The Dormant Neuron Phenomenon in Multi-Agent Reinforcement Learning Value Factorization

Authors: haoyuan  qin
chennan  ma
mian  deng
zhengzhu  liu
songzhu  mei
xinwang  liu
cheng  wang
siqi  shen
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-14 16:48:01

Abstract: In this work, we study the dormant neuron phenomenon in multi-agent reinforcement learning value factorization, where the mixing network suffers from reduced network expressivity caused by an increasing number of inactive neurons. We demonstrate the presence of the dormant neuron phenomenon across multiple environments and algorithms, and show that this phenomenon negatively affects the learning process. We show that dormant neurons correlates with the existence of over-active neurons, which have large activation scores. To address the dormant neuron issue, we propose ReBorn, a simple but effective method that transfers the weights from over-active neurons to dormant neurons. We theoretically show that this method can ensure the learned action preferences are not forgotten after the weight-transferring procedure, which increases learning effectiveness. Our extensive experiments reveal that ReBorn achieves promising results across various environments and improves the performance of multiple popular value factorization approaches. The source code of ReBorn is available in \url{https://github.com/xmu-rl-3dv/ReBorn}.

Main paper: 
 introduction: 
 In cooperative Multi-Agent Reinforcement Learning (MARL) [1] , a group of agents whose value function is approximated using deep neural networks must cooperate to achieve a common goal. Deep neural network is the key driving force that scales MARL for complex decision-making tasks [2] . Recently, researchers have discovered the scaling laws that deep neural network models can increase their capacity by enlarging the size of the model and the dataset. However, single-agent reinforcement learning does not obey the scaling law and suffers from network expressivity issues [3, 4] .To alleviate the network expressivity issues in single-agent RL, researchers have proposed parameter perturbing methods. Igl et al. [5] periodically resets some layers of the value network. ReSet [6] resets the last few layers of the neural network while maintaining experience in the replay buffer. ReDo [4] periodically re-initializes the input weights of some neurons and zero out the neuron's output weights. Albeit these methods can improve the performance of single-agent reinforcement learning, it is unclear whether they work for MARL.Compared to single-agent RL, MARL is more challenging, including issues such as partialobservability [7] and the non-stationary of other learning agents' policies. The Centralized Training with Decentralized Execution (CTDE) paradigm [8] is widely adopted in this context. In CTDE, it is a common practice to use value factorization [2, 9] , which factorizes a joint state-action value function Q tot into individual agent utilities Q i . Each agent acts according to Q i , which is approximated using a deep neural network, named the agent network. Q i are mixed through a neural network, the mixing network, to form joint value function Q tot .In this work, we explore the reasons behind the reduction in network expressivity issues in cooperative MARL. Specifically, we study dormant neurons [4] , which remain inactive with low activation levels during learning. We demonstrate that the dormant neuron phenomenon, the number of dormant neurons increases during the training process, exists in multiple popular value-based MARL algorithms (QMIX [2] , QPLEX [10] , DMIX [11] , and RMIX [12] ) across various environments (e.g., SMAC [13] , SMACv2 [14] , predator prey [15] ). We find that the proportion of dormant neurons increases with the number of agents, and that dormant neurons mainly exist in the mixing network. Moreover, we identify the existence of over-active neurons, whose activation score accounts for a significant portion of the activation scores for all the neurons. Typical network parameter perturbing approaches used in single-agent RL (such as Reset [5, 6] and ReDo [4] ) do not work efficiently in MARL. Parameter perturbing methods, which change the weights of neurons, may lead to forgetting of learned knowledge, especially in MARL with high cooperation demands. The cooperation knowledge should not be forgotten even after parameter perturbation. We formulate a memorization requirement that the learned cooperative action preferences remain unchanged after parameter perturbation as the Knowledge Invariant (KI) principle. We theoretically show that existing approaches [5, 6, 4] cannot guarantee adherence to the KI principle. Failing to satisfy the KI principle can lead to the violation of the Individual-Global-Max (IGM) principle, which is widely adopted in MARL.We propose, ReBorn, a simple but effective method that transfers the weights from over-active neurons to dormant neurons. It periodically detects dormant and over-active neurons, and balances the weights among them. We theoretically show that ReBorn satisfies the KI principle for various value factorization approaches (e.g., QMIX and QPLEX), distributional value factorization approaches (i.e., DMIX and DDN [11] ), and risk-sensitive value factorization approach (i.e., RMIX [12] ). Through extensive experiments, we demonstrate that ReBorn can improve the performance of multiple MARL value factorization methods, and it performs better than multiple parameter perturbing methods by effectively remembering previously learned knowledge.Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?Answer: [Yes]Justification: We make the main claims in the abstract and introduction.Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. 
dec-pomdps: 
 We consider Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) [16] in modeling cooperative multi-agent reinforcement learning (MARL) scenarios. A Dec-POMDP can be defined by a tuple G = ⟨S, {U i } N i=1 , P, r, {O i } N i=1 , {σ i } N i=1 , N, γ⟩, where N is the set of agents, S is the states set, and U i is the action set for agent i. At time step t, each agent i chooses an action u t i , forming a joint action u t , leading to a state transition s t+1 ∼ P (•|s t , u t ) and a joint reward r t . In consideration of partial observability, each agent can only make decisions based on its local observation o t i ∼ σ i (•|s t ) ∈ O i . Each agent i act according to its individual policy π i (u i |τ i ) based on its local action-observation history τ i = (O i × U i ) * , forming a joint policy π =< π 1 , . . . , π N >. The joint policy π has a joint action-value function: Q π (s t , u t ) = E st+1:∞,ut+1:∞ [R t | s t , u t ], where R t = ∞ i=0 γ i r t+i is the discounted return, γ is the discounting factor.In value factorization methods [17, 2, 9, 10, 18] , per-agent utilities Q i is approximated using the agent network, and they are mixed through the mixer network to form the joint state-action value function Q tot . For value factorization, the Individual-Global-Max (IGM) principle [9] is a critical criterion that ensure the consistency between local and joint optimal action selections. It is defined as follows:Definition 1 (IGM [9] ). For a joint state-action value function Q jt : T N × U N → R, where τ ∈ T N is a joint action-observation history and u is the joint action, if there exists individual state-action functions [Q i : T i × U i → R] N i=1 , such that the following conditions are satisfied arg maxEQUATIONthen, we can state that [Q i ] N i=1 satisfy IGM for Q jt under τ , or Q jt (τ , u) is factorized by[Q i (τ i , u i )] N i=1 .Definition 2 (α-dormant neuron [4, 19] ). Consider a fully connected layer ℓ within a neural network, where H ℓ denotes the total number of neurons in this layer. For an input distribution D, let h ℓ i (x) represent the activation of neuron i in layer ℓ under input x ∈ D. The normalized activation score of neuron i is defined as follows:EQUATIONThen a neuron i in layer ℓ can be defined as α-dormant if its score s ℓ i ≤ α. (i.e., 0.1) Definition 3 (α-dormant ratio [4] ). The α-dormant ratio of a neural network ϕ can be defined as follows:EQUATIONN ℓ α is the count of neurons that are α-dormant in layer ℓ, H ℓ is number of neurons in layer ℓ.The dormant neuron phenomenon refers to the steady increase in the dormant ratio of the neural network throughout training.3 Related WorkQuestion: Does the paper discuss the limitations the work performed by the authors?Answer: [Yes]Justification: We have discussed limitations and future work in the appendix.Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
value factorization: 
