C-GAIL: Stabilizing Generative Adversarial Imitation Learning with Control Theory

Summary

This paper theoretically analyzes the training dynamics of GAIL, a widely discussed issue in GANs, pointing out that the original GAIL cannot converge to the desired equilibrium. From a control theory perspective, the paper propose C-GAIL, which can achieve asymptotic stability. The paper demonstrate that C-GAIL, compared to several baseline methods, accelerates convergence, reduces oscillations, and more closely approximates the expert distribution in 5 typical MoJoCo control tasks.

Strengths

- Well-written paper with clear objectives. The authors have the intention to share the code. - The idea is novel for GAIL, although it draws on concepts from GAN. - Theoretical analysis is complete. - The method is simple to implement and can be easily applied to various existing GAIL methods.

Weaknesses

- The theoretical analysis is based on quite a few assumptions, and the final implementation method is only a rough approximation of the theoretical results. - The experimental section is not comprehensive enough. Given that the method is simple and easy to deploy, can its effectiveness be validated in more GAIL variants and environments? - There is a lack of comparison with the latest GAIL variant algorithms; only GAIL (2016) and GAIL-DAC (2018) are shown in Figures 1, 2, and 3. - There is a divergence between the theoretical motivation of the paper and the final algorithm implementation.

Questions

- What are the main differences between C-GAIL and similar methods in GANs? It is recommended to provide a separate discussion. - The authors claim that the reason for the original GAIL's failure to converge to equilibrium is due to the entropy regularization term. Removing entropy can ensure convergence to equilibrium at the cost of exploration. However, if $V^{\prime}_{\pi}$ is not computable, will it affect the policy's exploration? Compared to directly removing entropy, does C-GAIL show an advantage in exploration? - The theoretical analysis is based on the original GAIL, which measures JS divergence. For variants like WGAIL, LS-GAIL, and f-GAIL, can convergence and stability still be guaranteed? - How long is each expert demonstration in the experiments? How were the expert demonstrations obtained? - In Figure 2, what causes the significant drop in the blue line in the Hopper environment? Were the curves plotted using the averages of multiple experiments? - $\bar{s}$ and $\bar{a}$ in line 89 are undefined. - Table 2 lacks the expert reward baseline as a reference.

Rating

5

Confidence

3

Soundness

3

Presentation

2

Contribution

2

Limitations

The limitations of the method have been outlined in the discussion.

Summary

This paper proposes a stabilized version of the Generative Adversarial Imitation Learning (GAIL) through control theory, addressing limitations related to achieving equilibrium and slow convergence. The authors conduct a theoretical analysis using control theory to investigate the properties that influence equilibrium achievement. Empirical validation demonstrates that the proposed modifications improve performance and training stability.

Strengths

- The paper addresses an important problem in the stability of GAIL, which is crucial for the practical implementation of imitation learning techniques. - The paper provides a theoretical foundation, analyzes the GAIL objective, and demonstrates its limitations and proposed improvements. - The experimental results validate the theoretical claims, showing improved performance and stability in training.

Weaknesses

- It is unclear how the one-step GAIL, a simplified version, generalizes to the full GAIL framework and impacts policy learning. - The practical settings used in the experiment do not guarantee convergence, raising questions about the need for evaluating one-step GAIL. - The paper mentions using a linear negative feedback controller to reduce oscillations but lacks details on its implementation and usage.

Questions

1. How does the simplified one-step GAIL compare to the full GAIL in terms of performance and convergence? 2. Can the authors provide a quantitative analysis of training oscillations shown in Figure 1 and correlate them with training stability? It would be beneficial to quantify these oscillations, as they are a major contribution to the paper. It is mentioned 3 times for Walker2d at line 296, but how is this number computed? Similarly, 10x is mentioned in line 298. Additionally, how do these oscillations indicate training stability, and what is the correlation? 3. How is the controller designed and implemented in the system evaluated? Is there a way to automate the design of controllers u_1 and u_2, and what are the empirical hyperparameters involved? 4. In Figure 2, what is the high distance value on the y-axis for C-GAIL-DAC? Could the authors explain the initial higher values? 5. The number of demonstrations (four) mentioned (line 273) and used in the paper seems small. Can the authors elaborate on how this number suffices for learning effective policies?

Rating

7

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

Yes. The authors have addressed the limitations.

Summary

The paper formulated training process of GAIL as a dynamic system. From control theory’s view, authors pointed out GAIL would not converge to the desired state where the generator perfectly matches with the expert policy and the discriminator cannot distinguish generated from expert trajectories. Hence, authors proposed a new regularizer to stabilize GAIL.

