Integrating Suboptimal Human Knowledge with Hierarchical Reinforcement Learning for Large-Scale Multiagent Systems
Authors: Dingbang Liu
Shohei Kato
Wen Gu
Fenghui Ren
Jun Yan
Guoxin Su
Venue: NeurIPS 2024 poster (2024)
Keywords: Multi-agent system
Multi-agent reinforcement learning
Transfer learning
Human agent interaction
Scalability
Primary area: reinforcement_learning
TL;DR: In this study, we introduce a novel hierarchical learning framework for enhancing coordination in large-scale MAS by leveraging suboptimal human knowledge in an end-to-end manner.

Abstract: Due to the exponential growth of agent interactions and the curse of dimensionality, learning efficient coordination from scratch is inherently challenging in large-scale multi-agent systems. While agents' learning is data-driven, sampling from millions of steps, human learning processes are quite different. Inspired by the concept of Human-on-the-Loop and the daily human hierarchical control, we propose a novel knowledge-guided multi-agent reinforcement learning framework (hhk-MARL), which combines human abstract knowledge with hierarchical reinforcement learning to address the learning difficulties among a large number of agents. In this work, fuzzy logic is applied to represent human suboptimal knowledge, and agents are allowed to freely decide how to leverage the proposed prior knowledge. Additionally, a graph-based group controller is built to enhance agent coordination. The proposed framework is end-to-end and compatible with various existing algorithms. We conduct experiments in challenging domains of the StarCraft Multi-agent Challenge combined with three famous algorithms: IQL, QMIX, and Qatten. The results show that our approach can greatly accelerate the training process and improve the final performance, even based on low-performance human prior knowledge.

Integrating Suboptimal Human Knowledge with Hierarchical Reinforcement Learning for Large-Scale Multiagent Systems
Dingbang L2 Shohei Kato", Wen Gu', Fenghui Ren', Jun Yan', Guoxin Su!
University Wollongong', Nagoya Institute of Technology". Japan Advanced Institute of Science and Technology d19560uovmail.c edu au, thoney@nitech.ac... fren@uow. edu.eduuunro au, jyanduow. edu.au, guoxinθuow au au
vgu@jaist. ac.
Abstract
Due to the exponential growth of agent interactions and curse of dimensionality, learning efficient coordination from scratch is inherently challenging in large-scale multi-agent systems. While agents' learning data-driven, sampling from millions of steps, human learning processes quite different. Inspired by the concept of Human-or cattino-oottee---eee the-Loop and the daily human hierarchical control, we propose a novel knowledge-guide multi-agent reinforcement learning framework (hhk-MARL), which combines human abstract knowledge with hierarchical reinforcement learn- ing address the learning difficulties among large number of agents. In this work, fuzzy logic is applied to represent human suboptimal knowledge, and agents are allowed to freely decide how to leverage the proposed prior knowledge. Addi- tionally, a graph-basee group controller is built to enhance agent coordination. The proposed framework is end-to-end and compatible with various existing algorithms. We conduct experiments in challenging domains of the StarCraft Multi-agent Chal- lenge combined with three famous algorithms: IQL, QMIX, and Qatten. The results show that our approach can greatly accelerate the training process and improve the final performance, even based on oow-performance human prior knowledge.
Introduction
As an essential attribute of multi-agent reinforcement learning (MARL), scalability deserves more attention since it contributes to autonomous collective learning behaviors among agents. In many engineering and scientific disciplines, algorithms must possess sufficient scalability to cooperate properly 1 2
3 Unfortunately, training large number of agents presents inherent challenges. The joint action-state space increases exponentially with the number of agents, resulting in the curse of dimensionality 4 () Agents, suffering from sparse rewards and sample inefficiency 7) encounter 'start-up' problems (8] and often get trapped in local optima, to the extent that learning becomes impossible in the worst cases [9] [[O].
To alleviate the exploration burden and overcome the curse of dimensionality, knowledge transfer methods have attracted significant research interest in dealing with aarge-scale multi-agent systems (MAS) | 12 [3] As the most intuitive and common source, transferring prior knowledge from humans has received considerable attention [14 15]. An important line of research involves extracting prior knowledge from expert trajectories through imitation learning to address sequential decision- making problems [16 17]. However, despite the emphasis on Human-on-the--Lonn (18), most research still focuses on step-by-step action demonstrations, which require high-quality and comprehensive prior knowledge [1]44] [7]. The deployment of this type of human knowledge becomes increasingly
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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difficult in complex tasks, necessitating overwhelming human effort. Additionally, creating human- guided state-action pairs for each scenario is so time-consuming that even human experts struggle to anticipate actions in these highly challenging tasks.
Fortunately, human guidance is not limited to step-by-step action demonstrations, and other high-level knowledge exists to reduce the human effort involved [14] Human prior knowledge can be abstracted and transferred agents through abstract rules or heuristics [9 20 21). Although the provided knowledge is suboptimal, it can greatly reduce the computational burden and improve algorithm performance. However, current discussions are still limited to single- or two-player scenarios. Unfortunately, utilizing human prior knowledge properly is significantly more challenging in MAS. Due to stationarity and multiple Nash equilibria, most single-agent methods are unsuitable for multi-agen scenarios. Additionally, human knowledge is usually applied indiscriminately. and mapping knowledge from humans to agents is still in its early stages [15).
To better transfer knowledge from humans, it's essential understand the nature of human knowledge. Despite accomplishing many complex tasks in daily life. human activities do not require much active attention (Figure D. When deciding to get up and walk, the brain uses the prefrontal cortex to generate commands, but the intricate coordination of sensory inputs and muscles that follows does not require any conscious attention. Instead, it's mostly executed by lower nerve network in the spinal cord, sometimes called central pattern gen- erators (CPG) [22] Indeed, humans are naturally adept at abstracting and providing high-level knowledge, and asking them to provide detailed step-by-step action guides is overly demanding. It may be preferable to have humans deliver abstract knowledge at the top level, while agents spontaneously decide on the utilization of the proposed knowledge based on their 'CPG'.
COMMAN
Figure 1: Human daily hierarchical control.
Inspired by the hierarchical control of human daily activity, we propose a novel knowledge-guide guidedd MARL framework to integrate abstract human knowledge into MARL algorithms in an end-to-end manner. As several works have demonstrated, a hierarchical structure 2 and graphical models can greatly benefit large-scale MAS. We believe our approach, the hierarchical human knowledge multi-agent reinforcement learning framework (hhk-MARL), can alleviate learning difficulties among large number of agents. In our framework, trainable fuzzy logic rules are applied to represent human knowledge, Since the prior knowledge is suboptimal, our framework allows agents to adjust the utilization of proposed knowledge through hyper-network based knowledge integration. Additionally, to enhance agent coordination, we construct a graph to determine the importance of agents and simplify their relationships. By applying human knowledge at the top level while maintaining agents' ability to develop self-policies at the bottom level, our hicrarchical method helps "warm-star'' the training process and overcomes the learning difficulties of large- scale MAS. Experimental results from challenging tasks in the StarCraft Multi-agent Challenge (SMAC) (24) demonstrate that our approach can be easily combined with various MARL algorithms, significantly improving their learning efficiency.
2 Preliminaries
2.1 Partially observable Markov game
We view our problem as a cooperative multi-agent task. This task can be modeled as a decentralized partially observable Markov decision process (Dec-POMDP) (25. given by tuple G:
G = USSSUP P.r. 2,0,n,7)
where S defines the global environment state. The observations of each agent N {1...., n) are partially observable of e O', which are determined by the observation function (ss, : S x N + p()). Based on its local observation o, each agent selects its action u, E U2 at each time step according to its stochastic policy n, : O₂ x U, - [0, 1]. Then, based on the state transi- tion function P. SxU1 x x XU, + S, the joint action of all agents य E Õ changes the environment into new state. All agents share the same reward function r(s, ū)) S x U + R, and aim to learn poli-

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cies to maximize action-value functions (sst, dt) = Bu - - EEi= Th-t
where y the discount factor and Th is the time horizon.