 Value factorization approaches [20] are widely adopted in MARL. These methods construct the joint state-action value function Q tot based on individual utility Q i . VDN [17] models the joint value function as the sum of individual utility function, while QMIX [2] models the monotonic increasing relationship among Q tot and Q i . Qatten [18] models the relationship through using the attention mechanism. QPLEX [10] factorizes Q tot into a value function and an advantage function. QTRAN [9] and ResQ [21] decompose the value function into easy-to-factorized forms. For distributional MARL, DMIX [11] factorizes value function through mean-shape decomposition.A few work [12, 22] explore risk-sensitive value factorization. RMIX [12] models the monotonic increasing relationship among Q tot and the CVaR measure of each agent's distributional utility. RiskQ [22] ensures that the collection of greedy selection of risk-sensitive individual actions is equal to the greedy selection of risk-sensitive joint actions.These methods focus on modeling the representation ability and functional relationships between the joint state-action value function and individual utilities. Our work, ReBorn, is orthogonal to these approaches, can be used to improve their overall performance by reducing dormant neurons.In deep reinforcement learning, neural networks tend to lose their expressive power as training progresses [3] . Various studies explore the loss of expressiveness from different perspectives and propose corresponding methods to mitigate this issue.Lyle et al. [23] show that the instability of the target can cause the network to lose expressive ability. ReSet [6] addresses early agent experience bias by periodically resetting the last layer of the neural network. The loss of expressive ability can also be attributed to over-fitting, a phenomenon analyzed in depth by Kirk et al. [24] and Zhang et al. [25] within reinforcement learning. To enhance generalization, researchers propose network randomization [26] , convolution architectures [27] , and soft data augmentation [28] . Researchers [29] find that the loss of plasticity is deeply connected to changes in the curvature of the loss landscape, and plasticity injection [30] is used to enhance the learning ability of neural networks for new data. D'Oro et al. [31] and Yang et al. [32] propose Reset Replay to improve the sample efficiency. ReDo [4] discovers that dormant neurons occur due to the instability of the target in reinforcement learning. DRM [19] finds that the dormant neuron phenomenon is related to agent exploration. When the dormancy ratio is high, the agent gradually cease exploration.ReBorn is a parameter perturbing method for MARL. It can effectively reduce the number of dormant and over-active neurons. Moreover, it ensures that learned action knowledge is not forgotten after parameter perturbation. 4 The Dormant Neuron Phenomenon in MARL Dormant neurons mainly exist in the mixing network of MARL. To verify the existence of the dormant neuron phenomenon in MARL, we analyze the number of dormant neurons during the training of QMIX [2] and QPLEX [10] across multiple tasks in SMAC [13] . The percentage of dormant neurons are illustrated in Figure 1 , presented separately for the agent and the mixing networks. We discover that the dormant neuron phenomenon primarily occurs in the mixing network of MARL. The percentage of dormant neurons the mixing network is initially high and continues to increase, while the percentage of dormant neurons in agent networks is low. This observation is consistent across various algorithms and environments as it is depicted in Appendix D.4. The number of agents in the three tasks are 3, 10, and 27, respectively. As shown in Figure 1 (a) to (c), with the increasing number of agents, the percentage of dormant neurons increases. Dormant neurons hurt the expressive power of mixing networks. In MARL value factorization methods, the mixing network plays a crucial role in integrating individual utilities into a joint value function. As shown in [9, 20, 21] , the expressive power of the mixing network significantly impacts the performance of MARL value factorization methods. The expressive power of neural networks is related to both their depth [33, 34] and width [35, 36, 37] . We study expressive power of mixing networks from the perspective of dormant neurons, We use a mixing network with 2 Multi-layer Perceptron (MLP) layers, and fit it to a simple value function. This network consists of 4 neurons, and we change the number of dormant neurons from 0 to 3. As depicted in Figure 2 (a), with increasing dormant neurons, the mean square error (MSE) loss that fits the target value increases. This indicates that an increase in dormant neurons leads to reduced expressive power. Please refer to Appendix D.3 for details.TD target non-stationarity exacerbates dormant neurons in MARL. The TD target in reinforcement learning is non-stationary [38] . In the MARL training process, target networks for mixing networks are typically used to stabilize TD targets. We study the impact of target non-stationarity by varying its update interval, where a smaller interval indicates greater non-stationarity. As analyzed in Figure 1 , the dormant neuron phenomenon primarily exists in the mixing network, so we only control the target network of the mixing network, and the comparison focuses on the dormancy ratio in the mixing network. Experimental results for the QMIX method are presented in Figure 2 (b) . As depicted, with a smaller update interval, the ratio of dormant neurons increases, indicating that increased non-stationarity in the target network results in a higher presence of dormant neurons in the MARL mixing network.The presence of over-active neurons correlate with dormant neurons. Through careful inspection of the neurons during MARL network training, we observe an interesting phenomenon that has not been discovered before: some neurons exhibit very large normalized activation scores (NAS) throughout the training process. We study the percentage contribution of the average NAS of each neuron to the total average NAS of all neurons. To this end, we examine such percentage in the last layer (with 64 neurons) of QMIX's mixing network in 27m_vs_30m from SMAC. Figure 2 (c ) depict the top 25 neurons which have the largest percentage. Neurons whose percentage is over 5% is depicted in red, neurons whose percentage are too low are not plotted, while the other neurons are plotted in green. The results show that most NAS are concentrated on a few neurons, while the NAS of other neurons are relatively low. We refer to these neurons with large NAS as over-active neurons, and define them as follows. Definition 4 (over-active neuron). A neuron i is an over-active neuron if its score s ℓ i ≥ β (i.e., 3).In Figure 3 (a), the percentage contribution of the numbers of dormant neurons to all neurons, and the percentage contribution of the number of over-active neurons to all neurons, along with the percentage contribution of the sum of NAS for over-active neurons to the sum of NAS of all neurons, are depicted in red, blue and green, respectively. We find that, albeit there are only a few over-active neurons, their NAS takes up a large percentage of the neural network's NAS. This percentage increases steadily with the training process, correlating with the increase of dormant neurons. As the percentage of the over-active neurons' NAS continues to increase, the percentage of NAS for the other neurons decreases. We conjecture that the presence of over-active neurons impacts the existence of dormant neurons.Dormant/Over-active neurons remain dormant/over-active. To study the impact of over-active neurons on dormant neurons, we examine the percentage of dormant/over-active neurons that remain dormant/over-active. As depicted in Figure 3 (b), there is a significant overlap among dormant/overactive neurons. The presence of over-active neurons appears to be a significant factor contributing to the dormant neuron phenomenon, which has never been considered in previous studies. We use a parameter perturbing method [4] to periodically recycle the dormant neurons. Then we depict the percentage of dormant neurons that re-enter dormancy within 0.2 Million steps and 0.6 Million steps in Figure 3 (c ). As it is depicted in the Figure, there is still a significant overlap among dormant neurons. This indicates that parameter perturbing methods (such as Redo [4] ) may not work efficiently for MARL, as it does not consider over-active neurons. We conjecture that this may be due to the fact that methods developed for single-agent RL may change the neural network weights regarding agent cooperation, which lead to forgetting learned cooperative knowledge that is encoded in neural network.Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?Answer: [Yes]• It should be clear whether the error bar is the standard deviation or the standard error of the mean. • It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified. • For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates). Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact. • Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.• The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
the reborn method: 
 In this section, we describe the Knowledge Invariant Principle, which ensures that learned action preferences do not change after perturbing neurons. We show that methods failing to satisfy this principle could lead to the violation of the individual-Global-Max (IGM) principle, which is important for MARL. Then, we present the ReBorn method, which satisfies the KI principle. It balances the weights among dormant neurons and over-active neurons for the mixing network.Multi-agent Reinforcement Learning suffers from the dormant neuron phenomenon and the existence of over-active neurons which make the learning process inefficient. Researchers have proposed several methods [4, 5, 6] that change the weights of neurons. However, these methods overlook the complex interactions among multi-agents, and their learned knowledge may be forgotten after perturbing neurons. We formulate the memorization requirement for learned cooperation knowledge after neuron perturbations as the Knowledge Invariant Principle, which is defined as follows. Definition 5 (Knowledge Invariant Principle (KI)). A joint state-action value function is represented asQ θ, ϕ tot (τ , u) = f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )), where f θ is the mixing function that mixes Q i into Q tot , τ is joint observation-action history, u = [u 1 , ...u N ] is the joint action of multi-agent, g : R → R is a function that maps weights in θ to θ , g(θ) = θ. h : R → R, h(ϕ) = φ, h map the weights in ϕ to φ. If the following condition holds:Q θ, ϕ tot (τ , u) ≥ Q θ, ϕ tot (τ , u ′ ) ⇒ Q θ, φ tot (τ , u) ≥ Q θ, φ tot (τ , u ′ ), ∃!k : u k ̸ = u ′ k (4)then, the two functions g and h satisfy the Knowledge Invariant Principle for Q θ, ϕ tot , where[Q i (τ i , u i )] Ni=1 is individual agent utility function, N is the number of agents, τ i and u i are the observation-action history and action of agent i, respectively. ∃! represents the concept of unique existence.Q θ, ϕ tot to Q θ, φ tot ∃!k : u k ̸ = u ′k , the learned knowledge that u is preferred over u ′ before applying g and h does not change after applying the two functions. With the KI principle, we show the following