Strengths

1. I have appreciated the logical framework regarding training process of GAIL as a dynamics system, where more control theory tools could be introduced in. 2. Theoretical analyses are solid, making proposed regularized more convincing. 3. The topic selection is meaningful, revealing the issue of training instability in GAIL. Proposed controller is quite necessary for stabilizing GAIL.

Weaknesses

1. This work showed GAIL cannot converge to the only desired state because of biased entropy term. Is it possible that entropy term introduces subtle bias in but improves stability a lot? The case will make your work meaningless. I think more experiment should be interpreted from this view. 2. The GAIL actually minimizes JS divergence between $\rho_{\pi_{E}}$ and $\rho_{\pi}$. For simplicity, the proposed 'C-GAIL' substituted $\rho_{\pi}$ with $\rho$. Does it ignore differences on state distribution? Why the performance still be good? 3. Did this work just substitute a biased regularizer with an unbiased one? It seems that authors should refer success of experiments only to strong convexity of applied controller. I think more details should be supplemented for making your analysis meaningful. 4. More advanced benchmarks should be compared in the experimental section.

Questions

1. Is there a missing parenthesis in the formula at line 181? $\tilde{V}_D(D, \pi)=\iint_0 p(s) \pi(a \mid s) \log D(s, a)+\pi_E(a \mid s) \log (1-D(s, a)) d s d a,$ 2. It seems tricky that theoretical analysis is done under a strict condition, where one-time step environment is considered and controllers are applied both on policy and discriminator, but original policy objective is applied for updating in implementation, although experimental results are good. Could you explain it more, making it convincing?

Rating

6

Confidence

4

Soundness

3

Presentation

3

Contribution

2

Limitations

The authors have discussed the limitations and future work in Section 7.

Summary

The paper titled "C-GAIL: Stabilizing Generative Adversarial Imitation Learning with Control Theory" addresses the challenge of training instability in Generative Adversarial Imitation Learning (GAIL), a method used to train a generative policy to imitate a demonstrator's behavior. The authors analyze GAIL's optimization from a control-theoretic perspective and identify that GAIL does not converge to the desired equilibrium due to the entropy term in its objective. To resolve this, they propose Controlled-GAIL (C-GAIL), which introduces a differentiable regularization term to the GAIL objective to stabilize training. Empirical results demonstrate that C-GAIL improves upon existing GAIL methods, including GAIL-DAC, by accelerating convergence, reducing oscillation, and more closely matching the expert's policy distribution. The paper contributes a novel control-theoretic approach to stabilize adversarial training in imitation learning, offering both theoretical insights and practical algorithmic advancements.

Strengths

1. The paper introduces a novel application of control theory to stabilize the training process of Generative Adversarial Imitation Learning (GAIL). By analyzing GAIL from a control-theoretic perspective, the authors provide a deeper understanding of the optimization challenges inherent in GAIL and propose a theoretical solution that ensures asymptotic stability. 2. The authors develop Controlled-GAIL (C-GAIL), a practical algorithm that incorporates a regularization term derived from control theory. This algorithm is shown to improve the stability and convergence of GAIL in empirical tests, offering a tangible advancement that can be applied to existing GAIL methods to enhance their performance. 3. The paper provides extensive empirical evidence to support the effectiveness of C-GAIL. Through experiments on MuJoCo control tasks, the authors demonstrate that C-GAIL achieves faster convergence, reduces the range of oscillation in training, and more closely matches the expert's policy distribution compared to both the original GAIL and other variants, showcasing the robustness and practical applicability of their approach.

Weaknesses

1. While the paper proposes a theoretically sound controller for stabilizing GAIL training, the practical implementation of the controller is only applied to the discriminator's objective function. The paper acknowledges that the generator's portion of the controller, which would require knowledge of the expert policy, is not used during training. This limitation means the full potential of the control-theoretic approach is not realized in practice. 2. The paper formulates GAIL training as a continuous dynamical system for the purpose of stability analysis. However, in actual practice, the updates to the generator and discriminator are discrete. The discrepancy between the theoretical model and the practical implementation could potentially affect the real-world applicability of the proposed controller. 3. The stability guarantees provided by the paper rely on certain assumptions, such as specific conditions on the hyperparameters of the controller. These assumptions might not hold in more general settings or across different problem domains, which could limit the broad applicability of the results. Additionally, the paper does not fully explore how violations of these assumptions might impact the performance of C-GAIL.

