A Study of Plasticity Loss in On-Policy Deep Reinforcement Learning

Arthur Juliani, Jordan T. Ash·May 29, 2024

Summary

This collection of research papers investigates plasticity loss in on-policy deep reinforcement learning, focusing on the decline in adaptability of neural networks to new tasks. The study finds that many mitigation techniques from other learning domains, like supervised or off-policy RL, are not effective or even detrimental in on-policy settings. Key findings include: 1. Regenerative methods consistently address plasticity loss across various environments, from gridworlds to complex games like Montezuma's Revenge and ProcGen. 2. The study identifies three types of distribution shifts and analyzes their impact on performance, with a focus on understanding the need for tailored solutions in on-policy RL. 3. Architectural interventions like CReLU and Plasticity Injection are less effective, while regularization methods like shrink+perturb, LayerNorm, and regenerative regularization show promise. 4. Weight magnitude, dead units, and gradient norms are significant factors affecting plasticity loss and generalization, with interventions that control weight growth being beneficial. 5. Experiments with different environments and tasks, such as gridworlds, CoinRun, and Montezuma's Revenge, demonstrate the effectiveness of specific interventions in mitigating plasticity loss and improving performance. In conclusion, the research highlights the importance of understanding and addressing plasticity loss in on-policy deep reinforcement learning, as well as the need for tailored solutions that are effective across diverse environments and distribution shifts.

Key findings

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Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to address the issue of plasticity loss in on-policy deep reinforcement learning, which is a challenge where a neural network trained online shows a decreased ability to adapt to new tasks . While plasticity loss has been extensively studied in supervised learning and off-policy reinforcement learning, it has received less attention in the on-policy deep RL setting . The study conducted in the paper demonstrates that plasticity loss is prevalent under domain shift in the on-policy regime and proposes various mitigation methods to tackle this issue . This problem is not entirely new, as plasticity loss has been recognized in other learning settings, but the paper sheds light on its implications and solutions specifically in the context of on-policy deep reinforcement learning .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate the scientific hypothesis related to plasticity loss in on-policy deep reinforcement learning. It explores the phenomenon of plasticity loss in the on-policy reinforcement learning setting and introduces various forms of distribution shift to analyze this issue . The study extends the investigation of plasticity loss and the warm-start problem to the on-policy regime, highlighting the persistent nature of these challenges across different environmental distribution shift conditions . Additionally, the paper provides an in-depth analysis of the correlates of plasticity loss, studying different environmental settings, model architectures, and previously proposed mitigation approaches in the context of on-policy reinforcement learning .


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

The paper on plasticity loss in on-policy deep reinforcement learning introduces several new ideas, methods, and models to address this issue . One key contribution is the introduction of three distinct kinds of distribution shift to facilitate analysis, along with various environments and tasks for study . The paper highlights the persistence of plasticity loss across different environmental distribution shift conditions and provides an in-depth analysis of the correlates of these pathologies . Additionally, the study includes generalization trends in the consideration of these phenomena .

The paper characterizes properties of methods necessary for successful interventions in addressing plasticity loss and ensuring maintained generalization performance . It discusses the limitations of existing methods designed for supervised learning or off-policy reinforcement learning when applied to the on-policy setting or under the proposed forms of distribution shift . The study also describes several techniques that effectively resolve plasticity loss in the considered environments .

One of the proposed methods to address plasticity loss is Continual Backprop, which is a form of regularization towards the initialization distribution, selectively on a per-neuron basis . This approach is similar to ReDo and DrM, which are also analyzed in the paper . The study emphasizes the importance of continual regularizers over intermittent interventions in resolving plasticity loss in on-policy deep reinforcement learning .

Moreover, the paper discusses the class of regularization methods, including L2 regularization, ReDo, shrink+perturb, and regenerative regularization, which significantly mitigate plasticity loss in experiments . Among these methods, soft shrink+perturb displays the best generalization performance and can be combined with layer normalization, which has been effective in addressing plasticity loss in the on-policy setting . The regularization methods normalize network parameters towards their initial distribution, reducing weight magnitude and dead or saturated activation units . The paper on plasticity loss in on-policy deep reinforcement learning introduces novel methods with distinct characteristics and advantages compared to previous approaches . One key method, Shrink+Perturb, involves periodically reducing the magnitude of all weights in the network and adding noise sampled from a new weight initialization, leading to improved performance in batched continual learning settings . This method entangles two factors to sum to one, enhancing its effectiveness .