theorem. Theorem 1. Parameter perturbing methods that do not satisfy the Knowledge Invariant (KI) principle cannot guarantee adherence to the Individual-Global-Max (IGM) principle.We have theoretically shown that a parameter perturbing method that does not satisfy the KI principle could lead to the violation of the IGM principle, which is the most important principle in MARL value factorization methods [2, 9, 20, 10] . Furthermore, we theoretically show that two state-of-the-art RL parameter perturbing methods, Redo [4] and ReSet [5] , do not satisfy the KI principle, as detailed in Theorem 2 and Theorem 3, respectively. These theorems and proofs are detailed in Appendix B.To address the issues caused by the dormant neuron phenomenon and the existence of over-active neurons, which reduce network expressivity, we propose ReBorn, a simple but effective method that shares the weights from over-active neurons with dormant neurons.ReBorn uses an identity function h(θ) = θ to map the parameters of agent networks to themselves, and uses function g(θ) to perturb the parameters θ of mixing networks. The process of g(θ) is described as follows. For each over-active neuron x, we randomly select M dormant neurons that belong to the same layer as x. Here, M is an random integer between 2 to 5. The selected dormant neurons, indexed by i, will share weights with neuron x. After weight sharing, these neurons will not be selected again. We denote w in x as the input weights for neuron x, b x as the bias of neuron x, w out x as the output weights. The main procedure of the ReBorn method is depicted in Figure 4 .The input weights of dormant neurons w in i are reborn as β i w in x , and the input weight of the overactive neuron x becomes β 0 w in x . The output weights for neuron x and i are reborn as 1 β0 α 0 w out x and 1 βi α i w out x . The biases for the over-active and dormant neurons are set toβ 0 b x , β i b x . [β i ] M i=0are sampled between 0.5 and 1.5. They are used to ensure more variation among neurons.[α i ] M i=0is obtained through sampling M + 1 from a normal distribution, and then a Softmax operator is performed on them to ensureM i=0 α i = 1.For dormant neurons that are not selected, we use Xavier initialization to reset their weights.Although ReBorn is simple, we have theoretically demonstrated that it satisfies the KI principle for QMIX through the following theorem.Theorem 2. ReBorn satisfies the KI principle for the QMIX [2] value factorization method.Moreover, we have theoretically shown that ReBorn satisfies the KI principle for a value factorization method: QPLEX in Theorem 4, a distributional value factorization method DMIX in Theorem 5, and a risk-sensitive value factorization method RMIX in Theorem 6. Furthermore, we show that after using ReBorn, the value functions Q tot learned by QMIX, QPLEX, DMIX, and RMIX still satisfy the IGM principle in Corollary 1 to 4. These theorems and proofs are listed in Appendix B. 
empirical evaluations: 
 In this section, we present experimental results and discuss their implications. We begin with a brief overview of our experimental setup in Section 6.1. Subsequently, we examine ReBorn's robust applicability to various MARL value factorization algorithms in Section 6.2. Furthermore, we demonstrate that ReBorn outperforms other parameter perturbing methods that are extended to MARL in Section 6.3. Lastly, we conduct a series of ablation studies in Section 6.4. All detailed experimental results can be found in Appendix D.4.Environments. In our experiments, we employ three distinct environments that challenge the coordination and adaptability of MARL algorithms. Predator-prey simulates a grid world where multiple predators collaborate to capture preys dispersed throughout the map. A successful capture requires at least 2 predators to execute the capture action simultaneously, posing a great challenge for the algorithm's coordination ability. The StarCraft Multi-Agent Challenge (SMAC) [13] is a popular benchmark used extensively in MARL, where multiple ally units controlled by MARL algorithms aim to defeat enemy units controlled by the game's built-in AI. SMACv2 [14] features units that are randomly generated and positioned, enhancing stochasticity and significantly increasing the complexity of the scenarios. Please refer to Appendix D.2 for detailed descriptions.Baselines and training. ReBorn, as a parameter perturbation mechanism, is applicable to various value factorization algorithms. We select 4 classical algorithms with different types: QMIX, QPLEX, DMIX and RMIX. ReDo, ReSet, SR [31] and MARR [32] four common parameter perturbation methods in deep RL, are adapted to MARL variants to serve as baselines. Detailed implementations and parameter configurations for each algorithm are available in Appendix D.1. (d-f ) the dormant percent for the the 3s5z_vs_3s6z, the MMM2, and the predator-prey small environment.In this section, we investigate the applicability of ReBorn through validating ReBorn's ability to enhance performance across various value factorization algorithms (QMIX, QPLEX, RMIX) in different experimental scenarios (3s5z_vs_3s6z, MMM2, predator-prey small). According to the experimental results presented in Figures 5, ReBorn can improve the performance of multiple algorithms and effectively reduce the dormant ratio of the mixing networks in diverse settings. More detailed experimental results can be found in Appendix D.4.1 and Appendix D.4.5.We explore the superiority of ReBorn by applying different parameter perturbing methods to QMIX across various experimental scenarios (MMM2, 27m_vs_30m, predator-prey large). We added ReDo, Reset, SR and MARR for comparison and further analyzed the dormant ratios and the over-active sum ratios. ReDo and ReSet are common parameter perturbation methods in deep RL, while SR and MARR are reset replay methods. All of them are adapted to MARL variants to serve as baselines.The results depicted in Figure 6 illustrate the win rates, the dormant ratios and the over-active sum ratios (the ratio of the sum of normalized activation scores of over-active neurons to the total sum of scores of all neurons) across different scenarios. The results indicate that compared to ReDo and ReSet, ReBorn can further enhance algorithm's performance and more effectively reduce both the dormant and over-active sum ratios of the mixing network. Please refer to Appendix D.4.4 for more experimental results.In this section, we demonstrate the importance of adhering to the Knowledge Invariance (KI) principle. Our analysis in Appendix B shows that applying ReBorn only to the mixing network adheres to the KI principle, while using it on the entire network results in a violation. We compared the performance of value factorization algorithms under the MMM2 scenario in SMAC, focusing on those that either adhere to or violate the KI principle. As illustrated in Figure 7 , maintaining KI with ReBorn enhances the performance across all baseline algorithms, whereas violating it leads to performance drop in QMIX and QPLEX, highlighting the great importance of satisfying the KI principle. In this section, we explore various forms of the weight perturbation function g(θ) in ReBorn based on QMIX, while keeping the function h(θ) = θ constant. In ReBorn, g(θ) transfers weights from overactive neurons to dormant neurons. In ReBorn (ReDo), g(θ) periodically re-initializes the weights of dormant neurons. In ReBorn (ReSet), g(θ) periodically resets the parameters of the last layer of the neural network. In ReBorn (Reverse ReDo), g(θ) periodically resets the input and output weights of over-active neurons. In ReBorn (Pruning), g(θ) periodically prunes dormant neurons. To ensure the accuracy of our conclusions, we conducte experiments across various value factorization algorithms. The experimental results shown in Figure 8 demonstrate that compared with other methods, ReBorn significantly enhance the performance of value factorization algorithms. The ablation study in Figure 9 illustrates the impact of different hyperparameter settings in QMIX-ReBorn, focusing on the ablation of the dormant threshold α, the over-active threshold β, and the ReBorn interval T . The default configuration of QMIX-ReBorn is α = 0.1, β = 3, and T = 0.2M . We modify each hyperparameter individually, and the experimental results indicate that appropriate hyperparameters help to better balance network activation, thereby enhancing overall performance. 
conclusion: 
 In this work, we identify the dormant neuron phenomenon in Multi-Agent Reinforcement Learning (MARL) Value Factorization. Such a phenomenon mainly exists in the mixing network, which hurts its expressive ability. We discover the existence of over-active neurons, which correlate with dormant neurons. Existing parameter perturbing methods do not work efficiently for the dormant neurons in MARL, due to the ignorance of over-active neurons and the forgotten of learned knowledge. We formulate the memorization requirement for learning agents' cooperation knowledge as the Knowledge Invariant (KI) principle. In this work, we propose ReBorn, which is a simple but effective parameter perturbing method. We show that it satisfies the KI principle and can improve the performance of multiple value factorization methods better than other parameter perturbing methods. 
safeguards: 
