in Figure 2(a) MADDPG quickly gets stuck in the local optimum within 200k timesteps, while MADDPG (with CPG) robustly converges to the optimal policy. Figure 2 visualises the differencess between the per-agent and centralised policy gradients, demonstrating that the per-agent policy gradient can be wrong in continuous matrix game and our centralised policy gradient is necessary to take advantage of the centralised critic. In Section [ we further demonstrate the benefits of our centralised gradient estimator in more complex tasks.
3.3 Discrete Policy Learning
As FACMAC requires differentiable policies and the sampling process discrete actions from a cate- gorical distribution is not differentiable, we the Gumbel-Softmax estimator [14] to enable efficient learning of FACMAC on cooperative tasks with discrete actions. The Humbel-Softmall estimator is a continuous distribution that approximates discrete samples from categorical distribution to produce differentiable samples. Moreover, we use the Straight-Through Gumbel-Softtax Estimator [14] to ensure the action dynamics during training and evaluation are the same. Specifically, during training, we sample discrete actions ua from the original categorical distribution in the forward pass, but the continuous Gumbel-Softmas sample Tg in the backward pass to approximate the gradients: Vo, R Vo_ To- We can then update the agent's 's policy using our centralised policy gradient:
VaJ(x) ED V (T, 2............ s) where x = (. In. is the set of continuous samples that approximates the discrete agent actions. The softmax temperature hyperparameter is set to be in our experiments.
4 Multi-Agent MuJoCo
The evaluation of continuous MARL algorithms has recently been largely limited to the simple multi-agent particle environments 233. We believe the lack of diverse continuous benchmarks is one factor limiting progress in continuous MARL. To demonstrate FACMAC's scalability to more complex continuous domains and to stimulate more progress in continuous MARL,, we develop Multi-Agent MuJoCo (MAMuloCo), a novel benchmark for continuous cooperative multi-agent robotic control. Starting from the popular fully observable single-agent robotic MuJoCo [4] control suite included with OpenAI Gym (5), create wide variety of novel scenarios in which multiple agents within a single robot have to solve a task cooperatively.
This design offers important benefits. It facilitates comparisons to existing literature on both the fully observable single-agent domain 29], as well as settings with wwwbbandiithh communication [45]. More importantly, it allows for the study of novel MARL algorithms for decentralised coordination isolation (scenarios with multiple robots may add confounding factors such as spatial exploration), which is currently gap in the research literature. MAMuJoCo also includes scenarios with larger and more flexible number of agents, which takes inspiration from modular robotics [49 [9]. Compared traditional robots, modular robots are more versatile, configurable, and scalable. We thus

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A)
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Slite jaint (glatse))
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Figure 3: Agent partitionings for MAMuJoCo environments: A) Manyagent Swimmer, B) 3- Agent Hopper [3x1], C) 2-Agent HalfCheetah [2x3], D) 6-Agent HalfCheetah [6x E) 2-Agent Humanoid and 2-Agent HumanoidStandup (each [1x9.I88), F) 2-Agent Walker [2X3]. G) 2-Agent 2-Agent Ant [2x4], 1) 2-Agent Ant Diag [2x4], 4-Agent Ant [4x2], and K) Manyagent Ant. Colours indicate agent partitionings. Each joint corresponds to a single controllable motor. Split partitions indicate shared body segments. Square brackets indicate [(number of agents) x (joints per a.ent)]. Joint IDs are in order of definition in the corresponding OpenAl Gym XML asset files [5]. Global joints indicate degrees of freedom of the center of mass of the composite robotic agent.
Reacher [2x1], H)
develop two scenarios named ManyAgent Swimmer and Many Ant, which one can configure an arbitrarily large number of agents (within the memory limits), each controlling consecutive segment of arbitrary length.
Single-robot multi-agent tasks in MAMuJoCo arise by first representing a given single robotic agent body graph, where vertices (joints) are connected by adjacent edges (hody segments), as shown in Figure 3] We then partition the body graph into disjoint sub-graphs, one for each agent, each of which contains one or more joints that can be controlled. Note that in ManyAgen Swimmer (see Figure 3A) and ManyAgen Ant (see Figure 3K) the number of agents are not limited by the given single robotic agent. See Appendix for more details about MAMuloCo.