Questions

1. While the paper demonstrates the effectiveness of C-GAIL in the context of MuJoCo control tasks, how well does the proposed control-theoretic approach generalize to other domains, such as autonomous driving or game playing, where the dynamics of the environment and the complexity of the tasks might be significantly different? 2. Given that the practical updates in GAIL training are discrete whereas the theoretical model assumes a continuous dynamical system, what is the impact of this discrepancy on the long-term stability and performance of the learned policies, especially in tasks with high stochasticity or where the environment reacts non-linearly to actions? 3. The paper mentions that a proper selection of the hyperparameter k is crucial for the effectiveness of the C-GAIL controller. Can the authors provide more insights on how to determine the optimal values for these hyperparameters in a data-driven manner, without relying on extensive hyperparameter tuning, and how sensitive is the performance of C-GAIL to these choices?

Rating

5

Confidence

3

Soundness

2

Presentation

2

Contribution

2

Limitations

1. The paper formulates GAIL as a continuous dynamical system for the purpose of stability analysis, but in practice, updates to the generator and discriminator are discrete. This discrepancy between the theoretical model and practical implementation may impact the applicability of the theoretical results in real-world scenarios. 2. The practical implementation of the controller is applied only to the discriminator's objective function. The paper does not provide a method for incorporating a controller for the policy generator, which would require knowledge of the expert policy that is not available during training. 3. The stability guarantees are based on certain assumptions, such as hyperparameter conditions. The paper does not fully explore how the results might be affected when these assumptions do not hold, which could limit the generalizability of the findings to different settings or problem domains.

Summary

This paper addresses the problem of unstable training of Generative Adversarial Imitation Learning (GAIL). To this end, the paper studies the convergence of GAIL from a control-theoretic perspective and proposes to employ a regularization term for the discriminator loss function, which can stabilize the training. The experiments in the locomotion domain, e.g., Half-Cheetah and Walker2D, show that the proposed method leads to learned policies that match experts better, achieve better performance, and converge faster. I believe this work provides insightful analyses, presents a promising method, and sufficiently evaluates the proposed method. Hence, I recommend accepting this paper.

Strengths

**Motivation and novelty** - The motivation for stabilizing GAIL training is convincing. - Studying this from a control-theoretic perspective is novel to the best of my knowledge. **Clarity** - The overall writing is clear. **Experimental results** - The experiments in the locomotion domain, e.g., Half-Cheetah and Walker2D, show that the proposed method leads to learned policies that match experts better, achieve better performance, and converge faster.

Weaknesses

**Figure 2 standard deviation** - Are the results reported in Figure 2 aggregated from five random seeds? Since Figure 2 does not show standard deviation, I am unsure if the gaps are statistically significant. **Table 1 Hopper results** - I am wondering why BC (2830) outperforms the expert (2631) in Hopper. **Limited domains for evaluation** - The evaluation is limited to locomotion, e.g., Half-Cheetah and Walker2D. Experimenting with the proposed method and the baselines in other domains, such as navigation (grid world or point maze in D4RL), robot arm manipulation (OpenAI Fetch or Shadow Dexterous Hand), and games (Atari) would significantly strengthen the results. **Visualized state distributions** - I appreciate the authors showing the state Wasserstein distance between expert and learned policies in Figure 2. I feel it would be informative to visualize the state distributions of expert and learned policies. For example, we can use a grid world navigation task with discrete state and action spaces. Then, we can visualize the state distributions of expert and learned policies as heatmaps and put them side by side for comparison. I believe this would make the claim that C-GAIL-DAC can match the expert state distributions better and more convincing. **Related work** - Including the descriptions of more recent IL methods could make the related work more comprehensive, such as - Diffusion policy (https://arxiv.org/abs/2303.04137v4 https://arxiv.org/abs/2403.03954) - Consistency Policy (https://arxiv.org/abs/2405.07503) - Diffusion BC (https://arxiv.org/abs/2302.13335) - DiffAIL (https://arxiv.org/abs/2312.06348) / DRAIL (https://arxiv.org/abs/2405.16194v1)

Questions

See above

Rating

8

Confidence

5

Soundness

3

Presentation

3

Contribution

3

Limitations

Yes

Re: Rebuttal by Authors

I appreciate the authors for reporting the error bars, and providing additional Atari experiments on and comparisons to DiffAIL. I believe this paper presents solid contributions and should be accepted. Hence, I increased my score to 8 (strong accept).

Thanks for your clarification

Thanks for your rebuttal. I still think that there is a significant difference between the theoretical foundation of the paper and the actual algorithm presented. However, competitive experimental results have alleviated this concern. I decided to improve my score to 5.