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 Appendix: A.1 Dec-POMDPsWe consider Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) [16] in modeling cooperative multi-agent reinforcement learning (MARL) scenarios. A Dec-POMDP can be formally described by the tuple G = ⟨S, {U i } N i=1 , P, r, {O i } N i=1 , {σ i } N i=1 , N, γ⟩, where N represents the set of agents, S is a finite set of states, and U i is the set of actions available to agent i. At time step t, each agent i chooses an action u t i ∈ U i , forming a joint action u t ∈ U N = U 1 × . . . × U N . This leads to a transition to a new state s t+1 ∼ P (•|s t , u t ) and a joint reward r t .. In consideration of partial observability, each agent can only access an individual observationo t i ∈ O i , which is drawn from o t i ∼ σ i (•|s t ).γ denotes the discounting factor. Each agent acts base on individual policy π i (u i |τ i ), τ i = (O i × U i ) * represents agent's local action-observation history. the global action-observation history is denoted as τ ∈ T N := τ 1 × . . . × τ N , on which it conditions the joint policy π =< π 1 , . . . , π N >. The joint policy π has a joint action-value function:Q π (s t , u t ) = E st+1:∞,ut+1:∞ [R t | s t , u t ], where R t = ∞ i=0 γ i r t+i is the discounted return.For cooperative multi-agent reinforcement learning tasks with partial observability challenges, agents are supposed to select actions solely based on their local observations. This presents significant challenges to global coordination in scenarios where communication is unavailable. To efficiently solve this problem, centralized training with decentralized execution (CTDE) was proposed as a popular paradigm. During centralized training, access to global information is available, while only local action-observation histories are accessible during decentralized execution phase. Value factorization is a class of effective value-based methods under the CTDE paradigm, where agents make decisions based on individual utility functions. The mixing network is employed during training to fit the relationship between the joint value function and individual utility functions. Among all value factorization methods, the Individual-Global-Max (IGM) principle proposed by [9] is a critical criterion that must be adhered to, ensuring the consistency between local and joint optimal action selections. The definition of the IGM principle is as follows: Definition 6 (IGM). For a joint state-action value function Q jt : T N × U N → R, where τ ∈ T N is a joint action-observation history and u is the joint action, if there exists individual state-action functions[Q i : T i × U i → R] N i=1, such that the following conditions are satisfiedarg max u Q jt (τ , u) = (arg max u1 Q 1 (τ 1 , u 1 ), . . . , arg max un Q N (τ N , u N )), (A.1)then, we can state that[Q i ] N i=1 satisfy IGM for Q jt under τ , or Q jt (τ , u) is factorized by [Q i (τ i , u i )] N i=1 .In recent years, ensuring the adherence to the IGM principle, a series of value factorization methods have been proposed. VDN imposes additive constraints on the mixing network, and QMIX enhances VDN's representation ability by imposing monotonicity constraints. These constraints are sufficient conditions for IGM, limiting the representational ability of the joint value function. QTRAN transforms the IGM principle into a linear constraint and proposes an easily factorizable form.Qatten uses the attention mechanism to model each agent's impact on the global situation. QPLEX decomposes the state-action value function into a state value part and an advantage value part. ResQ converts the joint value function into the sum of a main function and a residual function, deriving optimal policy through masking.Theorem 1. After the ReBorn process, the learned value function of the QMIX [2] value factorization method still satisfy the KI principle. whereQ θ, ϕ tot (τ , u) = f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) + V θ (τ ) ∂f ∂Q ϕ i ≥ 0 (B.2) h(w) = w, ∀w ∈ ϕ h is an identity function (B.3) g(w) =                          β i w inQ θ, ϕ tot (τ , u) = f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N ))is the joint state-action value funtion, f θ is the value factorization function of QMIX. In Reborn, g maps the parameters θ of the mixing network and the parameters ϕ of the agent network to θ.Proof. Through the use of non-negative activation function (e.g. absolute) and hypernet [39] , QMIX can ensure the following property. It indicates that if Q ϕ i increase, then the value of f increases. Proof. To prove this Corollary is equal to prove that the maximal action remain the same after the ReBorn method. It is shows that the ReBorn method satisfy the KI principle for QMIX, thus the following condition is satisfy. 19) shows that the IGM principle is still preserve after applying ReBorn on the joint state-action value Q tot of QMIX.Q θ, ϕ tot (τ , u) ≥ Q θ, ϕ tot (τ , u ′ ), ∃!k : u k ̸ = u ′ k (B.6) Q θ, ϕ tot (τ , [u 1 , ..., u N ]) ≥ Q θ, ϕ tot (τ , [u ′ 1 , ..., u ′ N ]) expand u (B.7) f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) + V θ (τ ) ≥ f θ (Q ϕ 1 (τ 1 , u ′ 1 ), ..., Q ϕ N (τ N , u ′ N )) + V θ (τ ) (B.8) f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) ≥ f θ (Q ϕ 1 (τ 1 , u ′ 1 ), ..., Q ϕ N (τ N , u ′ N )) (B.9) Q ϕ k (τ k , u k ) ≥ Q ϕ k (τ k , u ′ k ) , ∃!k : u k ̸ = u ′ k because of (B.5) (B.10) f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) ≥ f θ (Q ϕ 1 (τ 1 , u ′ 1 ), ..., Q ϕ N (τ N , u ′ N )) (B.11) f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) + V θ (τ ) ≥ f θ (Q ϕ 1 (τ 1 , u ′ 1 ), ..., Q ϕ N (τ N , u ′ N )) + V θ (τ ) (B.12) Q θ, ϕ tot (τ , u) ≥ Q θ, ϕ tot (τ , u ′ ) (B.13) (B.9) to (B.10) is because u i = u ′ i , ∀i ̸ = i ,Q θ, ϕ tot (τ , u) ≥ Q θ, ϕ tot (τ , u ′ ) → Q θ, ϕ tot (τ , u) ≥ Q θ, ϕ tot (τ , u ′ ) , ∃!k : u k ̸ = u ′ k (B.14) Q θ, ϕ tot (τ , ū) ≥ Q θ, ϕ tot (τ , u ′ ) ū = arg max u Q θ, ϕ tot (τ , u), ∀u ′ (B.15) ū = [ ū1 , ..., ūN ] ūi = arg max ui Q ϕ i (τ i , u i ) IGM Principle (B.16) Q θ, ϕ tot (τ , ū) ≥ Q θ, ϕ tot (τ , u ′ ) → Q θ, ϕ tot (τ , ū) ≥ Q θ, ϕ tot (τ , u ′ ) ∀u ′ KI Principle (B.17) Q θ, ϕ tot (τ , ū) ≥ Q θ, ϕ tot (τ , u ′ ), ∀u ′ (B.18) ū = arg max u Q θ, ϕ tot (τ , u) = arg max u Q θ, ϕ tot (τ , u) (B.19) (B.Theorem 2. ReDo [4] with function g and h does not guarantee satisfying the KI principle for the QMIX [2] value factorization method which is defined as follows. Proof. We prove this theorem by providing an example that ReDo does not satisfy the KI principle. We assume that the mixing network, parameterized by θ is a three layer neural work. As it is depicted in Figure 1 , the input layer neurons are used for joint state-action history τ . It also takes actions u as input. There are in total four joint actions represent asQ θ, ϕ tot (τ , u) = f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) + V θ (τ ) ∂f ∂Q ϕ i ≥ 0 (B.u 1 = [0, 0], u 2 = [0, 1], u 3 = [1, 0], u 4 = [1, 1]. There are two agents, each has two actions represent as 0 and 1, respectively. The action of the first/second agent is fed into the second/third neuron of the input layer. The weights of each neurons are marked on the edges and we assume bias b = 0. According to the definition 2 and the weights, the blue neuron is a dormant neuron. Assuming τ = 1, we can obtain the relationship of Q(τ , u) corresponding to each action:Q(τ, u 3 ) > Q(τ, u 4 ) > Q(τ, u 1 ) > Q(τ, u 2 ) (B.23)For the dormant neuron (colored), ReDo B.22 reinitialized the input weights of the neuron using Xavier initialization, the output weights of the neurons are set to zero. The weights after ReDo are as depicted in the right part of Figure 1 , and we assume that the bias for each neuron is zero. We can obtain the relationship of Q ′ (τ , u) corresponding to each joint action:Q(τ, u 4 ) > Q(τ, u 3 ) > Q(τ, u 2 ) > Q(τ, u 1 ) (B.24)Since the original optimal action u 3 in B.23 is different from the one u 4 in B.24 after Redo, we can draw a conclusion that ReDo does not satisfy the KI principle. Theorem 3. ReSet [6] with function g and h does not guarantee satisfying the KI principle for the QMIX [2] value factorization method which is defined as follows. Proof. We prove this theorem by providing an example that ReSet does not satisfy the KI principle. Consider a three-layer mixing network parameterized by θ, which takes joint action-observation history, represented as τ , and actions u as input, shown in Figure 2 . There are in total four actions represent asQ θ, ϕ tot (τ , u) = f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) + V θ (τ ) ∂f ∂Q ϕ i ≥ 0 (B.u 1 = [0, 0], u 2 = [0, 1], u 3 = [1, 0], u 4 = [1, 1]. There are two agents, each has two actions represent as 0 and 1, respectively. The action of the first/second agent is fed into the second/third neuron of the input layer. The weights of each neurons are marked on the edges and we assume bias b = 0. Assuming τ = 1, we can obtain the relationship of Q(τ , u) corresponding to each action:Q(τ, u 3 ) > Q(τ, u 4 ) > Q(τ, u 1 ) > Q(τ, u 2 ) (B.28)The weights of the last layer are reinitialized using Xavier initialization according to B.27. The weights after ReDo are as depicted in the right part of Figure 2 . We can obtain the relationship of Q ′ (τ , u) corresponding to each joint action:Q(τ, u 4 ) = Q(τ, u 3 ) > Q(τ, u 2 ) = Q(τ, u 1 ) (B.29)Since the original optimal action u 3 in B.28 is different from the optimal action u 4 in B.29 after Reset, we can draw a conclusion that Reset does not satisfy the KI principle. Theorem 4. ReBorn with functions g and h satisfies the KI principle for the QPLEX [10] value factorization method. where f θ is the value factorization function of QMIX. In Reborn, g map the parameters θ of the mixing network to θ.Q θ, ϕ tot (τ , u) = V θ, ϕ tot (τ ) + A θ, ϕ tot (τ , u) (B.30) A θ, ϕ tot (τ , u) = f θ (A ϕ 1 (τ 1 , u 1 ), ..., A ϕ N (τ N , u N )) ∂f ∂A ϕ i ≥ 0 (B.31) Q ϕ i (τ i , u i ) = A ϕ i (τ i , u i ) + V ϕ i (τ i ) V ϕ i (τ i ) = max ui Q ϕ i (τ i , u i ) (B.32) V θ ϕ tot (τ ) = max u Q θ,ϕ tot (τ , u) (B.33) g(w) =                          β i w inProof. QPLEX uses non-negative weighted attention network to implement f θ which satisfies the following property. Proof. The proof is the same as the proof for showing after the ReBorn process, QMIX satisfies the IGM principle. It is omitted for brevity.