Another innovative approach proposed in the paper is Plasticity Injection, which replaces the final layer of a network with a new function that combines the final layer's output with the output of a newly initialized layer, leading to performance improvements in off-policy RL agents . This method involves blocking the gradient in both the original layer and the subtracted new layer, showcasing its unique characteristics .

Additionally, the study introduces Continuous Interventions, which are applied at every step of optimization without the need to detect distribution shifts, making them practical for mitigating plasticity loss . This method includes techniques like L2 Norm and LayerNorm, which involve regularizing the network using the L2 norm and applying layer normalization before the ReLU activation at each layer, respectively .

Furthermore, the paper discusses the advantages of the class of regularization methods, including L2 regularization, ReDo, shrink+perturb, and regenerative regularization, in significantly mitigating plasticity loss in experiments . Among these methods, soft shrink+perturb displays the best generalization performance and can be easily combined with layer normalization, showcasing its effectiveness and versatility . These regularization methods normalize network parameters towards their initial distribution, reducing weight magnitude and addressing dead or saturated activation units, which is crucial for mitigating plasticity loss .


Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

Several related research studies exist in the field of plasticity loss in on-policy deep reinforcement learning. Noteworthy researchers who have contributed to this topic include Ash and Adams , Lyle et al. , Nikishin et al. , and Schulman et al. . These researchers have explored various aspects of plasticity loss, policy collapse, and methods to address these challenges in deep reinforcement learning.

The key to the solution mentioned in the paper is the utilization of "regenerative" methods. The study demonstrates that regenerative methods consistently mitigate plasticity loss in on-policy deep reinforcement learning across different environments and distribution shifts. These regenerative methods act as continual regularizers, effectively addressing plasticity loss and improving performance in tasks like gridworld tasks, Montezuma’s Revenge, and ProcGen environments .


How were the experiments in the paper designed?

The experiments in the paper were designed to systematically characterize plasticity loss and its resolution in the on-policy setting by conducting a suite of experiments using different environments and distribution change conditions . The experiments involved three distinct forms of distribution shift organized into rounds, where each round supplied a set number of environments from a specific distribution to the agent for training and evaluation . The environmental modifications included strategies like permuting input pixels, using a window approach with new environments for the same task, and expanding the dataset with additional environments . These modifications induced significant performance changes and were aimed at studying plasticity loss in deep reinforcement learning .


What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study is the CoinRun environment from the ProcGen suite of tasks . The code used in the study is not explicitly mentioned as open source in the provided context.


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide strong support for the scientific hypotheses that need to be verified regarding plasticity loss in on-policy deep reinforcement learning. The study systematically characterizes plasticity loss and explores methods to address it in the on-policy setting . The experiments involve simulating environmental distribution shifts and testing various interventions to mitigate plasticity loss .

The paper conducts experiments using different environments such as a 2D gridworld, CoinRun environment, and the Atari game Montezuma’s Revenge, all trained using Proximal Policy Optimization (PPO) algorithms . These experiments aim to assess the impact of plasticity loss on learning performance and evaluate the effectiveness of interventions like regenerative regularization .

Furthermore, the results of statistical tests comparing different methods to baselines in various conditions provide valuable insights into the performance of interventions in mitigating plasticity loss . The study analyzes factors such as weight magnitudes, dead unit count, and gradient norms to predict plasticity loss and assess the effectiveness of different mitigation strategies .

Overall, the experiments and results in the paper offer a comprehensive analysis of plasticity loss in on-policy deep reinforcement learning, providing substantial evidence to support the scientific hypotheses under investigation and offering insights into effective strategies to address this phenomenon .


What are the contributions of this paper?