2.2
Fuzzy logic
Since human knowledge is highly abstract and uncertain, it is inappropriate to represent knowledge with hard rules [26]. On the contrary, fuzzy logic can tackle issues of uncertainty and lexical vagueness, pacing its way to depict human imprecise knowledge [20]. A fuzzy logic rule is usually in the form of 'IF X is and Y is B THEN Z C" with a membership function μ for each fuzzy set used to calculate the truth value T of each precondition:
T = na (xo) X - [0, 1]. TB PB (B(()) Y - [0,
where zo and you the observation values for X and Y, respectively. To derive the conclusion of this fuzzy rule, both preconditions must be satisfied:
AnD (No, vo) min(u (B(())
Finally, the conclusion's 's strength, w, is obtained as follows:
w min Tn) -
(L (10)
Therefore, a fuzzy logic rule takes the observation values inputs and outputs the value of the conclusion to illustrate how likely it is to operate the designed actions under the current observations.
2.3 Knowledge representation and integration
Although human knowledge is highly instructive, such prior knowledge is suboptimal and covers only a small part of the state space. Applying it indiscriminately can hinder the training process. To avoid negative knowledge transfer, agents should have the freedom to decide the utilization of transferred knowledge. For better intuition, a teacher (human) and student (agent) model could be considered. To guide student research, the mentor might give the doctoral student some comments. For example, a comment for literature review could be: 'Read paper with high citation score', which can be expressed in the fuzzy logic rule 'IF O is high, THEN action is read". Here, O is the observation of the citation score, and high is a fuzzy set M whose membership function could simply be, Whhgh (o) (0.5,, 0, 1]. Therefore, the higher the score, the stronger the action read will be. Apparently, such knowledge is abstract and proposed for a specific state in the research process. Indeed, is unrealistic to require the mentor to design comprehensive checklist, and uncertainty and lexical vagueness are inevitable. The student is expected to autonomously decide when to follow the mentor's advice and when trust their own judgment. Inspired by the CPG of human hierarchical control (Figure I), to integrate abstract human knowledge into the agent learning process, we design knowledge 'CPG' for the agent to freely decide how to leverage the suboptimal knowledge.
3 Human knowledge guided hierarchical framework
In this section, we will illustrate novel human knowledge-guided MARL hierarchical framework (hhk-MARL) that integrates abstract human knowledge into MARL in an end-to-end manner to enhance agents' learning efficiency. The overall architecture is shown in Figure which is divided into three levels, mimicking the human hierarchical control (Figure D.. Inspired by the CPG of humans, hyper-network based knowledge integration is built to allow agents elegantly leverage the proposed human prior knowledge. The details of each module will elaborated in the following sections, and the meanings of symbols can be found in Appendix A.3
3.1 Knowledge controller
Since requiring humans to provide comprehensive step-by-step demonstrations for large-scale MAS is unrealistic, we focus on abstract and suboptimal human knowledge to reduce the human effort involved. As introduced in Section 2.2 fuzzy logic applied to capture human imprecise knowledge. Compared to other knowledge representation methods, fuzzy logic is closer to the structure of human knowledge, making more interpretable. Furthermore, has been proven that fuzzy logic is more suitable for training large-scale multi-agent systems with the advantage of generalization
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Figure 2: The overall framework of the human knowledge guided hierarchical MARL. The general architecture is proposed in the middle which separated into three levels. Agents can develop their own policies with traditional MARL algorithm shown at bottom left. The graph-based group controller is depicted at top right to enhance agents' coordination. The knowledge controller comprised with fuzzy logic rules to represent human knowledge which is demonstrated at bottom right. The hyper-networks of knowledge integration is illustrated at top left to allow agents freely decide the use of proposed human knowledge.
27 Inspired by previous works on knowledge representation with fuzzy logic 20 27
we leverage
fuzzy logic to abstract human prior knowledge in this work. The general form of each rule can be represented as:
Rule L: IF O1 is Mr, AND O2 is ML AND AND O₂ is ML. THEN Action is ukk
Here, O are variables about the system extracted from agent i's observations, and Mj, are fuzzy sets for the corresponding variables Oz. The strength of Rule L on corresponding actions is obtained:
(5) where of are observation values for O and μ² are membership functions for the fuzzy sets Mi. An example of fuzzy logic rule design is illustrated in Section 2.3 for clarity. For fairness, humans are only allowed to propose guidance based agent's local observations.
W1 min(fL, (01), HL2 (L),....,,II((....
As the transferred human knowledge is very rough, inspired by (20), we add trainable weights / to adapt proposed knowledge to current tasks. With these trainable weights, the knowledge can be optimized similarly to a neural network. For each rule, there are z + I corresponding weights: the first weights adjust the causal degree of each precondition, and the last weight B241 indicates the confidence in the proposed knowledge. Therefore, the human preference vector QF, for fuzzy rule L on each action can be represented as (an example of human preference vector is in Appendix A.6):
Qr. (ui,..., mx) BI.., min [3,, fLz, (01), BI., (02) Br, 1LL, (o=)]
These trainable weights are initialized at I to avoid disturbing the prior knowledge, and then adjusted through the reinforcement learning based the reward signal. However, it is worth mentioning that a fuzzy rule can be initialized with higher weight when there is high confidence in it.
We refer to this knowledge representation module as the knowledge controller, shown in Figure 2 bottom right. To maintain the merit of scalability, this knowledge controller shared among all agents. Specifically, for agent the knowledge controller takes the agent i's observation of input

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Algorithm Human knowledge guided hierarchical MARL
Input: MARL algorithm, Knowledge controller, Group controller, Knowledge integration Output: Human knowledge guided MARL model
1:
Initialize the parameters of MARL algorithm, knowledge controller, group controller, knowledge integration
2: for episode = 1 to max-episode do
3: for 1 to max-episode-lengee
do
4:
for agent 2 to N do
5:
Calculate Qooc based on MARL algorithm
6:
Use fuzzy rules for Q'r {Qr, ..... Qr
7:
Input {QLoc. Q'r} into knowledge integration for knowledge guided vector Q; Sample action u' from Q; with e-greedy policy
8:
9:
end for Execute (u'....,"" w to obtain reward and new observation o' from environment Store (o, u, u, in replay buffer D, and o t 0 Sample random minibatch of G samples (o u _,,
10:
12:
r 0'9)
13:
Obtain {Aa..... A
set Qrat, and update the Q-network by minimizing the loss: Leot
14:
end for
15:
end for
and outputs L number of human preference vectors based on built-in fuzzy logic rules:
OF = (Q' P 2F.}}
3.2 Knowledge integration
Although trainable weights are added to the knowledge controller to mitigate the knowledge mismatch problem, the proposed knowledge is still quite rough, covering only small portion of the state space. Since humans and agents have different perceptions and knowledge structures, appropriate to allow agents determine the utilization of prior knowledge. To not distort human knowledge and avoid negative knowledge transfer, we propose a hyper-networks based knowledge integration to integrate human prior knowledge into agents' policies. Similar human CPG (Figure []. this approach allows humans to design abstract knowledge from a high-level, while agents can autonomously decide whether to accept the proposed knowledge and how leverage it.
more
Although applying concatenated neural network as the knowledge integration is straightforward, it is difficult to capture the dynamic knowledge requirements in different states. To allow agents to automatically adapt to human guidance, motivated by previous research [20], we propose a hyper- networks based knowledge integration that allows agents to refine the proposed prior knowledge based on the local observation. As shown Figure (top left), the knowledge integration consists of two networks that take the human preference vectors Q'r and the agent preference vector Q QLoc as input, and output the knowledge-guid guidgge action preference vector Qi based on the agent i's local observation. Formally, the first network takes the observation of of agent i input and generates weights for the second network, which combines the agent's 's policy with human knowledge:
Qi = Ka (Q'r QLoC)
(8)
where:
0= h= (o')
(9)
Here, (.).) (+) is the hyper-network that generates the weights for the integration ko To encourage agents to frequently explore human knowledge at the start, hyperparameter Q is considered:
0 mar(ha,
(10)
This hyperparameter initialized to and quickly decreases to zero to not impair the agents' autonomy in knowledge adjustment. Similar to the knowledge controller, the knowledge integration also trained based on the reinforcement learning process and this module also shared among all agents.