∂f θ ∂A ϕ i ≥ 0 ∀i, ∀θ, ∀ϕ monotonicity property (B.36) Q θ, ϕ tot (τ , u) ≥ Q θ, ϕ tot (τ , u ′ ) ∃!k : u k ̸ = u ′ k (B.37) V θ, ϕ tot (τ ) + A θ, ϕ tot (τ , u) ≥ V θ, ϕ tot (τ ) + A θ, ϕ tot (τ , u ′ ) (B.38) V θ, ϕ tot (τ ) + A θ, ϕ tot (τ , [u 1 , ..., u N ]) ≥ V θ, ϕ tot (τ ) + +A θ, ϕ tot (τ , [u ′ 1 , ..., u ′ N ]) (B.39) V θ, ϕ tot (τ ) + f θ (A ϕ 1 (τ 1 , u 1 ), ..., A ϕ N (τ N , u N )) ≥ V θ, ϕ tot (τ ) + f θ (A ϕ 1 (τ 1 , u ′ 1 ), ..., A ϕ N (τ N , u ′ N )) (B.40) f θ (A ϕ 1 (τ 1 , u 1 ), ..., A ϕ N (τ N , u N )) ≥ f θ (A ϕ 1 (τ 1 , u ′ 1 ), ..., A ϕ N (τ N , u ′ N )) (B.41) A ϕ k (τ k , u k )) ≥ A ϕ k (τ k , u ′ k )) (B.42) f θ (A ϕ 1 (τ 1 , u 1 ), ..., A ϕ N (τ N , u N )) ≥ f θ (A ϕ 1 (τ 1 , u ′ 1 ), ..., A ϕ N (τ N , u ′ N )) (B.43) V θ, ϕ tot (τ ) + f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) ≥ V θ, ϕ tot (τ ) + f θ (Q ϕ 1 (τ 1 , u ′ 1 ), ..., Q ϕ N (τ N , u ′ N )) (B.44) Q θ, ϕ tot (τ , u) ≥ Q θ, ϕ tot (τ , u ′ ) (B.45) (B.41) to (B.42) is because u i = u ′ i , ∀i ̸ = k ,Theorem 5. ReBorn with functions g and h satisfies the KI principle for the DMIX [10] value factorization method. DMIX is a distribution MARL algorithm which models the distributional return Z tot of multi-agent system. In Reborn, g map the parameters θ of the mixing network to θ.Z θ, ϕ tot (τ , u) = Z θ, ϕ mean (τ , u) + Z θ, ϕ shape (τ , u) (B.46) Q θ, ϕ tot (τ , u) = Z θ, ϕ mean (τ , u) = f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) + V θ (τ ) ∂f ∂Q ϕ i ≥ 0 (B.47) Q ϕ i (τ i , u i ) = E[Z ϕ i (τ i , u i )] expectation over possible outcome of Z i (B.48) Z θ ϕ shape (τ i , u i ) = N i=1 (Z ϕ i (τ i , u i ) -Q ϕ i (τ i , u i )) (B.49) h(w) = w, ∀w ∈ ϕ h is an identity function (B.50) g(w) =                          β i α i w inProof.Q θ, ϕ tot (τ , u) ≥ Q θ, ϕ tot (τ , u ′ ) ∃!k : u k ̸ = u ′ k (B.52) Q θ, ϕ tot (τ , [u 1 , ..., u N ]) ≥ Q θ, ϕ tot (τ , [u ′ 1 , ..., u ′ N ]) expand u (B.53) f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) + V θ (τ ) ≥ f θ (Q ϕ 1 (τ 1 , u ′ 1 ), ..., Q ϕ N (τ N , u ′ N )) + V θ (τ ) (B.54) f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) ≥ f θ (Q ϕ 1 (τ 1 , u ′ 1 ), ..., Q ϕ N (τ N , u ′ N )) (B.55) Q ϕ k (τ k , u k )) ≥ Q ϕ k (τ k , u ′ k )) ∃!k : u k ̸ = u ′ k (B.56) f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) ≥ f θ (Q ϕ 1 (τ 1 , u ′ 1 ), ..., Q ϕ N (τ N , u ′ N )) (B.57) f θ (Q ϕ 1 (τ 1 , u 1 ), ..., Q ϕ N (τ N , u N )) + V θ (τ ) ≥ f θ (Q ϕ 1 (τ 1 , u ′ 1 ), ..., Q ϕ N (τ N , u ′ N )) + V θ (τ ) (B.58) Q θ, ϕ tot (τ , u) ≥ Q θ, ϕ tot (τ , u ′ ) (B.59)Thus, we show that after the ReBorn process, the learned action preference of DMIX does not change.Corollary 3. After the ReBorn Process, the value function of DMIX remain satisfies the IGM principle.Proof. The proof is the same as the proof for showing after the ReBorn process, QMIX satisfies the IGM principle. It is omitted for brevity.Quantile functions (inverse CDF) θ of a random variable Z is defined as follows.θ Z (α) = inf{z ∈ R : ω ≤ CDF Z (z)}, ∀ω ∈ [0, 1] (B.60)where CDF Z (z) is the cumulative distribution function of Z. We denote θ Z (ω) as θ(ω) for simplicity..CV aR α (Z) = E Z [z|z ≤ θ(α)] (B.61)where α is the confidence level (risk level), θ(α) is the quantile function (inverse CDF) defined in (B.60). CVaR is the expectation of values z that are less equal than the α-quantile value (θ(α)) of the value distribution.Theorem 6. ReBorn with functions g and h satisfies the KI principle for the RMIX [12] value factorization method. RMIX is a risk-sensitive MARL algorithm which consider risk in multi-agent system. Its joint state-action value function is defined as follows. In Reborn, g map the parameters θ of the mixing network to θ.Q θ, ϕ tot (τ , u) = f θ (C ϕ 1 (τ 1 , u 1 ), ..., C ϕ N (τ N , u N )) + V θ (τ ) ∂f ∂C ϕ i ≥ 0 (B.62) C ϕ i (τ i , u i ) = CV aR α [Z ϕ i (τ i , u i )] (B.63) h(w) = w, ∀w ∈ ϕ h is an identity function (B.64) g(w) =                          β i w inProof.Q θ, ϕ tot (τ , u) ≥ Q θ, ϕ tot (τ , u ′ ) ∃!k : u k ̸ = u ′ k (B.66) f θ (C ϕ 1 (τ 1 , u 1 ), ..., C ϕ N (τ N , u N )) + V θ (τ ) ≥ f θ (C ϕ 1 (τ 1 , u ′ 1 ), ..., C ϕ N (τ N , u ′ N )) + V θ (τ ) (B.67) f θ (C ϕ 1 (τ 1 , u 1 ), ..., C ϕ N (τ N , u N )) ≥ f θ (C ϕ 1 (τ 1 , u ′ 1 ), ..., C ϕ N (τ N , u ′ N )) (B.68) C ϕ k (τ k , u k )) ≥ C ϕ k (τ k , u ′ k )) (B.69) f θ (C ϕ 1 (τ 1 , u 1 ), ..., C ϕ N (τ N , u N )) ≥ f θ (C ϕ 1 (τ 1 , u ′ 1 ), ..., C ϕ N (τ N , u ′ N )) (B.70) f θ (C ϕ 1 (τ 1 , u 1 ), ..., C ϕ N (τ N , u N )) + V θ (τ ) ≥ f θ (C ϕ 1 (τ 1 , u ′ 1 ), ..., C ϕ N (τ N , u ′ N )) + V θ (τ ) (B.71) Q θ, ϕ tot (τ , u) ≥ Q θ, ϕ tot (τ , u ′ ) (B.72)Thus, we show that through ReBorn, the learned knowledge about action preference of RMIX does not change.Corollary 4. After the ReBorn Process, the value function of RMIX remain satisfies the IGM principle.Proof. In RMIX, each agent acts greedy according toC ϕ i (τ i , u i ) = CV aR α [Z ϕ i (τ i , u i )]. It could be viewed as Q phi i (τ i , u i ) in QMIX.By this way, we can prove this Corollary in the same approach as for showing after the ReBorn process, QMIX satisfies the IGM principle. It is omitted for brevity.The ReBorn algorithm is described in Algorithm 1. Loss(θ, ϕ) = (Q(s, a; θ, ϕ) -y s,a ) 2Update θ and ϕ and by Loss if e mod T == 0 then Calculate the s ℓ i of each neuron in mixing network 16:Get dormant neurons dorm ℓ i which s ℓ i < α 17:Get over-active neurons over ℓ i which s ℓ i > β 18:for each over ℓ i do 19:Randomly select K dorm ℓ i that have not been selected before 20:over ℓ i assign weights to K dorm ℓ i 21:end forReinitialize input weights of unassigned dorm ℓ We select 4 classical algorithms (QMIX, QPLEX, DMIX, RMIX) with different types to test the generality of ReBorn. QMIX and QPLEX are two well-known value-based MARL value factorization algorithms. DMIX is a distributional MARL value factorization algorithm, while RMIX is a risksensitive MARL value factorization algorithm. These four algorithms cover multiple directions in the field of value factorization, demonstrating the strong applicability of ReBorn. Below is the brief descriptions of these algorithms. Brief Description QMIX3 [2] Learns a mixer of individual utilities with monotonic constraints QPLEX4 [10] Learns a mixer of advantage functions and state value functions DMIX5 [11] Integrates distributional RL with QMIX RMIX6 [12] Integrates risk-sensitive RL with QMIXWe implement these algorithms based on their open-source repositories to carry out performance analyses, with hyperparameters consistent with those in PyMARL. Our methods are implemented within the PyMARL framework, and each is evaluated using 5 random seeds, with 95% confidence intervals. Specific hyperparameters of different algorithms are listed in Table 2 . We conduct experiments on a cluster equipped with multiple NVIDIA GeForce RTX 3090 GPUs. The StarCraft Multi-Agent Challenge (SMAC) [13] is a popular benchmark used extensively in the domain of multi-agent reinforcement learning. Built on the StarCraft II game engine, SMAC specializes in micromanagement scenarios where each agent is controlled by an independent agent that must make decisions based on local observations. MARL algorithms coordinate a team of agents to engage in combat against an opposing team managed by the game's built-in AI. The performance of these algorithms is quantitatively evaluated by the test win rate or the test return of the gameplay. Table 5 depicts the overview of SMAC scenarios used in the experiment.SMACv2 [14] addresses several critical limitations of SMAC, including the lack of stochasticity and partial observability. Unlike SMAC, SMACv2 features units that are randomly generated and positioned, enhancing stochasticity and significantly increasing the complexity of the scenarios. Table 6 depicts the overview of SMACv2 scenarios used in the experiment.To analyze the impact of the dormant ratio on the expressive power of the mixing network, we consider an illustrative example that requires mixing individual utilities of three agents. For this purpose, we design a simple 2-layer MLP network. The input layer, with a size of 3, receives individual utilities[Q i ] 3 i=1 .The hidden layer contains 4 neurons and uses ReLU as the activation function. The output layer, with a size of 1, produces Q tot . The objective is to fit the mixing functionQ tot = 0.5 * Q 5 1 + Q 3 2 + 1.5 * Q 3 , Q i ∼ N (0, 1). We control the dormant ratio by varying the number of dormant neurons in the hidden layer. Figure 2 (a) illustrates the expressive performance of networks with different dormant ratios. Number = n indicates that there are n dormant neurons in the hidden layer. We use Mean Squared Error as the loss function. According to the results, an increase in the dormant ratio will lead to reduced expressive power of the mixing network. predator-prey small Our research primarily concentrates on the technical and theoretical aspects of multi-agent reinforcement learning, aiming to enhance the performance of these agents across a variety of tasks. While we do not foresee any direct negative consequences arising from our research, we are committed to maintaining an open dialogue. We highly appreciate and value constructive feedback from the community to ensure our work's contributions are beneficial and ethically sound.Although our proposed simple recycling method has achieved good results across various algorithms, there is still room for further improvement. We have defined dormant neurons and over-active neurons in a straightforward manner. However, their identification should not be limited to normalized activation values. More precise identification could be achieved by considering additional factors such as update gradients and output weights.We studied the phenomenon of dormant neurons in discrete multi-agent environments. Future work should explore whether our method can be extended to continuous environments. Regarding different thresholds and recycling periods, setting a threshold too high or recycling too frequently can disrupt the network's normal learning process. Conversely, low thresholds and infrequent recycling can reduce the effectiveness of the recycling process. Therefore, developing adaptive thresholds and recycling mechanisms will be a key focus of future work.NeurIPS Paper Checklisthttps://github.com/oxwhirl/pymarlhttps://github.com/wjh720/QPLEXhttps://github.com/j3soon/dfachttps://github.com/yetanotherpolicy/rmix 