The contributions of the paper "A Study of Plasticity Loss in On-Policy Deep Reinforcement Learning" include:

  • Extending studies of plasticity loss and the warm-start problem to the on-policy regime, highlighting their persistence across various environmental distribution shift conditions .
  • Providing an in-depth analysis of the correlates of plasticity loss, studying different environmental settings, model architectures, and proposed mitigation approaches related to on-policy reinforcement learning, while considering generalization trends .
  • Characterizing properties of successful intervention methods to address plasticity loss and maintain generalization performance, along with providing recommendations based on these insights .

What work can be continued in depth?

Further research in the field of plasticity loss in on-policy deep reinforcement learning can be expanded in several directions based on the existing studies:

  • Investigating the impact of regenerative methods: Research can delve deeper into the effectiveness of regenerative methods in mitigating plasticity loss in various contexts, including gridworld tasks and challenging environments like Montezuma’s Revenge and ProcGen .
  • Exploring the distinction between ray interference and plasticity loss: Future studies could focus on distinguishing between ray interference and plasticity loss in the reinforcement learning setting, particularly for complex tasks like CoinRun or Montezuma’s Revenge, where unique sub-tasks may interfere with each other .
  • Studying the effectiveness of continual regularizers: Further analysis can be conducted on the performance of methods acting as continual regularizers, such as soft shrink+perturb and regenerative regularization, especially when combined with layer normalization, to address plasticity loss in on-policy deep reinforcement learning .
  • Investigating the impact of environmental distribution shift: Research can continue to simulate different forms of distribution shift to understand how plasticity-preserving interventions can mitigate plasticity loss in on-policy reinforcement learning, particularly in scenarios where data modifications induce performance degradation .
  • Evaluating the effectiveness of regularization methods: Future studies can focus on evaluating the efficacy of various regularization methods, such as L2 regularization, ReDo, and regenerative regularization, in addressing plasticity loss in deep neural networks, especially in the context of on-policy reinforcement learning .

Introduction
Background
Overview of plasticity loss in deep RL
Importance of adaptability in on-policy learning
Objective
To investigate mitigation techniques for plasticity loss in on-policy settings
To identify effective strategies across diverse environments
Methodology
Data Collection
Selection of environments: gridworlds, Montezuma's Revenge, ProcGen, CoinRun
On-policy deep reinforcement learning algorithms
Data Analysis
Distribution Shifts
Type 1: Task variations
Type 2: Environment dynamics
Type 3: Curriculum learning
Impact on performance and adaptability
Mitigation Techniques
Regenerative methods
Architectural interventions (CReLU, Plasticity Injection)
Regularization methods (shrink+perturb, LayerNorm, regenerative regularization)
Experimental Design
Performance evaluation in different scenarios
Control experiments with weight growth management
Key Findings
Regenerative Methods
Consistent improvement across environments
Distribution Shift Analysis
Impact on performance and tailored solutions
Architectural Interventions
CReLU and Plasticity Injection limitations
Promising regularization methods
Factors Affecting Plasticity Loss
Weight magnitude, dead units, gradient norms
Weight growth control strategies
Environment and Task Specificity
Success stories in gridworlds, CoinRun, Montezuma's Revenge
Conclusion
The need for tailored solutions in on-policy deep RL
Importance of understanding plasticity loss for generalization
Future directions and open challenges in the field
Basic info
papers
machine learning
artificial intelligence
Advanced features
Insights
What is the primary focus of the research papers discussed?
Why are many mitigation techniques from other learning domains not effective in on-policy deep reinforcement learning?
What are the key findings regarding regenerative methods and their impact on performance in various environments?
What architectural interventions were found to be less effective in addressing plasticity loss, and which ones showed promise?