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3.3 Group controller
Besides the 'start-up' problem from the curse of dimensionality, another difficulty in large-scane scale MAS is the intricate interactions among agents, which intensify as the number of agents increases. To enhance agent coordination and further improve scalability, motivated by the graph 's ability to simplify relationships [ [8). a simple neural network is applied to generate a cooperation graph among agents (Figure 2 top right). This group controller uses local observation to output cooperation tendency among agents. Specifically, based on o', agent i can propose the allies it wants to cooperate with, following the tendency strength An.5
A (A.,1,..,,A,....
(11)
where A is the cooperation tendency of agent i toward agent j. After agents deliver their tendencies, this will form relationship graph (an example is shown in Figure 9
(AI....,AN: AN
(12)
Here, an agent's importance is considered based on other allies' cooperation tendencies toward it: (A'....,,X) > = so ftmar htttt/maaummmaii (sum(()1..... Aw} dim = -2)
(13)
where X" is the importance weight of agent i and will be used to weight the agent's 's selected action. The group controller also shared among all agents. Additionally, to not violate the principle of centralized training with decentralized execution (CTDE), this module will only be applied during the training process.
3.4 Knowledge guided hierarchical MARL
To transfer knowledge from humans, we integrate abstract human knowledge into the agent learning process by mimicking the hierarchical control of human daily activities. As demonstrated in Figure
2 human can easily propose abstract knowledge at a high-level, while agents autonomously form specific action-state strategies based the MARL algorithm. This learning framework is end-to-end and can be combined with various MARL algorithms. To clarify this process, QMIX (29 algorithm is applied
example here. Initially, the agent i's preference vector ('oc is calculated based its local Q network. Then, the human preference vectors ('=(o') are generated from the knowledge controller, mentioned in Section 3.1 Next, following Equation [8] the human knowledge is integrated into agent i's policy, forming the knowledge-guide action preference vector Qi. This vector Q; is used to sample the action u' of agent based on the e-policy with the Q value Qi(o', u²). To imply the importance of agents in the group, the importance weight X is obtained from Equation 13 to weight (o", u²) and form the weighted Q value Q'(o', w²') Finally, the weighted Q values from all agents are aggregated derive the global value Qior using the QMIX mixing network:
Qior u) Niwooggeetwork( etwork(A' Qi(o', ud),.". . QN(oN (.M)
(14)
Subsequently, Qiot is trained to minimize:
Liot = E (ot.of (of.of-n.ud.t ( [Qeor ut) (m))) yrl2
(15)
where y is calculated as follows, and r, is the reward at time step t:
yt = r, + y- MiiiingNeeworrkk (0b41) 1)+ 2N (o ا(,ii
(16)
To comply with the CTDE, the group controller and mixing network only applied during the training process, while the local Q network, knowledge controller and knowledge integration are applied at both stages. The pseudo-code of our method is provided in Algorithm
4 Experiments and analysis
In our experiments, we aim to answer the following questions: (1) Can the proposed framework improve the scalability of MARI. algorithms? (2) What's the function of each module in our framework? (3) Is using suboptimal human knowledge justified, and how does its quality influence the learning process? To answer these questions, we conduct our experiments on challenging scenarios of the StarCraft Multi-Agent Challenge (SMAC) (24] with an increasing number of agents involved.
4.1 Experimental setting

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Figure 4: Experimental results for our approaches and their corresponding baselines in five scenarios. The shaded region denotes standard deviation of average evaluation over trials.
Focusing on micromanagement control, SMAC has been proposed as common benchmark for MARL methods. In the following experiments, we test our framework on challenging scenarios in SMAC from the 'Hard' and 'Super Hard' categories, set- ting the game AI difficulty to 'Very Hard'. To demonstrate the impact of the agent number on algorithm performance, we add two self-designed scenarios with more agents involved. To verify the effect of our end-to-end framework, we combine method with three famous MARL algorithms: IQL [30], QMIX (29). and Qatten [II, naming the corresponding approaches hhkIQL, hhkQMIX, and hhkQatten, respectively. In this study, each algorithm and its corresponding approach are figured with the same hyperparameters and neural network structures. Furthermore, all experimental results are derived across three separate trials with different random seeds, with 32 test episodes in each trial. The shaded region in Figure 4 and 7 and the error bar in Figure denote standard deviation in this work. Details of the hyperparameter settings are in Appendix A.5
Figure 3: Membership function: 'e d is small. X- X-axis denotes the observation value for vari- able e_d and Y-axis denotes the truth value.
Instead of requiring high-quality expert demonstrations, this work aims to transfer suboptimal knowledge from humans, considering eight pieces of knowledge for challenging tasks in SMAC. Due space limitations, As illustrated in Section 3.1 this abstract knowledge can be represented with a fuzzy logic rule:
the human prior knowledge: 'Attack the closest enemy' as example.
IF e_d is small, THEN action is attackEnemyld.
Here, e_d represents the agent's observation of the distance between itself and enemies. The corresponding membership function for the fuzzy set small elaborated Figure Jand is defined as simple linear function. More details about the applied human suboptimal knowledge can be found in Appendix A.6 As demonstrated, these fuzzy logic rules are abstract, suboptimal, and designed for specific states (c.g., attack actions are not always available), resulting in win rate of 0% when
7

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agents are solely manipulated by the proposed knowledge. Nonetheless, these rules are interpretable and easy design and understand from the human aspect. All rules are designed based on the agent's 's local observation. Furthermore, it is worth mentioning that the proposed human prior knowledge is not well-crafted and is highly subjective, with no strict requirement for its appropriateness. Anyone can develop their fuzzy logic rules based on their own experience.
4.2 Result and evaluation
To answer the first question, we deploy the approaches in scenarios with an increasing number of agents. The learning curves for all approaches across all tasks are illustrated in Figure 4 and the performance comparison based on the number of agents is elaborated in Figure []] In conclusion, the experimental results indicate that even based on highly abstract and now-performance human prior knowledge, our knowledge-guuce approaches not only significantly accelerate the training process but also enhance the final performance across scenarios with various numbers of agents.
As the number of agents increases, the joint action-state space expands exponentially, making it exceedingly challenging for agents to learn from scratch. Despite these challenges, our approaches still manage overcome the 'start-up' issue (Figure 4). By alleviating learning difficulties. while baseline algorithms fail tasks with many agents (IQL in Figure ((d) IQL and QMIX Figure
4(e), our approaches help agents overcome the initial learning challenges, improving scalability. Furthermore, as demonstrated by the win rate curves in Figure 4[a) our approaches greatly accelerate the training process, benefiting the initial stages of agent learning. Notably, our method (hhkIQL),
even combined with the least effective baseline algorithm (IQL), achieves performance comparable to the best baseline algorithm (QMIX).