Experimental Results
In this section we present our experimental results on our cooperative variants of the continuous
simple tag environment introduced by Lowe et al. 23 (we refer to this environment as Continuous Predator-Prey), our novel continuous benchmark MAMuloCo, and the challenging SMAC (35] benchmark with discrete action spaces. In discrete cooperative tasks, we compare with state-of-the-ae
multi-agent actor-critic algorithms MADDPG (23) COMA 19, CentralV (). DOP (46), VDAC-mix [4). and value-based methods QMIX (31) and QPLEX [44). In continuous cooperative tasks, we compare with MADDPG 23 and independent DDPG (IDDPG), as well as COVDN and COMIX. two novel baselines described below. We also explore different forms of critic factorisation to better understand the advantages of factoring centralised critic. More details about the environments, experimental setup, and training details are included in Appendix D and Code is available at https://gi thub. com/ wowo////hil//acaaaa
COVDN and COMIX. We find that not many multi-agent value-based methods work off the shelf with continuous actions. To compare FACMAC against value-based approaches in continuous cooperative tasks, we use existing continuous Q-learning approaches in single-agent settings to extend VDN and QMIX continuous action spaces. Specifically, we introduce COVDN and COMIX, which use VDN-style and QMIX-style factorisation respectively and both perform approximate greedy action selection using the cross-entropy method (CEM) 77. CEM a sampling-base based derivative-fres free
"We utilise 10,,4.10., which is used by the latest PyMARL 35 framework. The original results reported in Samvelyan et al. [35] and Rashid et al. [35] use SC2.4.6. Performance not always comparable across versions.
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Figure 4: Mean episode return Continuous Predator-Pres with different number of agents and preys. The mean across seeds is plotted and the 95% confidence interval is shown shaded. The numbers in square brackets in the figure legend represent the number of random seeds used to run each method (similarly for all other figures).
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Figure 5: Mean episode return on different MAMuJoCo tasks. In ManyAgent Swimmer, we configure the number of agents to be 10, each controlling consecutive segment of length 2. The mean across 7 seeds is plotted and the 95% confidence interval shown shaded.
heuristic search method that has been successfully used to find approximate maxima of nonconvex Q-networks in single-agent robotic control tasks [15). The centralised but factored Qtot allows us to use CEM to sample actions for each agent independently and to the per-agent utility Qa to guide the selection of maximal actions. We do not consider COVDN and COMIX significant algorithmic contributions but instead merely baseline algorithms. See Appendix for more details about them.
FACMAC outperforms MADDPG and other baselines in both discrete and continuous action the mean episode return attained by different methods on Continuous
tasks. Figure 4 Predator-Prey with varying number of agents and different MAMuJoCo tasks, respectively. We can see that FACMAC significantly outperforms MADDPG on all these continuous cooperative tasks, both in terms of absolute performance and learning speed. On discrete SMAC tasks, Figure 6 shows that FACMAC performs significantly better than MADDPG 4 out of 6 maps tested, and achieves similar performance to MADDPG on the other maps. Additionally, on all 6 SMAC maps, FACMAC significantly outperforms all multi-agent actor-critic baselines (COMA. CentralV, DOP, and VDAC-mix), while DOP is recently claimed to be the first multi-agent actor-critic method that outperforms ofate-of-the-arr valued- salued-based methods SMAC. FACMAC is also competitive with state-of-the-art based methods (QMIX and QPLEX), with significantly better performance on MMM, bane bane, MMM2, and 27m _sp__ss_____________ 30mm These results demonstrate the benefits of our method for improving performance in challenging cooperative tasks with discrete and continuous action spaces.
and and
In Continuous Predator- Prey, FACMAC-vdn scales better than FACMAC when the number of agents increases. However, on MAMuJoCo, FACMAC-vdn performs drastically worse than FACMAC in 2-Agent Humanoid and ManyAgent Swimmer (with 10 agents). demonstrating the necessity of the non-linear mixing of agent utilities and conditioning on the central state information in order to achieve competitive performance in such tasks. Furthermore, on SMAC, Figure [3] in Appendix Flshows that FACMAC is noticeably more stable than FACMAC-vdn and FACMAC-vdn-s across different maps, and achieves significantly better performance on the super hard map MMM2.