A Study of Plasticity Loss in On-Policy Deep Reinforcement Learning

Arthur Juliani, Jordan T. Ash·May 29, 2024

Summary

This collection of research papers investigates plasticity loss in on-policy deep reinforcement learning, focusing on the decline in adaptability of neural networks to new tasks. The study finds that many mitigation techniques from other learning domains, like supervised or off-policy RL, are not effective or even detrimental in on-policy settings. Key findings include: 1. Regenerative methods consistently address plasticity loss across various environments, from gridworlds to complex games like Montezuma's Revenge and ProcGen. 2. The study identifies three types of distribution shifts and analyzes their impact on performance, with a focus on understanding the need for tailored solutions in on-policy RL. 3. Architectural interventions like CReLU and Plasticity Injection are less effective, while regularization methods like shrink+perturb, LayerNorm, and regenerative regularization show promise. 4. Weight magnitude, dead units, and gradient norms are significant factors affecting plasticity loss and generalization, with interventions that control weight growth being beneficial. 5. Experiments with different environments and tasks, such as gridworlds, CoinRun, and Montezuma's Revenge, demonstrate the effectiveness of specific interventions in mitigating plasticity loss and improving performance. In conclusion, the research highlights the importance of understanding and addressing plasticity loss in on-policy deep reinforcement learning, as well as the need for tailored solutions that are effective across diverse environments and distribution shifts.
Mind map
Overview of plasticity loss in deep RL
Importance of adaptability in on-policy learning
Background
To investigate mitigation techniques for plasticity loss in on-policy settings
To identify effective strategies across diverse environments
Objective
Introduction
Selection of environments: gridworlds, Montezuma's Revenge, ProcGen, CoinRun
On-policy deep reinforcement learning algorithms
Data Collection
1. Type 1: Task variations
2. Type 2: Environment dynamics
3. Type 3: Curriculum learning
Impact on performance and adaptability
Distribution Shifts
Regenerative methods
Architectural interventions (CReLU, Plasticity Injection)
Regularization methods (shrink+perturb, LayerNorm, regenerative regularization)
Mitigation Techniques
Data Analysis
Performance evaluation in different scenarios
Control experiments with weight growth management
Experimental Design
Methodology
1. Regenerative Methods
Consistent improvement across environments
2. Distribution Shift Analysis
Impact on performance and tailored solutions
3. Architectural Interventions
CReLU and Plasticity Injection limitations
Promising regularization methods
4. Factors Affecting Plasticity Loss
Weight magnitude, dead units, gradient norms
Weight growth control strategies
5. Environment and Task Specificity
Success stories in gridworlds, CoinRun, Montezuma's Revenge
Key Findings
The need for tailored solutions in on-policy deep RL
Importance of understanding plasticity loss for generalization
Future directions and open challenges in the field
Conclusion
Outline
Introduction
Background
Overview of plasticity loss in deep RL
Importance of adaptability in on-policy learning
Objective
To investigate mitigation techniques for plasticity loss in on-policy settings
To identify effective strategies across diverse environments
Methodology
Data Collection
Selection of environments: gridworlds, Montezuma's Revenge, ProcGen, CoinRun
On-policy deep reinforcement learning algorithms
Data Analysis
Distribution Shifts
Type 1: Task variations
Type 2: Environment dynamics
Type 3: Curriculum learning
Impact on performance and adaptability
Mitigation Techniques
Regenerative methods
Architectural interventions (CReLU, Plasticity Injection)
Regularization methods (shrink+perturb, LayerNorm, regenerative regularization)
Experimental Design
Performance evaluation in different scenarios
Control experiments with weight growth management
Key Findings
Regenerative Methods
Consistent improvement across environments
Distribution Shift Analysis
Impact on performance and tailored solutions
Architectural Interventions
CReLU and Plasticity Injection limitations
Promising regularization methods
Factors Affecting Plasticity Loss
Weight magnitude, dead units, gradient norms
Weight growth control strategies
Environment and Task Specificity
Success stories in gridworlds, CoinRun, Montezuma's Revenge
Conclusion
The need for tailored solutions in on-policy deep RL
Importance of understanding plasticity loss for generalization
Future directions and open challenges in the field
Key findings
11

Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to address the issue of plasticity loss in on-policy deep reinforcement learning, which is a challenge where a neural network trained online shows a decreased ability to adapt to new tasks . While plasticity loss has been extensively studied in supervised learning and off-policy reinforcement learning, it has received less attention in the on-policy deep RL setting . The study conducted in the paper demonstrates that plasticity loss is prevalent under domain shift in the on-policy regime and proposes various mitigation methods to tackle this issue . This problem is not entirely new, as plasticity loss has been recognized in other learning settings, but the paper sheds light on its implications and solutions specifically in the context of on-policy deep reinforcement learning .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate the scientific hypothesis related to plasticity loss in on-policy deep reinforcement learning. It explores the phenomenon of plasticity loss in the on-policy reinforcement learning setting and introduces various forms of distribution shift to analyze this issue . The study extends the investigation of plasticity loss and the warm-start problem to the on-policy regime, highlighting the persistent nature of these challenges across different environmental distribution shift conditions . Additionally, the paper provides an in-depth analysis of the correlates of plasticity loss, studying different environmental settings, model architectures, and previously proposed mitigation approaches in the context of on-policy reinforcement learning .


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

The paper on plasticity loss in on-policy deep reinforcement learning introduces several new ideas, methods, and models to address this issue . One key contribution is the introduction of three distinct kinds of distribution shift to facilitate analysis, along with various environments and tasks for study . The paper highlights the persistence of plasticity loss across different environmental distribution shift conditions and provides an in-depth analysis of the correlates of these pathologies . Additionally, the study includes generalization trends in the consideration of these phenomena .

The paper characterizes properties of methods necessary for successful interventions in addressing plasticity loss and ensuring maintained generalization performance . It discusses the limitations of existing methods designed for supervised learning or off-policy reinforcement learning when applied to the on-policy setting or under the proposed forms of distribution shift . The study also describes several techniques that effectively resolve plasticity loss in the considered environments .

One of the proposed methods to address plasticity loss is Continual Backprop, which is a form of regularization towards the initialization distribution, selectively on a per-neuron basis . This approach is similar to ReDo and DrM, which are also analyzed in the paper . The study emphasizes the importance of continual regularizers over intermittent interventions in resolving plasticity loss in on-policy deep reinforcement learning .

Moreover, the paper discusses the class of regularization methods, including L2 regularization, ReDo, shrink+perturb, and regenerative regularization, which significantly mitigate plasticity loss in experiments . Among these methods, soft shrink+perturb displays the best generalization performance and can be combined with layer normalization, which has been effective in addressing plasticity loss in the on-policy setting . The regularization methods normalize network parameters towards their initial distribution, reducing weight magnitude and dead or saturated activation units . The paper on plasticity loss in on-policy deep reinforcement learning introduces novel methods with distinct characteristics and advantages compared to previous approaches . One key method, Shrink+Perturb, involves periodically reducing the magnitude of all weights in the network and adding noise sampled from a new weight initialization, leading to improved performance in batched continual learning settings . This method entangles two factors to sum to one, enhancing its effectiveness .

Another innovative approach proposed in the paper is Plasticity Injection, which replaces the final layer of a network with a new function that combines the final layer's output with the output of a newly initialized layer, leading to performance improvements in off-policy RL agents . This method involves blocking the gradient in both the original layer and the subtracted new layer, showcasing its unique characteristics .

Additionally, the study introduces Continuous Interventions, which are applied at every step of optimization without the need to detect distribution shifts, making them practical for mitigating plasticity loss . This method includes techniques like L2 Norm and LayerNorm, which involve regularizing the network using the L2 norm and applying layer normalization before the ReLU activation at each layer, respectively .

Furthermore, the paper discusses the advantages of the class of regularization methods, including L2 regularization, ReDo, shrink+perturb, and regenerative regularization, in significantly mitigating plasticity loss in experiments . Among these methods, soft shrink+perturb displays the best generalization performance and can be easily combined with layer normalization, showcasing its effectiveness and versatility . These regularization methods normalize network parameters towards their initial distribution, reducing weight magnitude and addressing dead or saturated activation units, which is crucial for mitigating plasticity loss .


Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

Several related research studies exist in the field of plasticity loss in on-policy deep reinforcement learning. Noteworthy researchers who have contributed to this topic include Ash and Adams , Lyle et al. , Nikishin et al. , and Schulman et al. . These researchers have explored various aspects of plasticity loss, policy collapse, and methods to address these challenges in deep reinforcement learning.