To better visualize our method in scenarios with different numbers of agents, we summarize the algorithms' performance in Figure 5 By lever- aging human prior knowledge, our end-to-end method consistently helps MARL algorithms improve their per- formance across various numbers of agents. Additionally, it is worth men- tioning the improvement brings to the IQL algorithm, shown in the first image of Figure As one of the oldest fully decentralized MARL algorithms. IQL inherently struggles to handle coordination in large-scale MAS. displaying low performance in all scenarios. By contrast, benefiting from the integration of human knowledge and the relationship graph to mitigate 'start-up' issues and enhance cooperation, our approach significantly improves the scalability of the IQL. algorithm.
100
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Cutton VS MnAQuaton
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Figure Performance comparison between baselines and our methods under the number of agents increase. The error bar based on standard deviation
4.3 Ablation study
To answer the following two questions, we design two ablation experiments: one to identify the function of each module and another to assess the influence of human suboptimal knowledge. Considering our improvement on the IQL algorithm, we use it the basis in the '10m 1 1m scenario to provide clear comparison. The ablation results are detailed in Figure 7
4.3.1 Module function
The experiment results on module functions are depicted in Figure 7(a) where 'thkIQL-graphOnly represents our method with only the group controller, 'nbkrQL-humannnlly indicates our method integrating solely human knowledge, and "hhkIQL-fixedKnon denotes our method without trainable parameters fuzzy logic rules.
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Figure 7: Ablation studies under '10m vs Im' scenario. (a) ablation study on the function of each module in our method; (b) ablation study on the influence of various suboptimal human knowledge.
Effect of group controller: To elaborate on the role of the group controller, we first present agents' cooperation graph in Figure The lationship graph reveals that the cooperation demand changes controller, agents can independently choose al- lies to collaborate with, and important agents are emphasized. As depicted in Figure ((a) the group controller enhances cooperation among agents and accelerates the training process, evi- denced by higher convergence rate compared to that of the IQL algorithm.
time. With the group
Figure 6: After the training of hhkIQL in '10m vs 1 Im scenario, the change of each agent's during a battle episode. The nodes are agents and the edges are agents' tendency to cooperate with others. is time step. The died agents are not shown in the graph (full details are in Appendix A.7).
Effect of human knowledge: Although the transferred knowledge is suboptimal, human prior knowledge significantly improve per- formance. The knowledge integration, functioning as a 'CPG', allows human to effortlessly provide abstract knowledge from a high-level perspective. As result Figure the knowledge-guided algorithm achieves overall better performance than the baseline algorithm. However, it is worth noting that this ablation algorithm evidenced by comparing it to the hhkIQL approach.
be further improved with the group controller installed, as
Trainable knowledge: The benefits of trainable knowledge demonstrated in Figure both approaches achieve similar performance, the approach with trainable fuzzy logic rules realizes a faster convergence rate than its ablation counterpart. With the trainable knowledge controller, the prior knowledge is constantly optimized during training, enhancing the adaptation of the provided knowledge to the current task. As result, agents can make better of proposed knowledge and learn faster.
( Although
4.3.2 Human suboptimal knowledge influence
In this section, we explore the impact of suboptimal human knowledge and how our approach addresses inappropriate knowledge. The ablation results are described Figure 7 To assess the effect of knowledge quality, we consider human knowledge with more fuzzy logic rules to be more comprehensive. For fairness, these rules are inherited among ablation approaches. For example, "hhkIQL (8 rules)' will include the rules used in 'hhkIQL (5 rules)', and so forth. Since knowledge from humans highly subjective, is hard to judge whether transferred knowledge inappropriate. To identify how our approach deals with inappropriate knowledge, we substitute the values in human preference vectors Qj. with random value to represent inappropriate knowledge, which is denoted as "hhkIQL (random)) in Figure 7(b)

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As demonstrated in Figure 7(b) more comprehensive human knowledge can help agents achieve better performance. Although I rules)' can achieve faster learning speed than 'hhkIQL (3 rules)' and "h (5 rules)", it results in lower final performance. We guess that with fewer rules applied, there is a reduced learning burden on knowledge utilization, but this also leads to lower final outcomes. Notably, even though more comprehensive human knowledge is beneficial, the performance of these approaches remains similar. Furthermore, as the learning curve of "hhkIQL (random)" indicates, the knowledge integration module can efficiently filter out negative knowledge. While it takes agents more time to learn how to utilize the proposed knowledge, "hhkIQL (random)" still outperform the baseline algorithm, highlighting the importance of the knowledge integration module. conclusion, our approach does not rely on high-quality human knowledge, and the knowledge integration module can successfully mitigate the negative knowledge transfer problem, allowing humans to propose any knowledge they consider useful for agents.
5 Conclusion and future work
In this study, introduce novel hierarchical learning framework for enhancing coordination in large-scale MAS by leveraging suboptimal human knowledge. This framework consists of the group controller, the knowledge controller, and the knowledge integration, allowing humans to provide knowledge at the top level while agents develop their own policies at the bottom. Evaluated in SMAC with three famous algorithms, our end-to-end methods surpass corresponding baselines in learning speed and final performance, even with low- ww-performance human knowledge integrated. Furthermore, this framework successfully improves the scalability of algorithm, handling scenarios with numerous agents where standard MARL algorithms fail. In the future, we will apply our approach in domains with even more agents involved, and explore its application to heterogeneous agents.
Acknowledgment
This work was supported in part by the Ministry of Education, Culture, Sports, Science and Technology-Japan, Grant-in-Aid for Scientific Research under grant #JP24H00741, and part by the commissioned research by National Institute of Information and Communications Technology (NICT), JAPAN.
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A Appendix supplemental material
A.1 Fuzzy logic
Since human knowledge is highly abstract and uncertain, it is inappropriate to use hard rules to represent such prior knowledge [26]. Different from crisp sets, fuzzy logic, based on fuzzy set theory, can apply partial membership functions to represent fuzzy knowledge [32]. For a fuzzy set F, the æ in it can be described by a membership function (x) with range from 0 to 1, allowing the element partially belong to it:
PF X [0
where X refers to the universal set in specific problem.
The fuzzy logic rule usually the form of 'IF X and Y is B THEN is C". Here, 'X A' and "Y is B' are called preconditions of the fuzzy rule, and % is C' is the conclusion. The X, Y and Z are variables. And the A, B and C are fuzzy sets, also known as linguistic values. For each fuzzy set, it has a membership function μe to calculate the truth value T of each precondition:
Ta = (#)) X + [0, 1], TB = (
- [0, 1]
where zgg and yo are observation values for X and Y, and T' and T' are truth values for preconditions X is A' and 'Y is B". To get the conclusion of this fuzzy rule, needs satisfy both preconditions and the conjunction operator is applied:
AnD (Zo, 3o) = min(us (20), (B0)))
Finally, we will get the conclusion's 's strength w. sometimes seen as the satisfaction level of the rule:
minn(Ta Tn) min (nin(u(())) (B()))
Summarizing, to abstract human prior knowledge with fuzzy logic rules, we need first to design the rules in the form of 'IF... THEN sentence. Then membership functions per should be built for each preconditions to calculate their truth value T. Finally, the conjunction operator min is applied to satisfy all the preconditions and get conclusion's 's strength w. Therefore, a fuzzy rule takes the observation values as input and outputs the value conclusion to illustrate how likely to operate designed actions under current observation.