Decision: This paper studies the dormant neuron phenomenon in value factorization of multi-agent reinforcement learning (MARL) and finds that the dormant neurons negatively affect the learning process. With observing that dormant neurons correlate with the existence of overweight neurons, the authors propose ReBorn that transfers the weights from overweight neurons to dormant neurons with some theoretical analysis and promising empirical results. Overall, the story path of this paper is interesting, and the proposed method is important for making CTDE MARL methods more effective. During the rebuttal phase, the authors provided satisfactory responses to ease the concerns of the reviewers. As a result, I recommend acceptance of this paper.

Reviews: review: paper_summary: paper_summary: This work proposes a new method for resetting dormant neurons in multi-agent RL settings. It replicates previous observations on unit dormancy in deep RL in the multi-agent regime, finding that inactive neurons are correlated with reduced ability to improve performance. The proposed method differs from ReDO, which resets dormant neurons' incoming weights to that of a random initialization, by distributing the weights of highly active "overweight" neurons among those identified as dormant during reset steps so as to avoid changing the output of the network.
strength_weakness: strength_weakness: I have two main concerns with this paper which prevent me from confidently recommending its acceptance: the first is the validity of the theoretical results, and the second is signficance of the empirical results. I list more minor concerns later, which may benefit the paper but which will not affect my decision.