Interestingly, we find that FACMAC performs similarly to COMIX on both Continuous Predator- Prey and MAMuJoCo tasks. FACMAC and COMIX use the same value factorisation as QMIX and are both off- off-policy, this suggests that, in these continuous cooperative tasks, factorisation of the
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Figure 6: Median test win % on six different SMAC maps, including 2s3z (easy), MMM (easy), 2c vs_ ps_642g (hard), bane vs bane (hard), MMM2 (super hard), and 27m_ vs 3_30mm (super hard). The median across 5 seeds is plotted and the 25 75% percentiles is shown shaded. The performance of the heuristic-based algorithm is shown as a dashed line. We report the median instead of the mean as recommended by Samvelyan et al. 35 in order to avoid the effect of any outliers.
joint Q-value function plays a greater role in performance than the underlying algorithmic choices. On SMAC, however, FACMAC performs significantly better than QMIX on MMM, bune_vs vs_bane, MMM2, and 27m_vs_30mm
For instance, on sane_vs_bane a task with agents, while QMIX struggles to find the optimal policy with 2 million timesteps, FACMAC, with exactly the same value factorisation, can quickly recover the optimal policy and achieve 100% test win rate. This shows the convergence advantages of policy gradient methods in this type of multi-agent settings [43].
FACMAC scales better as the number of agents (and/or actions) and the complexity of the task increases. As shown in Figure 4(b and 4(c) MADDPG performs poorly if we increase the number of agents in Continuous Predator- Prey,, while both FACMAC and FACMAC-vdn achieve significantly better performance. The monolithic critic in MADDPG simply concatenates all agents' observations into a single input vector, which can be quite large when there are many agents and/or entities and make it more difficult to learn good critic. Factoring the critic enables scalable critic learning, by combining individual agent utilities that condition on much smaller observations into joint action- value function. On MAMuJoCo (shown in Figure similarly, the largest performance gap between FACMAC and MADDPG can be seen on Many Agent Swimmer (with 10 agents), a task with the largest number of agents among three MAMuJoCo tasks tested.
On SMAC (shown Figure op. the largest performance gap between FACMAC and MADDPG can be seen on the challenging MMM2 and 27m_vs vs_30m with large number of agents, which are classified as super hard SMAC maps due to current methods' poor performance 35. We can see that FACMAC is able to learn to consistently defeat the enemy, whereas MADDPG fails to learn anything useful in both tasks. The second largest performance gap between FACMAC and MADDPG can be seen on the hard map 2c_vs_ vw__4gg where MADDPG not only performs significantly worse but also exhibits significantly more variance than FACMAC across seeds. While there are only agents in this scenario. the number of actions each agent choose is the largest among all 6 maps tested as there are 64 enemies. These results further demonstrate that FACMAC scales better when the number of agents (and/or actions) and the complexity of the tasks increases.
Factoring the critic can better take advantage of our centralised gradient estimator to optimise the agent policies when the number of agents and/or actions is large. We conduct ablation experiments to investigate the influence of factoring the critic and using the centralised gradient estimator in our method. FACMAC (without CPG) is our method without the centralised policy gradient. It uses naive adaptation of the deterministic policy gradient used in MADDPG (shown in (6). Thus, the only difference between FACMAC (without CPG) and MADDPG is that the previous

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one learns a non-linearly factored critic while the latter one learns a monolithic critic. We also evaluate MADDPG with our centralised policy gradient and refer as MADDPG (with CPG).