A.2 Related work
Due to the expensive exploration, knowledge transfer has become an indispensable approach to hance the scalability of MARL [ On the one hand, the most straightforward implementation is to repurpose solutions from previous tasks obtained by agents [13. On the other hand, various studies also emphasize the reuse of knowledge from auxiliary sources, such as human expert demonstrations
33
As the "black box" approach unsuitable for critical applications, the transfer method should be interpretable, prompting increasing concern Human-on Hlmman-on-the-Lowe -n-the-Loop [15). By personally executing tasks, humans provide demonstrations for agents to record in state-action pairs which agents can mimic based on imitation learning [33] 34) inverse reinforcement learning 35 36), and other human- focused methods IT 37]. Unfortunately. these mainstream researches require step- step-by-ster by-step action demonstrations, heavily relying high-quality and comprehensive expert demonstrations [16] [7].
While some efforts have aimed to mitigate the human burden, these solutions are generally limited to single- or two-player scenarios (20 21 38) Fuzzy logic has been applied in previous work for knowledge representation (20), while their focus on single-agent scenarios and the agent does not have self-policy development ability. As far as we know, the most successful work is from (27, who handle large-scale MAS with fuzzy agents. However, the use of human knowledge is not within their scope and their approach is more akin agent knowledge transfer. Compared to previous works, method, which can easily combine with various MARL algorithms, features a hierarchical learning scheme that human suboptimal knowledge is applied at top-level to enhance learning process of large-scale MAS. Based on the hyper- networss in knowledge integration, we are able to combine human preference with agent preference empower agents with more knowledge selection freedom.
39 However, in contrast to these existing studies that pay more attention to decomposing challenging long-horizon tasks into simpler subtasks, our focus here is to connect humans and agents under a hierarchical structure for leveraging human knowledge and achieving more efficient learning in large-scale MAS.
Our work also shares some similarities with the hierarchical RL methods 19 23
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A.3 Symbol meaning
The meanings of symbols this work illustrated in Table
!
Table 1: Symbol meaning
Symbol
Meaning
global state
r
reward
D
replay buffer
i
agent
{a1..... aN}
all agents
L
fuzzy logic rule
M
fuzzy set
u1,
uk
agent action space agent observation space observation values for fuzzy logic rule truth value of precondition membership function
(1.-.... Om
{o1 0z}
w
conclusion strength of fuzzy logic rule trainable weight of knowledge controller human preference action value agent preference action value knowledge guided action value of agent i cooperation tendency of agent toward agent j agent cooperation tendency toward other agents importance of agent in the group À weighted action value of agent
QF
QloG
Qi
Xi.
X
X
Q'
parameter of knowledge integration hyper-network weight of integration module generated by integration hyper-network hyperparameter of integration module
Qiot
global value from mixing network
Siot
loss
?
discount factor history for RNN action observation history exploration rate target network
c
A.4 Computational resource
In this work, we run our experiments in a computer with CPU (13th Gen Intel Core i7-13700F 2.10 GHz), GPU (NVIDIA GeForce RTX 4080), and RAM (128GB). It takes more than 550 GPU hours to finish all the experiments. It's worth mentioning that the '35m vs 40m' scenario is the most time-consuming experiment where single requires beyond 9 hours average.
A.5
Experiment hyperparameter
The hyperparameters for our experiments are shown Table 2
A.6
Suboptimal human knowledge applied in experiment
For challenging tasks in SMAC, the following pieces of human knowledge are considered:
Attack the closest enemy.
Attack the enemy with the lowest HP.
Get close the closest enemy.
Get close to the enemy with the lowest HP.
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Table 2: Hyperparameters of experiment
Parameter name
Value
Total timesteps
2050000
Number of environments
8
Number of test episodes
32
Test interval
5000
Update interval
200 episodes
Optimizer
Adam
0.99
3 initialization
1.0
Batch size
128
Buffer size
3000
Learning rate
0.001
RNN layer hidden size
64
Group controller RNN hidden size
64
1.0 - 0.05
Anneal time of
50000
QMIX mixing embed size QMIX hypernet embed size
32
64
Qatten query embed size of layer 1
64
Qatten query embed size of layer 2
32
Qatten key embed size
32
Qatten head embed size of layer Qatten head embed size layer
64
Qatten attention head
4
Qatten number of constraint value Knowledge integration hypernet size
32
64
Knowledge
1.0 - 0.0
Anneal time of knowledge f2
1000
Disperse when many agents are crowded together.
Gather when there are few agents and they are far away.
Get close the ally who is attacking.
Attack properly to avoid over-attacking.
The abstract knowledge can represented with fuzzy logic rules as follows:
IF e_d is small, THEN action is attackEEnmyIId
IF Tehppis small, THEN action is attack Enemyy
e_dlo_ PO, THEN action east; IF e_clo_x is N.,, THEN action is west; IF e_clo y is PO, THEN action is north; IF e_clo__ is N E, THEN action south.
IF e ___hp_ is PO, THEN action is east; IF e, e__hpp__ æ is N E. THEN action is west; IF e e_hhp_y PO, THEN action north; IF e Lhp_hppy is N THEN action is south.
IF allll is large AND g ally d is small AND ally is PO, THEN action is west; IF AND ally is N E. THEN action is east; IF AND ally y is PO, THEN action is south; IF AND olly y is N E. THEN action is north.
IF n rnally is small AND g g_ally is large AND ally x is PO. THEN action is east: IF AND ally_x N F., THEN action west; IF ... AND ally PO, THEN action is north; IF AND ally_y y is N.,, THEN action is south.
IF ally stll__attckingg.. is PO, THEN action is east; IF ally_attacking x is NE, THEN action is west: IF ally Sattlaattakkngg_ is PO, THEN action north; IF _ttll__ttaciig___ is N E, THEN action is south.
n. potential is large AND n. aatttcck is proper, THEN action is attackEnemyld.
The membership functions for the fuzzy sets in each rule elaborated in Figure
15

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(a) d is small
(b) e_ e_hp is small
(c) y PO
(d) x NE
(e) n_ally is large
(f) g_ally_ d small
n_ally is small
(h) g_lly d is large
(i potential is large
(i) n_ attatakk is proper
Figure 8: Membership functions used in SMAC.
A.7 Dynamic graph
The full image the dynamic graph based on group controller is elaborated Figure
A.8
Limitations and broader impact
In this section, we will discuss the potential limitations of this work, which we aim to address in future research. First, as the proposed modules are shared among agents, we assume that the agents are homogeneous to alleviate the difficulty of knowledge design and computation complexity. However, exploring our approach with heterogeneous agents, which may require different kinds of knowledge, interesting direction. Second, for knowledge abstraction, it is relatively primitive, and a better representation method required to further improve performance, which is consideration for future work. Third, in this work, consider integrating suboptimal human knowledge to improve the performance of MARL algorithm and propose a hyper-network to avoid negative knowledge transfer. However, illustrated in ablation studies, more comprehensive knowledge should be beneficial. Therefore, discussing what appropriate and how design effective knowledge is interesting
though fuzzy logic is promising technique
kinds of knowledge topic for future exploration. Finally, due to computational limitations, we only verify our approach in SMAC. Although have applied ablation studies to enhance convineingness, it would be helpful conduct experiments in other domains with more agents involved, which we plan for future work.
This work aims to contribute to the development of MARL algorithms. As with any field in machine learning, it is possible that improving the capabilities of these algorithms could lead to unethical uses. However, there also many potential benefits to better cooperative AI, such applications in disaster rescue robots among others. We believe that the potential benefits of developing more capable and cooperative Al outweigh the potential risks.
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Figure 9: The cooperation graph from hhkIQL during battle episode based the change of each agent's 's X under '10m vs 1m scenario.