- Major: while it is true that a parameter perturbation which changes the rankings of global actions can cause a function which previously satisfied the IGM principle to violate it, such a perturbation would also violate the assumption on the monotonicity of the global value w.r.t. agent utilities which is baked into methods like QMIX. Indeed, the proof of Theorem 1 does not provide a concrete example of a perturbation to the network parameters which violate the KI principle and violate the IGM principle, as such an example which satisfies [B.5] would require non-monotonicity of the mixing function. Since the algorithms studied in the paper do use monotone mixing functions, Theorem 1 does not seem relevant. 

- Major: I could not find anything in the proof of Theorem 2 which depends on the particular form of the ReBorn update. Instead it seems that Theorem 2 depends on the monotonicity of the QMIX mixing network (b.10), rather than any particular property of the perturbation to $\hat{\theta}$. This further reinforces the above concern that the proposed failing of parameter perturbation methods in the general case of Theorem 1 is in fact only a product of relaxing the assumption on the monotonicity of the mixing network.
    
- Major: In many instances, using ReDo appears to hurt performance compared to naive QMIX, despite reducing the dormancy percentage. Further, it appears that in some environments, applying ReDo does not change the number of dormant neurons. This causes me to wonder if the ReDo method has been appropriately tuned for the domains it is being applied to. 

- Minor: to me, a better name for the so-called 'overweight' neurons would be 'over-active', since it's not clear that the cause of their disproportionate activity is due to the magnitude of their weights or to the alignment of their incoming weights with the previous layer's features. This also makes it more clear their relationship with dormant neurons.

- Minor: there are a few grammatical issues in the paper that would benefit from review. For example, the word 'albeit' is typically used at the start of a phrase, and not a clause as is often done in the paper, where it can generally be replaced with 'although'.
questions: questions: 1. Can the authors comment on how they tuned ReDo and give some insight into why it seems to not have any effect on the number of dormant units in Figure 6?
2. Please address my questions regarding theorems 1 and 2. Are there instances where even with a monotone mixing network, a parameter-perturbing method will fail to satisfy IGM?
limitations: limitations: Yes
paper_summary: paper_summary: The paper explores the dormant neuron phenomenon, an active research topic in RL, in the context of MARL value factorization. It describes how dormant neurons manifest mostly in the mixing network, details their effect on performance and connects them to an opposite but correlated phenomenon, overweight neurons. The paper proposes a method to counter the dormant neuron phenomenon by redistributing the weights of overweight neurons among dormant neurons. In MARL value factorization, the proposed method is demonstrated to outperform general RL methods for dealing with dormant neurons.
strength_weakness: strength_weakness: The figures and figure captions are often hard to understand. Some plots are hard to interpret solely from the plot and caption text, e.g. to understand what 'Number' means in Figure 2a, one must look for explanations in the text body. Another example is Figure 4, which the reader is referred to for a depiction of the main method of the paper, but contains a total of 8 words in legends and caption combined. In contrast, the figures themselves are visually clear to understand.
This problem can be easily fixed by expanding some of the captions and using more expressive wording in figure legends and titles. I am willing to raise my score if the figures are presented in a more readable manner.
questions: questions: Suggestion:
Evaluation on more environments could strengthen the paper's claim of superiority over other methods. However, I find the current evaluation experiments sufficient to make that claim.
limitations: limitations: Limitation are not discussed in the main section, only in the appendix.
paper_summary: paper_summary: This paper introduces a novel approach for tackling the plasticity loss and securing sample efficiency in multi agent reinforcement learning (MARL). Different from the methods in single agent RL, this paper also shows the importance of not violating the knowledge invariant (KI) principle in MARL. With careful analysis and extensive experiments, the proposed method, ReBorn, outperforms other baselines such as ReDo or Reset. The authors said that the baselines, ReDo and Reset, violate the KI principle, thus they are not appropriate to be applied to MARL setting. However, the proposed method, ReBorn, can satisfy the KI principle, leading to achieve remarkable performance.
strength_weakness: strength_weakness: - The motivation behind scaling the weights in ReBorn is not clear. Though scaling the weights to ease the strength of the overweight neurons is straightforward, is it only way to reduce the number of overweight neurons? I'm quite confusing why we should use the scaling approach in ReBorn.

- I think there is a missing baseline [1]. This approach can also effectively resolve the plasticity loss problem, and achieves high sample efficiency in singe agent RL. Although this approach violates the KI principle, with high replay ratio, it may achieve good performance in MARL setting. Similar to [1], a recently proposed method [2]  show that resetting the network and training the network with high replay ratio in MARL setting can outperform the baselines. I know it is difficult to  compare ReBorn and the method in [2] at submission phase, but I wonder the method in [2] violating the KI principle is truly failed to overcome the plasticity loss.


[1] D'Oro et. al. ,Sample-Efficient Reinforcement Learning by Breaking the Replay Ratio Barrier, ICLR, 2023

[2] Yang et. al., Sample-Efficient Multiagent Reinforcement Learning with Reset Replay, ICML, 2024
questions: questions: Already mentioned in the Weakness section.
limitations: limitations: N/A
paper_summary: paper_summary: The paper proposes ReBorn to reactivate dormant neurons in the mixing network of multiagent value-mixing algorithms. Specifically, ReBorn transfers the weights from overweight neurons to dormant neurons and this method ensures the learned action preferences are not changed after the ReBorn operation. Experiments on SMAC, predator-prey, and SMACv2 demonstrate the effectiveness of the proposed method.
strength_weakness: strength_weakness: 1.	It seems that the ReBorn operation is time-consuming as it needs to compute and manipulate each neuron in the network. If the network is large, this ReBorn operation may become infeasible.
2.	The ReBorn is only validated in the multiagent value-mixing algorithms.
questions: questions: 1.	Could the authors compare the running time of the baselines and their ReBorn variants?
2.	Could ReBorn be applied to other MARL algorithms besides the multiagent value-mixing algorithms such as MAPPO and MADDPG?
limitations: limitations: NA.

Comments: comment: Dear Reviewer,

Thanks for your time and effort in reviewing our work. We greatly appreciate your insightful and detailed feedback. We have carefully addressed the concerns in the rebuttal. Please let us know if any aspects remain unclear, and we are happy to provide further clarification.

Best regards,

Authors
>Could the authors clarify what they mean by “functional property” in their response?

Functional property means the monotonicity or the constraints for a value factorization method to satisfy the IGM principle. 

For some mixers (e.g., QTRAN), although they follow the IGM principle, they may fail to satisfy it due to parameter perturbation. For QTRAN, the constraints (Theorem 1, Formula 4b in [1]) that guarantee the IGM principle are implemented through a mean-square loss, not through neural network features (such as absolute activation function). Through parameter perturbing, the IGM principle for QTRAN could be violated.  


>ReDo baseline: While I agree with the authors that ReDo is reducing the dormant neuron ratio relative to the baseline, the specific feature that drew my attention in Figure 6 was the relatively flat slope of the dormant neuron curve in the second half of training in the bottom middle panel, where it seems like each time the ReDo algorithm is called later in training it does not even transiently reduce the number of dormant neurons. This result would benefit from a brief discussion of why applying ReDo is not even temporarily reducing the number of dormant neurons.

ReDo is called every 0.2 million (roundly) steps, and we report the dormant ratio every 10,000 (roundly) steps. **Most of the time when ReDo is performed, the dormant ratio before ReDo is reported, not the ratio just after ReDo**. The middle top of Figure 6 depicts the ratio for MMM2. The ratio curve does experience a temporary drop after ReDo is called. 

The middle bottom of Figure 6 depicts the ratio for the 27m vs 30m scenario, which has more agents (27 agents) than MMM2 (12 agents). It is more non-stationary with a higher dormant ratio than MMM2. **When ReDo is called, the dormant ratio does drop immediately, but it increases quickly to its previous value within the next time window when the ratio is reported.** Thus, a temporary drop in the ratio is not observed. The following table shows the dormant ratio with respect to time steps for one run of ReDo on 27m vs 30m. For this table, "Report" indicates the dormant ratio is reported in a figure; "ReDo" indicates that ReDo is performed. For step 1796103, before ReDo is called, the dormant ratio is 30. At step 1796226, just after ReDo, the dormant ratio drops from 30 to 9. **This indicates that ReDo does work as it is designed.** Such ratio quickly increases from 9 to 29 at step 1806262, when the ratio is reported in a figure. Thus, such a temporary drop is not observed. 

|Time step|Dormant ratio|Action|
|-|-|-|
|1786065|31|Report|
|...|...|...|
|1796103|30|Report|
|1796226|9|ReDo|
|1796300|10||
|1796480|16||
|1796518|15||
|...|...|...|
|1801093|21||
|...|...|...|
|1806262|29|Report|


Reference

[1] Son et al. QTRAN: Learning to Factorize with Transformation for Cooperative Multi-Agent Reinforcement learning, ICML 2019
Dear Reviewer,

Thanks for your reply. We address your concerns as follows.