Figure 7 shows the ablation results on SMAC and MAMuJoCo. We can see that FACMAC (without CPG) performs significantly better than MADDPG on both SMAC maps tested, demon- strating the advantages of factoring the critic in challenging coordination problems. With the cen- tralised policy gradient. MADDPG (with CPG) performs significantly better than MADDPG on 2c vs 64Ig. However, on the harder map MMM2, MADDPG with both policy gradients fail to learn anything useful. By contrast, FACMAC signifi- cantly outperforms FACMAC (without CPG) on MMM2, and has lower variance across seeds on vs_64gg. Furthermore, on Many Agent Swim- mer with 2 agents, our centralised gradient esti- mator does not affect the performance of both MADDPG and FACMAC. However, on the same task with 10 agents, using the centralised gradient estimator significantly improves the learning performance when learning a factored critic. These results demonstrate that factoring the critic can better take advantage of our centralised gradient estimator optimise the agent policies when the number of agents and/or actions is large.
Ze_ vs B42g
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-1PLLO
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Figure 7: Ablations for different FACMAC com-
ponents on SMAC and MAMuloCo tasks.
Nonmonotonically factored critics can solve tasks that cannot be solved with monolithic or monotonically factored crities. In our
Episode Retums
Continusus Matrix Game
FACMAC [1o]
Episote Retums
40
Continoous Prodator Prey
FACMAC P]]
FACMAC ronmapononic [10)
FACKACara P1
MADOPG 110
22
MADUPU
multi-agent actor-critic framework, there are no
inherent constraints on factoring the critic, we thus also employ a nonmonotonic factorisation and refer to it as MCCMAC-nommoootee discussed in Section 3. As shown in Figure (8 (left), our continuous matrix game (as dis- AACMAC-nonmontommi robustly learn the optimal policy, while both FACMAC and MADDPG converge to some sub-optimal policy within 200k timesteps. On a variant of Continuous Predator-Prey task (see Appendix D.2 for more details about this task) with non- monotonic value functions (i.e., an agent's ordering over its own actions depends on other agents' actions (25 ), Figure & (right) shows that both FACMAC and MADDPG fail to learn anything useful, successfully learns to capture the prey. These results demonstrate that nonmonotonically factored critics can solve tasks that cannot be solved with monolithic or monotonically factored critics.
%
150
200
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(as
Figure 8: Mean episode return on (Left) Contin- uous Matrix Game and (Right) a variant of our Continuous Predator-Prey task (with 3 agents and 1 prey) with nonmonotonic value functions.
cussed in Section
while
It is important to note that the relative performance of FACMAC and FACMAC-nonmonooonis is task dependent. On the original Continuous Predator-Prey task (with 3 agents and 1 prey), FACMAC- nonmonotonic yields similar performance to FACMAC (see Figure 12 in Appendix [F. On SMAC (see Figure 13 in Appendix AFpendd FACMMAC-nommonotonic performs similarly to FACMAC on easy maps, but exhibits significantly worse performance on harder maps. This shows that, in this type of tasks, using an unconstrained factored critic could lead to an increase in learning difficulty. We thus be more useful in tasks with nonmonotonic value functions.
expect FACMAC-nonmonoton
6 Conclusion
This paper presented FACMAC, multi-agent actor-critic method that learns decentralised policies with centralised but factored critic, working for both discrete and continuous cooperative tasks. We showed the advantages of both factoring the critic and using the new centralised gradient estimator in our approach. We also introduced a novel benchmark suite MAMuJoCo to demonstrate FACMAC's scalability to more complex continuous tasks. Our results three different domains demonstrated FACMAC's superior performance over existing MARI. algorithms. Future work will explore more forms of nonmonotonic factorisation to tackle tasks with nonmonotonic value functions.
10

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Acknowledgements
We would like to thank Dr Martin Strohmeier and the members of the Whiteson Research Lab for their helpful feedback. We would also like to thank the anonymous reviewers for their constructive ments during the reviewing process. This project has received funding from the European Research Council (ERC), under the European Union's 's Horizon 2020 research and innovation programme (grant agreement number 637713). It was also supported by an EPSRC grant (EP/M5081 1/1, EP/N50971 1/1). Christian Schroeder de Witt is generously funded by Cyber Defence Campus, Sci- ence and Technology, Armasuisse, Switzerland. The experiments were made possible by generous equipment grant from NVIDIA.