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Reviews:
[{"review_id": "q6T9X3KnUr", "reviewer": "Reviewer_JxHm", "summary": "In this paper, the authors propose a novel method to tackle the multi-agent reinforcement learning problem. They do so by combining human abstract knowledge with hierarchical reinforcement learning. Specifically, human knowledge in the form of fuzzy logic rules is combined, at the top level, with each individual agent’s decisions, learned at the bottom level. Then, a graph-based group controller performs agent coordination to decide what the action at each step should be. The authors evaluate the proposed method on the StarCraft multi-agent Challenge, combined with three algorithms (IQL, QMIX, and Qatten). The results indicate that the proposed approach is capable of improving the overall performance.", "questions": "For the ablation studies of the impact of each component on the final performance, it would also be interesting to see how much of the agent’s Q is used vs how much of the human knowledge Q is used for the final Q prediction. That is, what is the magnitude of the impact that the human knowledge component has over the Q predictions?", "limitations": "The authors discuss the limitations of the work. No major concerns.", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The authors tackle the multi-agent reinforcement learning problem in a creative and novel way, combining human feedback with hierarchical techniques. Moreover, it is a very interesting idea to provide a general algorithm that can be coupled with any existing MARL technique. In this way, it is possible to take advantage of the benefits of previously proposed algorithms while also incorporating new ideas to improve overall performance.\n\nThe paper is well-written, and all the high-level ideas behind the different components are well-explained.", "weaknesses": "The empirical evaluation is thorough, and it indicates that the claims are correct. However, only three samples are rarely enough to draw strong conclusions.\n\nI believe some crucial parts of the algorithm were not very detailed. In particular, what are the learning rules/loss functions for each of the components? That is, how is $\\beta$ trained? How is the knowledge integration component trained? With the current description, I believe it would be very hard for someone to replicate the method.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for your review. We are pleased that you found our method to be creative and novel and that you thought we had set a general approach for MARL algorithms.\nWe address your concerns below and hope this will strengthen your support for the paper.\n\n> The empirical evaluation is thorough, and it indicates that the claims are correct. However, only three samples are rarely enough to draw strong conclusions.\n\nThank you for this comment. In our experiments, our results are based on three separate runs, with the number of the test episodes during each run being 32 (shown in Table 2). Therefore, the number of samples to draw the conclusions is actually 96. The reason we deploy three different trials is to avoid random initialization deviation, which is a common strategy in previous works [Böhmer et al., 2020 (4 trials); Zhou et al., 2022 (4 trials); Zhong et al., 2024 (3 trials)]. As the standard deviation shown in Figure 5 is relatively small, it confirms the consistency of our results. We believe such results are sufficiently strong to draw a conclusion. We will clarify it in our paper to avoid this misunderstanding.\n\nWe will revise the paper as follows:\n\n*Section 4.1: “Furthermore, all experimental results are derived across three separate trials with different random seeds, with 32 test episodes in each trial. The shaded region…”*\n\n* Böhmer, W., Kurin, V., & Whiteson, S. (2020, November). Deep coordination graphs. In International Conference on Machine Learning (pp. 980-991). PMLR.\n* Zhou, H., Lan, T., & Aggarwal, V. (2022). Pac: Assisted value factorization with counterfactual predictions in multi-agent reinforcement learning. Advances in Neural Information Processing Systems, 35, 15757-15769.\n* Zhong, Y., Kuba, J. G., Feng, X., Hu, S., Ji, J., & Yang, Y. (2024). Heterogeneous-agent reinforcement learning. Journal of Machine Learning Research, 25(1-67), 1.\n\n> I believe some crucial parts of the algorithm were not very detailed. In particular, what are the learning rules/loss functions for each of the components? That is, how is $\\beta$ trained? How is the knowledge integration component trained? With the current description, I believe it would be very hard for someone to replicate the method.\n\nThank you for your comment. We will add some details to the paper to further clarify these questions (in Section 3.1, 3.2, 3.4, and Algorithm 1). In general, all the components (including $\\beta$ and Knowledge Integration) follow the traditional Q learning process, and the overall loss function is proposed in Equation 15: \n\n$\\mathcal{L} _{tot} = \\mathbb{E} _{[ o_t^i,o _{t+1}^i,u_t^i,u _{t+1}^i ] _{i=1}^N }[Q _{tot}([ o_t^i,u_t^i ] _{i=1}^N)-y_t]^2$\n\n1. For $\\beta$, they are initialized to 1 and backpropagated from $Q_F$ in the Knowledge Controller, which is similar to a neural network. \n2. For the Knowledge Integration, the reward signal is backpropagated from the $Q_i$ to update the parameters of the integration $k_θ (\\cdot)$ and then further update the parameters of the hyper-network $h_α (\\cdot)$.\n\nWe will revise the paper as follows:\n\n*Section 3.4: “This learning framework is end-to-end and can be combined with various MARL algorithms where the training of the knowledge controller, knowledge integration, and group controller module is based on the traditional Q learning process. To clarify this process…”*\n\n*Section 3.1: “These trainable weights are initialized at 1 to avoid disturbing the prior knowledge, and then adjusted through the reinforcement learning based on the reward signal. However, it…”*\n\n*Section 3.2: “…in knowledge adjustment. Similar to the knowledge controller, the knowledge integration is also trained based on the reinforcement learning process and this module is also shared among all agents. ”*\n\n> For the ablation studies of the impact of each component on the final performance, it would also be interesting to see how much of the agent’s Q is used vs how much of the human knowledge Q is used for the final Q prediction. That is, what is the magnitude of the impact that the human knowledge component has over the Q predictions?\n\nThank you for noticing this. This is a very interesting question that is strongly related to designing beneficial human prior knowledge. To evaluate this, we can extract the weight of hyper-networks in the Knowledge Integration module to reveal the components of these two parts. As shown in our second ablation study (Figure 6(b)), the inappropriate knowledge will be automatically filtered out by agents, which may partially answer this question. Since our focus here is on connecting humans and agents in a hierarchical structure to boost the learning process, we do not consider this human knowledge representation aspect. We will address this question in our future work to guide users on how to design more advantageous human prior knowledge for better behavior guidance.", "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": "", "extra_scores": {}}, {"review_id": "JbR3BsS7MX", "reviewer": "Reviewer_kCt8", "summary": "This paper integrates an human in the loop to provide knowledge that improves learning in marl. This is done through a hierarchical structure, but ultimately it is up to the agents the final decision of accepting the human suggestions (hierarchy comes from human knowledge to agents). Overall, there is an integration of human knowledge with what the agents learn.", "questions": "In addition to the points above, I have some specific questions that I would like the authors to comment on:\n* what are the limitations of considering only a small set of human opinions, like the 8 ones defined in appendix 6?\n* if a certain human knowledge concerns only one specific agent, is it still given to the others as well? if yes, how does it affect learning? do the others get confused by that knowledge?\n* how do the agents decide if they accept a certain human suggestion? is it a joint decision? if yes, can they reason accurately if the decision concerns a specific agent, but has nothing to do with the others?\n* is the knowledge controller deterministic? or was it trained a priori with human knowledge?\n* it is stated in lines 179-180 that the group controller is used only during training to not violate CTDE; what about the knowledge integration, is it also used only during training? or also during execution? since it receives human knowledge from all agents too\n* the knowledge integration module seems to follow an interesting approach, since the weights of the second network are generated by an initial network based on the observations of the agents given as inputs; could the authors elaborate on the motivations for this approach? why are the weights generated from a first network and not only using one network?