>Nikishin et al. citation: Apologies for the ambiguity, Nikishin et al. reference I referred to was not the primacy bias work but rather the later paper on plasticity injection [1], which proposes to freeze the network parameters and initialize a new, trainable network whose output is added to that of the frozen network in order to increase trainability.

Thanks for the clarification. Plasticity injection (PI) is an interesting work. It aims to increase the plasticity without changing the neural network output by adding new parameters. Unlike PI, our work does not introduce new parameters. We will discuss it in the related work section.

We have applied PI in the agent network (Agent+PI), in the mixing network (Mixer+PI), and in both the agent and mixing network (Agent+Mixer+PI) for QMIX in the predator-prey small, predator-prey medium, MMM2 environments. For these experiments, we use the default hyperparameters of PI. The experimental results are listed as follows. The return is reported for predator-prey, and for MMM2, the win rate is reported. The experimental results show that PI performs inferior to ReBorn.



|QMIX|predator-prey small|predator-prey medium|MMM2|
|-|-|-|-|
|Agent+PI|106|173|46|
|Mixer+PI|67|114|64|
|Agent+Mixer+PI|73|125|44|
|Reborn|112|205|83|


>Monotonicity: I appreciate the provided example, ... The major aspect of my concern which is still unclear after the authors' response is what property of ReBorn ensures that it will satisfy the KI / IGM principle in a situation where ReDo does not. Providing a concrete worked example of such a case would help to address this concern.

Thanks for your question; we will make our writing clearer. We will discuss different variants of ReDo more clearly, and include related experiments. 

In single-agent RL, ReDo perturbs the parameters of the agent network. For MARL, ReDo perturbs the agent and mixing networks through functions $h$ and $g$, respectively. $h$ and $g$ are the same; they both use Xavier initialization to re-initialize the dormant neurons. As the parameters of the agent network are perturbed through $h$, **the local ranking of actions could be changed, and so does the global ranking**; thus, we state that it does not guarantee to satisfy the KI principle. 

In Section 6.4.2, we replace $h$ used by ReDo with an identity function $h(\theta) =\theta$ used by ReBorn, which **does not perturb agent network parameters**. The new method is named ReBorn(ReDo). We have stated in Section 6.4.2 that ReBorn(ReDo) **satisfies the KI principle**. The experimental results show that ReBorn(ReDo) performs inferior to Reborn (Figure 8). Additionally, we apply ReDo to the agent network only by using the function $g$ for the agent network and the identity function $h$ for the mixing network. In the following table, we show the result for using the $g$ function only for the agent network (Agent-ReDo), for the mixing network (Mixer-Redo), for both the agent network and the mixer network (ReDo), and ReBorn. Mixer-Redo is called ReBorn(ReDo) in Figure 8. For predator-prey small and predator-prey medium, the return is reported. For MMM2, the win rate is reported. 


|QMIX|predator-prey small|predator-prey medium|MMM2|
|-|-|-|-|
|Agent-ReDo|88|165|46|
|Mixer-ReDo|105|184|59|
|ReDo|92|177|55|
|ReBorn|112|205|83|


For Agent-ReDo and Mixer-ReDo, the identity function $h$ is applied to the mixing and agent networks, respectively. We find that by using $g$ only to the agent network (Agent-ReDo), its performance is poor due to the violation of KI and the existence of dormant neurons, mainly in the mixing network. Mixer-ReDo performs better than Agent-ReDo and ReDo, thanks to the satisfaction of the KI principle. However, all these variants of ReDo perform inferior to Reborn.


The $h$ and $g$ functions used by ReBorn are different from ReDo. As it is written in lines 226-227, $h$ is an identity function used for the agent network, and $g$ is applied for the mixing network through weight-sharing among over-active and dormant neurons. ReBorn perturbs the parameters of the mixing network rather than the agent network, thanks to the discovery that there exist few dormant neurons in the agent network. For ReBorn, as the agent network is not perturbed, **the local ranking of action is not changed, so does the global ranking of actions for a monotonic mixer**. We have stated in line 287 and 289 that, *if we applied the ReBorn function $g$ to the agent network, the KI principle will be violated*, and lead to poor performance in Section 6.4.1 (Figure 7).
Dear Reviewer, 

We are happy that we have addressed your concerns. We will add the results of baselines[1,2] and Reborn with higher replay ratios in SMAC and predator-prey. 

Best Regards,

Authors
I appreciate the authors for replying to my question. I have no further questions and I would like to maintain my score. But I recommend including the results of baselines [1, 2] and Reborn with higher replay ratios in SMAC and predator-prey for a fair comparison in the final revision.
Thank you for your response. Since you have addressed my concerns, I will raise my score to 7.
Dear Reviewer, 

We are happy that we have addressed most of your concerns. 

For SR[1] and MARR[2], we use their default replay ratios. The replay ratios for SR and MARR are 4 and 1, respectively. The replay ratio for ReBorn is 1. 

As per the Reviewer's suggestion, we've conducted a performance evaluation of ReBorn, SR, and MARR for QMIX on the Predata-prey environments at varying replay ratios (1, 5, and 10). Notably, the behavior of ReBorn remains consistent regardless of the replay ratio. However, for SR, the number of reset operations increases with the replay ratio, and for MARR, the number of 'random amplitude scale data augmentation' also increases with the replay ratio. 



For predator-prey small environments, the return and the time (hours) for different algorithms with different replay ratios are depicted as follows. The training time increases with the increase of the replay ratio. We find that ReBorn performs better than SR and MARR when the replay ratio is lower than 5. When the replay ratio is 10, the performance of ReBorn is slightly better than SR and MARR. 

|predator-prey small (time)|1|5|10|
|-|-|-|-|
|Reborn|4|9|13|
|SR|4|7|12|
|MARR|4|9|14|

|predator-prey small (return)|1|5|10|
|-|-|-|-|
|Reborn|112|115|114|
|SR|42|98|113|
|MARR|51|97|110|


For the predator-prey medium environments, the return and the time for different algorithms with different replay ratios are depicted as follows. We find that when the replay ratio is lower than 5, ReBorn performs better than SR and MARR. When the replay ratio is 10, ReBorn performs weaker than SR and MARR.



|predator-prey medium (time)|1|5|10|
|-|-|-|-|
|Reborn|7|13|20|
|SR|7|11|18|
|MARR|7|14|22|

|predator-prey medium (return)|1|5|10|
|-|-|-|-|
|Reborn|205|203|195|
|SR|78|162|203|
|MARR|89|182|208|

Based on our experimental results, it's clear that ReBorn should consider the replay ratio to achieve better performance. 


References

[1] D'Oro et. al., Sample-Efficient Reinforcement Learning by Breaking the Replay Ratio Barrier, ICLR, 2023

[2] Yang et al., Sample-Efficient Multi-agent Reinforcement Learning with Reset Replay, ICML, 2024
Thanks to the authors for their response. 

- **Nikishin et al. citation:** Apologies for the ambiguity, Nikishin et al. reference I referred to was not the primacy bias work but rather the later paper on plasticity injection [1], which proposes to freeze the network parameters and initialize a new, trainable network whose output is added to that of the frozen network in order to increase trainability.
- **Monotonicity:** I appreciate the provided example, however this example also seems to depend on an unconstrained mixing network in which there exist parameters under which the output is non-monotonic in the inputs. If I understood correctly, however, QMIX and related methods explicitly constrain their mixing networks to be monotonic under all possible parameterizations. The major aspect of my concern which is still unclear after the authors' response is what property of ReBorn ensures that it will satisfy the KI / IGM principle in a situation where ReDo does not. Providing a concrete worked example of such a case would help to address this concern.
- Could the authors clarify what they mean by “functional property” in their response?
- **ReDo baseline:** While I agree with the authors that ReDo is reducing the dormant neuron ratio relative to the baseline, the specific feature that drew my attention in Figure 6 was the relatively flat slope of the dormant neuron curve in the second half of training in the bottom middle panel, where it seems like each time the ReDo algorithm is called later in training it does not even transiently reduce the number of dormant neurons. This result would benefit from a brief discussion of why applying ReDo is not even temporarily reducing the number of dormant neurons.

[1] Nikishin, Evgenii, et al. "Deep reinforcement learning with plasticity injection." Advances in Neural Information Processing Systems 36 (2024).
Thank you for your reply. Most of my concerns are addressed. I have one remaining problem. 

For the new baselines [1, 2] that were compared, what are the replay ratios for them and ReBorn? It seems that the two methods are working with higher replay ratios larger than 1. Could you compare ReBorn and them at different replay ratio settings such as 1, 5, and 10?