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Checklist
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? [Yes]
(b) Did you describe the limitations of your work? [Yes] We mention that the relative
performance of FACMAC and FACMAC-nommonotonic is task dependent and discuss
some empirical results in the last paragraph of Section [
(c) Did you discuss any potential negative societal impacts of your work? [Yes] See Appendix [.T]]
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
2. If you are including theoretical results...
(a) Did you state the full set of assumptions of all theoretical results? [N/A]
(b) Did you include complete proofs of all theoretical results? [N/A]
3. If you ran experiments..
(a) Did you include the code, data, and instructions needed to reproduce the main exper- imental results (either in the supplemental material the code and instructions needed to reproduce the main experimental results in the supplemental material.
URL)? [Yes] We include
(b) Did you specify all the training details (c.g., data splits, hyperparameters, how they were chosen)? [Yes] See Appendix D
(c) Did you report error bars (e.g.. with respect to the random seed after running experi- ments multiple times)? [Yes] For all results on Continuous Matrix Game, Continuous Predator-Pres Prey, and MAMuJoCo, dence interval. For all results on SMAC, we report the median test win rate as well as the 25-75% percentiles (as in (B5)).
report the mean episode return and the 95% confi-
(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] We describe the type of GPUs used in Appendix E
4. If you using existing assets (e.g., code, data, models) curating/releusing assets...
(a) If your work uses existing assets, did you cite the creators? [Yes]
(b) Did you mention the license of the assets? [No] The license is already included in the
original code resource we cited and could change in the future.
(c) Did you include any new assets either in the supplemental material or as a URL? [Yes]
(d) Did you discuss whether and how consent was obtained from people whose data you're 're using/curating? [N/A]
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5. If you used crowdsourcing conducted research with human subjects...
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14


Reviews:
[{"review_id": "za2qr0XsDe9", "reviewer": "Reviewer_q18r", "summary": "The paper proposed the FACMAC method, an actor-critic approach for the cooperative MARL tasks. Under the centralized training with decentralized execution setting, FACMAC learns a centralized but factored critic and updates the decentralized policy of each agent using a centralized gradient estimator. Comparing to the existing approaches, the proposed approach 1) enjoys the flexibility to use nonmonotonic factored critics to handle the tasks that cannot be solved with monolithic or monotonically factored critics; and 2) using the centralized policy gradients for decentralized policy training prevents being stuck in suboptimal solutions.", "questions": "", "limitations": "", "rating": 7, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "The main novelty of the work is to use a centralized but factored critic and a centralized gradient for training decentralized policies. Some of the ideas are brought from existing approaches, but the authors are able to explain and compare the differences clearly. The extensive empirical studies show the potential power of the proposed approach, and also validates the advantages claimed in previous sections. The Multi-Agent MuJoCo benchmark built for continuous cooperative MARL can be meaningful. Overall, the materials are presented in a clear and precise way.\n\nMajor Questions:\n1. Can the authors comment on what kinds of tasks cannot be handled by FACMAC and may require a FACMAC-nonmonotonic approach?\n2. As there're no restrictions on the factored critics, is it possible for the proposed algorithm to go beyond cooperative tasks?", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The authors addressed them.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4"}, "extra_text": {}}, {"review_id": "eUiFMizX8xR", "reviewer": "Reviewer_oCU2", "summary": "This paper proposed an actor-critic-based multi-agent deep reinforcement learning approach in a fully cooperative setting. Specifically, instead of using a monolithic centralized critic, the authors proposed to use a factorized critic, where the individual agent’s value function is nonlinear combined into a joint value function. In addition, the authors proposed a centralized policy gradient estimator where joint actions are sampled from current policies. The approach is evaluated on MPE, SMAC, and  multi-agent MuJoCo, which is a new multi-agent environment. ", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "The paper applied the factorized value function, which is often used in value-based approaches such as QMIX, to actor-critic based methods such as MADDPG. It is impressive that the proposed approach achieves good experimental results on SMAC which was mostly dominated by value-based approaches. The paper is generally well written and easy to follow. However, the reviewer has some concerns about the motivation of the centralized gradient and the scalability of the proposed factorized critic. Please see the detailed comments and questions below. \n\n1. As the motivation for the centralized gradient, the authors mentioned that assuming all other agent’s action is fixed while optimizing one agent’s policy will lead to suboptimal policies. The reviewer doesn’t see any intuitive or theoretical reason why this leads to suboptimal policies. Could you elaborate?