\n* i can see the authors focused in environments involving marines only; is there a specific reason for that? is it because of the availability of prior human knowledge? or how hard it would be to create a knowledge controller network for other cases?", "limitations": "N/A", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper is well organized and it is interesting. The idea of integrating human knowledge is this kind of tasks is interesting and it makes sense. Mostly, the paper is easy to follow and understand, with some exception that I outline below.", "weaknesses": "While I find this paper interesting, I have some remarks, as noted below:\n* in line 131 it is stated that $M_L^I$ corresponds to a fuzzy set; however, it is not clear what $M$ is exactly, and how it relates to fuzzy logic in this context; it is not easy to understand how the relation between $O$ and $M$ is calculated and how is the membership function $\\mu$ implemented\n* from my understanding, when integrating the proposed approach with IQL, there is not a mixer as in the other value function factorization methods like QMIX; this leads me to think that the lack of a mixer could be the reason behind the huge improvements seen in Figure 4 for IQL when combined with this method; can it mean that the mixer can be slightly detrimental in the overall framework?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank you for your review and your kind words about our paper. We are pleased that you found our idea of integrating human knowledge to be interesting. \n\nBelow we have addressed your questions. We hope that this strengthens your support for the paper.\n\n>Weakness1: ...what $M$ is exactly, ...$\\mu$ implemented\n\nThank you for your comment. The fuzzy set $M$ and membership function $\\mu$ are the components of fuzzy logic rules that are designed by humans. $M$ denotes the fuzzy set and $\\mu$ represents the relationship between $O$ and $M$ as follows: $\\mu_M(o):O\\rightarrow [0,1]$. An example of the fuzzy logic rule is proposed in Section 2.3: ’IF $O$ is *high*, THEN *action* is *read*’ regarding the knowledge of ’Read paper with high citation score’. Here, $O$ is the observation of the citation score, and *high* is a fuzzy set $M$ whose membership function could simply be, $\\mu_{high}(o): clip[0.05 \\cdot o,0,1]$. It is worth mentioning that we give the users freedom to define these fuzzy logic rules and our approach does not rely heavily on the selection of the rules. We are deeply sorry that our Section 2 and Table 1 may not be clear enough, and we will modify the structure of our paper to further clarify it. \n\n>Weakness2:...can it mean that the mixer can be slightly detrimental...\n\nThank you for your comment. From our understanding, mixers can influence the cooperation among agents and different types of mixers may have diverse benefits, as even baseline algorithms exhibit different performances in different scenarios. Still, as shown in Figure 4, our framework can easily be combined with various MARL algorithms and enhance their performance. As in this work we just consider a general approach for MARL algorithms, we do not further discuss the influence of mixer and answer the question of what kinds of mixers are more suitable. We will investigate this in our future work.\n\n>Question1:What are the limitations of considering only a small set of human opinions...\n\nThank you for your comment. In this work, those human opinions are specifically designed for SMAC, and the design of knowledge is correlated with the applied domain. As proven by imitation learning and inverse reinforcement learning [33, 35], more comprehensive guidance should be more beneficial. As shown in our ablation study (Section 4.3.2), more comprehensive knowledge can improve the learning speed and final performance. However, because of the complexity of multi-agent systems, it is challenging to propose the overall demonstrations, while our approach allows the use of suboptimal human guidance. Even if a small set of human opinions is proposed, the Knowledge Integration module can allow agents to selectively adapt to the prior knowledge while maintaining self-learning ability. Based on the domain, if it is possible, then a larger set of human opinions can be more instructive, while a small set is still acceptable for our framework. \n\n>Question2:If a certain human knowledge concerns only one specific agent ... do the others get confused by that knowledge?\n\nThank you for your comment. In this work, we focus on the homogeneous agents where agents share similar goals, observations, etc. The proposed human prior knowledge is shared among all agents. As agents can selectively adapt to the proposed human knowledge based on the Knowledge Integration module, it should not affect the learning and other agents should not get confused.\n\n>Question3:How do the agents decide if they accept a certain human suggestion? is it a joint decision?...\n\nThank you for your comment. Agents use local observation to decide the utilization of the proposed human suggestions. This is not a joint decision, as each agent can use its Knowledge Integration to decide whether to accept a certain suggestion. \n\n>Question4:Is the knowledge controller deterministic...\n\nThank you for your comment. The Knowledge Controller module is deterministic and is set up by humans before the training and then adjusted by agents through the reinforcement learning process. \n\n>Question5:...about the knowledge integration, is it also used only during training? or also during execution...\n\nThank you for your comment. The Knowledge Integration module is applied during both training and execution. Each agent selectively adapts to the proposed knowledge based on its Knowledge Integration, which is shared among agents.  We will emphasize this in our paper. \n\n>Question6:...could the authors elaborate on the motivations for hyper-network...\n\nThank you for your comment. The hyper-network structure can offer more advantages than a concatenated neural network. Even though using a neural network is straightforward, it is hard to capture the dynamic knowledge requirements in different states. Moreover, using a feed-forward network to generate weights for another network, hyper-networks are more in line with the semantics of the Knowledge Integration module. It allows agents to selectively adapt to human guidance through local observation, which is hard to achieve in a single neural network. As hyper-networks have been proven to be more beneficial for knowledge refining in previous work [20], we apply such a structure in this work motivated by its advantages. We will emphasize the importance of hyper-networks in our paper. \n\n>Question7:...availability of prior human knowledge? or how hard it would be to create a knowledge controller...\n\nThank you for your comment. In this work, we focus on the homogeneous agent setting. As the marine is the most common unit in SMAC, we deploy our approach in scenarios with marines involved. It is worth mentioning that our method is not limited to a single scenario. To reduce human burden, we allow the proposed human knowledge to be suboptimal and give users the freedom to design the transferred knowledge. As empirical results show (Section 4.1 and Figure 6), our Knowledge Integration module can greatly reduce the knowledge design requirements.", "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": "", "extra_scores": {}}, {"review_id": "z87vz8Pdqk", "reviewer": "Reviewer_8Cur", "summary": "The authors proposed a new framework (hhk-MARL) that integrates human abstract knowledge with hierarchical reinforcement learning to address the learning challenges in large-scale multi-agent systems. The framework employs fuzzy logic to represent human knowledge and a graph-based group controller to enhance agent coordination. Experimental results in the StarCraft Multi-agent Challenge demonstrate that the proposed approach significantly accelerates the training process and improves the final performance of the agents, even with imperfect human prior knowledge.", "questions": "1. The paper employs fuzzy logic in the hhk-MARL framework for integrating human knowledge, but it does not provide a clear explanation in section 3.1 for choosing fuzzy logic over other methods such as Bayesian networks, a combination of reinforcement learning and heuristics, or neural network-based knowledge representation. These alternative methods could also handle uncertainty and abstract knowledge effectively. A more detailed justification for selecting fuzzy logic would enhance the understanding of its advantages in this context.\n\n2. The idea of incorporating fuzzy logic into hierarchical RL has been introduced in prior works such as KoGuN [20] and in Shi 2021 [a]. However, it is essential to explain the differences between these approaches and the proposed method in section 3.1. Highlighting these distinctions will clarify the unique contributions of this work and demonstrate how it advances beyond existing methodologies.\n\n3. In section 3.2 on Knowledge Integration, it is important to highlight the novel aspects of the proposed method. The integration of human knowledge using hypernetworks to dynamically generate weights based on agent observations presents a unique approach. However, the methodology bears similarities to existing works such as HAMXCS [21] which also incorporates heuristic knowledge into reinforcement learning, Hierarchical RL for Self-Driving [19] which uses hierarchical reinforcement learning for decision-making, and KoGuN, which refines fuzzy logic rules with hypernetworks. A clearer distinction of the innovative elements in comparison to these related works would strengthen the contribution of this paper.