The key to the solution mentioned in the paper is the utilization of "regenerative" methods. The study demonstrates that regenerative methods consistently mitigate plasticity loss in on-policy deep reinforcement learning across different environments and distribution shifts. These regenerative methods act as continual regularizers, effectively addressing plasticity loss and improving performance in tasks like gridworld tasks, Montezuma’s Revenge, and ProcGen environments .


How were the experiments in the paper designed?

The experiments in the paper were designed to systematically characterize plasticity loss and its resolution in the on-policy setting by conducting a suite of experiments using different environments and distribution change conditions . The experiments involved three distinct forms of distribution shift organized into rounds, where each round supplied a set number of environments from a specific distribution to the agent for training and evaluation . The environmental modifications included strategies like permuting input pixels, using a window approach with new environments for the same task, and expanding the dataset with additional environments . These modifications induced significant performance changes and were aimed at studying plasticity loss in deep reinforcement learning .


What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study is the CoinRun environment from the ProcGen suite of tasks . The code used in the study is not explicitly mentioned as open source in the provided context.


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide strong support for the scientific hypotheses that need to be verified regarding plasticity loss in on-policy deep reinforcement learning. The study systematically characterizes plasticity loss and explores methods to address it in the on-policy setting . The experiments involve simulating environmental distribution shifts and testing various interventions to mitigate plasticity loss .

The paper conducts experiments using different environments such as a 2D gridworld, CoinRun environment, and the Atari game Montezuma’s Revenge, all trained using Proximal Policy Optimization (PPO) algorithms . These experiments aim to assess the impact of plasticity loss on learning performance and evaluate the effectiveness of interventions like regenerative regularization .

Furthermore, the results of statistical tests comparing different methods to baselines in various conditions provide valuable insights into the performance of interventions in mitigating plasticity loss . The study analyzes factors such as weight magnitudes, dead unit count, and gradient norms to predict plasticity loss and assess the effectiveness of different mitigation strategies .

Overall, the experiments and results in the paper offer a comprehensive analysis of plasticity loss in on-policy deep reinforcement learning, providing substantial evidence to support the scientific hypotheses under investigation and offering insights into effective strategies to address this phenomenon .


What are the contributions of this paper?

The contributions of the paper "A Study of Plasticity Loss in On-Policy Deep Reinforcement Learning" include:

  • Extending studies of plasticity loss and the warm-start problem to the on-policy regime, highlighting their persistence across various environmental distribution shift conditions .
  • Providing an in-depth analysis of the correlates of plasticity loss, studying different environmental settings, model architectures, and proposed mitigation approaches related to on-policy reinforcement learning, while considering generalization trends .
  • Characterizing properties of successful intervention methods to address plasticity loss and maintain generalization performance, along with providing recommendations based on these insights .

What work can be continued in depth?

Further research in the field of plasticity loss in on-policy deep reinforcement learning can be expanded in several directions based on the existing studies:

  • Investigating the impact of regenerative methods: Research can delve deeper into the effectiveness of regenerative methods in mitigating plasticity loss in various contexts, including gridworld tasks and challenging environments like Montezuma’s Revenge and ProcGen .
  • Exploring the distinction between ray interference and plasticity loss: Future studies could focus on distinguishing between ray interference and plasticity loss in the reinforcement learning setting, particularly for complex tasks like CoinRun or Montezuma’s Revenge, where unique sub-tasks may interfere with each other .
  • Studying the effectiveness of continual regularizers: Further analysis can be conducted on the performance of methods acting as continual regularizers, such as soft shrink+perturb and regenerative regularization, especially when combined with layer normalization, to address plasticity loss in on-policy deep reinforcement learning .
  • Investigating the impact of environmental distribution shift: Research can continue to simulate different forms of distribution shift to understand how plasticity-preserving interventions can mitigate plasticity loss in on-policy reinforcement learning, particularly in scenarios where data modifications induce performance degradation .
  • Evaluating the effectiveness of regularization methods: Future studies can focus on evaluating the efficacy of various regularization methods, such as L2 regularization, ReDo, and regenerative regularization, in addressing plasticity loss in deep neural networks, especially in the context of on-policy reinforcement learning .
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