\n\n2. The authors claim that sample other agents’ action from the replay buffer leads to suboptimal policies. Again, it is unclear to the reviewer why this leads to suboptimal policies. \n\n3. The authors claim that the factorized critic is more scalable. How does it compare with GCN-based centralized critic, such as  [1, 2]? [1, 2] scales to hundreds of agents in the MPE environment. In this paper, only nine agents are considered in the MPE environment. \n\n[1] Graph Convolutional Reinforcement Learning, Jiang et. al. ICLR 2020\n\n[2] PIC: Permutation Invariant Critic for Multi-Agent Deep Reinforcement Learning, Liu et. al. CoRL 2019\n\n\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Yes, the authors discuss the limitation and  societal impact of their work. ", "review_text": "", "extra_scores": {"ethical_concerns": "No, the reviewer doesn't see any ethical issues with this paper. ", "needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "5 hours"}, "extra_text": {}}, {"review_id": "TBrYeikiAHf", "reviewer": "Reviewer_X7Th", "summary": "The paper proposes a centralized policy gradient actor-critic method for multiagent cooperation environments. The critic network follows the CTDE value-based training model, like VDN and QMix, but with flexible factorization forms. The actor network is updated by a centralized policy gradient. The proposed method is not just suitable for the continuous action space but also extends to the discrete action space. The method shows superior performance over other baselines in three domains, including a novel MAMujoco environment, which is first released with this paper.", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Policy gradient methods have achieved success in the single-agent task, and promote it to multi-agent tasks is a promising and important direction. This paper takes advantage of two kinds of existed multi-agent methods and proposes a novel combination.  A multiagent benchmark MAMujocu is also released, which may as a good testbed for multi-agent research.\n\nThe paper is written well and easy to follow, related work and existing methods are well placed and cited.\n\nThe experiments are conducted in three domains both in continuous and discrete action space. The evaluations are fairly sufficient and encourage. I believe it could drive more research to further explore the policy gradient methods in multi-agent tasks.\n\nSome weaknesses and questions:\n\n1. Some experiment results in figures are not consistent with the original paper,  such as in the MMM2 map, DOP reaches about 50% win in the original paper but only 20% in this paper. I don't check all the plots so I can't guarantee there existed no more mismatches. The author should explain how the experimental data are acquired? Why not directly use the data from other related papers.\n\n2. In my view, the whole method is essentially more like a centralized training method, if so, why not compare it with the centralized policy gradients methods, such as centralized DDPG or PPO? Does that may work? \n\n3. The DOP method utilizes offline training to enhance the efficiency of samples,  and the Q value target is combined with the online q target and tree-backup q target. I know FACMAC follows the deterministic policy gradient and extends to discrete tasks via Gumbel-softmax trick, but I still wonder why it works so nicely? Are there some advanced tricks or more analysis?\n\n4. Different critic factorization leads to inconsistent superiority in different tasks. I suggest the author make a deeper study and give more reasonable explanations.", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "None", "review_text": "", "extra_scores": {"ethical_concerns": "None", "needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "5"}, "extra_text": {}}, {"review_id": "Ll2z0z_3qmt", "reviewer": "Reviewer_ZyWj", "summary": "This paper presents a centralized multi-agent actor-critic method with a factored critic, which combines per-agent utilities (Q values) into a mixing function, as in QMIX. The difference is that it removes the constraint of monotonicity (using non-negative weights in the mixer) for higher representational capacity. It also proposes a centralized policy gradient estimator to fully take the advantage of the centralized critic, which updates policies over joint action space instead of optimising each agent's policy separately. Along with the FACMAC algorithm, Multi-agent MuJoCo, a new multi-agent benchmark suite, is introduced for cooperatively tasks with continuous control based on single-agent MuJoCo.", "questions": "", "limitations": "", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Generally, FACMAC is similar to a combination of MADDPG and QMIX in structure, e.g. the QMIX with actors or the MADDPG with a mixer. But this combination is valuable from the experimental results.