\n\n4. Appendix A.6 presents the suboptimal human knowledge rules, but it is unclear who determined these rules and to what extent they are incomplete or reasonable. Given that they are labeled as suboptimal, a clearer explanation of their limitations and adequacy is necessary, especially for readers unfamiliar with Starcraft. This information is crucial for understanding the potential applicability and adaptation of these rules to other tasks.", "limitations": "The authors have adequately addressed the limitations and potential negative societal impact of their work.", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "* Overall, the proposed hhk-MARL framework effectively integrates human knowledge with hierarchical reinforcement learning, providing a flexible and adaptive approach for multi-agent systems.\n\n* Methodologically, the authors use fuzzy logic and hypernetworks to dynamically generate weights based on agent observations allowing for the seamless combination of human and agent preferences.\n\n* In the experimental results, the comprehensive experiments demonstrate the framework's efficacy and robustness, showing significant improvements over baseline methods in various scenarios.", "weaknesses": "While the paper is well-written overall, it lacks detailed comparisons with prior research and thorough explanations of the human knowledge used. Specifically, section 3.1 does not clearly justify the choice of fuzzy logic over other approaches, which could also handle uncertainty and abstract knowledge effectively. Additionally, the paper can explain how its approach differs from previous works such as KoGuN and Shi 2021, to clarify its unique contributions. In section 3.2, the new aspects of using hypernetworks for knowledge integration should be more distinctly highlighted in comparison to similar methodologies. For the details, see the following Questions.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for your kind review. We are pleased that you thought we have provided a flexible and adaptive approach for multi-agent systems.\n\nWe have addressed your comments below. We hope that this clarifies any concerns that you had and strengthens your support for the paper.\n\n>Question1:...it does not provide a clear explanation in section 3.1 for choosing fuzzy logic...A more detailed justification for selecting fuzzy logic would enhance the understanding\n\nThank you for your comment. We will revise Section 3.1 to further depict our motivation for selecting fuzzy logic. We consider fuzzy logic because it is closer to the human perceptions and knowledge structures. Compared to the mentioned alternative methods, fuzzy logic is more interpretable, giving humans more freedom and control over knowledge design and representation. Moreover, as the intermediary to control agents, using fuzzy logic can reduce complexity, making it more suitable for training large-scale multi-agent systems. Furthermore, the framework can benefit from the advantage of fuzzy logic in generalization. Since previous research has revealed these advantages of fuzzy logic on knowledge representation [20, 38], it motivated us to leverage fuzzy logic for human prior knowledge representation.\n\nWe will revise as:\n\n*Section 3.1: “Compared to other knowledge representation methods, fuzzy logic is closer to the structure of human knowledge, making it more interpretable. Furthermore, it has been proven that fuzzy logic is more suitable for training large-scale multi-agent systems with the advantage of generalization [38]. Inspired by previous works on knowledge representation with fuzzy logic [20, 38], we leverage fuzzy logic to abstract human prior knowledge in this work. The general form…”*\n\n>Question2:The idea of incorporating fuzzy logic into hierarchical RL has been introduced in prior works such as KoGuN [20] and in Shi 2021[a]. it is essential to explain the differences between these approaches and the proposed method in section 3.1...\n\nThank you for your comment. The comparison between our work and previous research is proposed in Appendix A.2. We will further clarify the difference in the related work section. KoGuN [20] applies fuzzy logic in the single-agent scenario where the agent only learns how to leverage human knowledge without self-policy development ability. In Shi 2021 [13], the authors consider an all-purpose cross-task transfer that transfers knowledge among agents based on features extracted from neural networks. Different from these two works, we leverage fuzzy logic to connect agents and humans in multi-agent systems. \n\nWe will revise as:\n\n*Appendix A.2: “…of MARL [11, 12]. On the one hand, the most straightforward implementation is to repurpose solutions from previous tasks obtained by agents [13]. On the other hand, various studies also emphasize the reuse of knowledge from auxiliary sources, such as human expert demonstrations [32]. ……Fuzzy logic has been applied in previous work for knowledge representation [20], while their focus is on single-agent scenarios and the agent does not have self-policy development ability. As far as we…”*\n\n>Question3:In section 3.2 on Knowledge Integration, it is important to highlight the novel aspects...\n\nThank you for your comment. Some discussion about knowledge transfer methods is given in Appendix A.2 to exhibit the novelty of our approach. We will detail the motivation for applying hyper-networks in Section 3.2 and further clarify the distinction in Appendix A.2. In general, through the hyper-networks based Knowledge Integration module, agents can still maintain learning ability from the local Q network, and the human prior knowledge is not distorted. In comparison, KoGuN [20] requires the global state information to refine the compressed human prior knowledge, and the agent action preference is not considered. HAMXCS [21] also requires global information for the two-player competitive game, and a neural network is applied to construct an opponent model. In the approach for self-driving [19], their focus is more on decomposing challenging long-horizon tasks into simpler subtasks. Although it mitigates the reliance on labelled driving data, the human demonstration still needs to be step-by-step samples. \n\nWe will revise as:\n\n*Section 3.2: “Although applying a concatenated neural network as the knowledge integration is straightforward, it is difficult to capture the dynamic knowledge requirements in different states. To allow agents to automatically adapt to human guidance, motivated by previous research [20], we propose a hyper-networks based knowledge integration that allows agents to refine the proposed prior knowledge based on the local observation. As shown in Figure 2… ”; Appendix A.2: “…large-scale MAS. Based on the hyper-networks in knowledge integration, we are able to combine human preference with agent preference to empower agents with more knowledge selection freedom.”*\n\n>Question4:...it is unclear who determined these rules and to what extent they are incomplete...explanation of their limitations and adequacy...\n\nThank you for your comment. In this work, these human knowledge rules are specifically designed for SMAC, and the design of knowledge is correlated with the applied domain. As declared in Section 4.1, the proposed knowledge for SMAC is suboptimal, resulting in a 0% win rate when agents are solely manipulated by the proposed knowledge. Furthermore, our approach does not rely heavily on the selection of the rules, and we give users the freedom to define these fuzzy logic rules based on their domain knowledge. As shown in our ablation study (Section 4.3.2), agents can selectively adapt to prior knowledge through the Knowledge Integration module, allowing humans to propose any knowledge they consider useful for agents. In the future, we will investigate which kinds of knowledge are more appropriate and how to design effective knowledge.", "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": "", "extra_scores": {}}]

Author rebuttal:
We sincerely thank the reviewers for their constructive comments. We are encouraged that all the reviewers think our paper is well organized and our approach to integrating human knowledge with multi-agent reinforcement learning is flexible and effective (Reviewer JxHm, kCt8, and 8Cur). It is a great honor that the reviewers find our idea interesting (Reviewer JxHm and kCt8). We are excited that you find our method to be novel (Reviewer JxHm) and technically sound (Reviewer kCt8 and 8Cur), with experiments that are thorough and comprehensive (Reviewer JxHm and 8Cur). We answer the comments from reviewers based on part 6 (weaknesses) and part 7 (questions), to address your concerns:

1. We further clarify the training process of our approach with more details added.
2. We further clarify our motivation for choosing fuzzy logic and using hyper-networks.
3. We further clarify the difference between our approach and previous works.
4. We further clarify the technical details about designing and leveraging fuzzy logic rules.
5. We explain the reason for our experimental setting.
6. We answer the specific comments from each reviewer. 

We will ensure that all the concerns are addressed in the revised paper. Our detailed response to the reviewers’ comments is shown below and hope this will strengthen your support for the paper.

Meta-review: The paper explored an interesting (and increasingly relevant with LLMs) approach to leveraging human knowledge with hierarchical RL for multi-agent systems. All reviewers agreed that it was a technically solid contribution. There were a few clarifications requested by the reviewers which should help make the final version clearer.
Decision: Accept (poster)