\n\nThe author claims there are no monotonic constraints in FACMAC but no directly theoretical proof is found in the paper, which is said to be important for maintaining consistency between policies in QMIX. Is this because of the use of Centralised Policy Gradients? If so, rigorous proof will be appreciated.\n\nIn terms of Centralised Policy Gradients, the author has not provided the theoretical proof for why optimising joint policy is better than optimising each agent’s policy separately as well.\n\nThe Multi-agent MuJoCo is quite useful when I trying to test it with some benchmark algorithms, all agents have a clear division of labor and their cooperation is well emphasized.\n\nIn the experiment, there are many classic scenarios in MuJoCo but only three of them are selected to be tested. If more scenarios are tested, the results on continuous control will be more persuasive.\n\nPros:\nCritic factorisation is more flexible without monotonic constraints.\nThe Multi-agent MuJoCo is a practical suite.\nThe Paper is overall well-written and clear.\n\nCons:\nLack of theoretical proof. e.g. Why monotonic constraints could be removed? Why do Centralised Policy Gradients help?\nNovelty may not be enough. What's the key difference comparing to QMIX with actors/MADDPG with a mixer?", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "N/A", "review_text": "", "extra_scores": {"ethical_concerns": "N/A", "needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4"}, "extra_text": {}}, {"review_id": "KAkUEzsNCPN", "reviewer": "Reviewer_JS3e", "summary": "In this paper, the authors propose a FACtored Multi-Agent Centralised PG (FACMAC) method to solve the fully cooperative MARL problems.  The proposed method is under the paradigm of centralized training with decentralized execution.  The critic of the proposed method is centralized and factored, in the sense that the joint action-value function is a combination of the utility of each agent. A new benchmark MAMuJoCo (multi-agent variant of MuJoCo) is proposed to measure the performance of FACMAC. And the proposed method behaves the best compared with several other popular MARL algorithms. \n\n\n", "questions": "", "limitations": "", "rating": 7, "confidence": 1, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "The reviewer is not an expert in this area. From the reviewer's point of view, the paper combines the technique of several MARL algorithms such as MADDPG and QMIX. The novelty is that compared to MADDPG which optimizes each agent separately while fixing other agents, the FACMAC directly optimizes the joint action. Compared to QMIX, FACMAC allows the user to apply richer value factorizations, which can be nonmonotonic. Because this work is not a theoretical study that focuses on the sample complexity of a certain algorithm, the practical performance of the proposed framework will be the main judging criteria. From this perspective, FACMAC shows advantages in various tested benchmark problems against the compared algorithms. Therefore, the reviewer considers this as a good submission. ", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "This work is an algorithm that solves certain high-level abstract RL problems, it does not focus on any specific problems that may have negative societal impacts.", "review_text": "", "extra_scores": {"ethical_concerns": "No ethical concern.", "needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "8"}, "extra_text": {}}]

Author rebuttal:

Meta-review: FACMAC uses the ideas of MADDPG and QMIX, where its structure has both a mixer and an actor. The proposed algorithm was empirical tested on MPE, SMAC, and multi-agent MuJoCo, and demonstrated superior performances. Reviewers appreciate the algorithm's empirical performances, especially because policy gradient-type methods didn't work well on such tasks (multi-agent mojuco) prior to this submission. Although the algorithmic idea is rather natural, the empirical results are strong for multi-agent cooperative RL. 

One remaining comment is that the paper is purely empirical and lacks theoretical proof to justify central policy gradient and policy consistency without monotonicity constraint. Although theoretical proof is not a must, we strongly recommend that the authors provide more theoretical justifications and explanations, so that people can learn useful insight from the pure empirical work. Another remaining comment is the method relies on centralized training and only the execution is decentralized. ers 
Decision: Accept (Poster)