REBEL: Reinforcement Learning via Regressing Relative Rewards

While originally developed for continuous control problems, Proximal Policy Optimization (PPO) has emerged as the work-horse of a variety of reinforcement learning (RL) applications, including the fine-tuning of generative models. Unfortunately, PPO requires multiple heuristics to enable stable convergence (e.g. value networks, clipping), and is notorious for its sensitivity to the precise implementation of these components. In response, we take a step back and ask what a minimalist RL algorithm for the era of generative models would look like. We propose REBEL, an algorithm that cleanly reduces the problem of policy optimization to regressing the relative reward between two completions to a prompt in terms of the policy, enabling strikingly lightweight implementation. In theory, we prove that fundamental RL algorithms like Natural Policy Gradient can be seen as variants of REBEL, which allows us to match the strongest known theoretical guarantees in terms of convergence and sample complexity in the RL literature. REBEL can also cleanly incorporate offline data and be extended to handle the intransitive preferences we frequently see in practice. Empirically, we find that REBEL provides a unified approach to language modeling and image generation with stronger or similar performance as PPO and DPO, all while being simpler to implement and more computationally efficient than PPO. When fine-tuning Llama-3-8B-Instruct, REBEL achieves strong performance in AlpacaEval 2.0, MT-Bench, and Open LLM Leaderboard.

Paper

Similar papers

Peer review

Reviewer zZ2j7/10 · confidence 3/52024-07-09

Summary

This paper reduces the complex policy optimization procedure of alignment to a simple regression objective, using the relation between optimal policy and reward. The paper conduct detailed theoretical analysis in revealing the relation between the proposed algorithm *REBEL* and *NPG/MD*. Comprehensive experiments in both text and image generation exhibit the effectiveness of *REBEL*.

Strengths

1. This paper studies simplified version of policy optimization in RLHF (compared to PPO), which is a research topic of interest. 2. The theoretical analysis of *REBEL* is detailed and insightful. 3. The presentation of this paper is logically clear and has good readability. 4. The experiments in this paper are comprehensive, and the experimental results are well presented.

Weaknesses

1. The statement "REBEL ... be extended to handle intransistive preferences ...." in the abstract is not adequately presented in the main content of the paper. As the major influence brought by intransistive preferences is the degradation of reward score accuracy, which is not addressed by this paper. 2. I would suggest the authors to summarize the limitations of the proposed method in a separate "Limitations" section.

Questions

none

Rating

7

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

none

Reviewer ihUH5/10 · confidence 4/52024-07-16

Summary

This paper proposes the REBEL algorithm that reduces policy optimization to iteratively solving squared loss regression problems on the difference in rewards between trajectories, based on DPO's analysis. The paper transforms the resulting equation for r(x, y) presented in DPO to a regression loss function, and avoids the intractable calculation of Z(x) by calculating the loss based on a pair of samples from the same input prompt x, i.e., (x, y) and (x, y'). One of the goals for REBEL is to serve as a simple and lightweight RL algorithm that eliminates the need for complex components like value functions and clipping heuristics used in PPO. The authors provide a theoretical analysis showing that Natural Policy Gradient can be seen as a special case of REBEL under some assumptions. The authors conduct two kinds of empirical analysis including language modeling and image generation tasks to demonstrate the performance of REBEL.

Strengths

- Originality: - This paper presents a new angle by transforming the analysis of the reward function presented in the DPO paper into a reward regression loss, leading to the proposed REBEL algorithm. - The authors make connections between REBEL and existing RL methods like NPG considering some assumptions, showing that these algorithms can be seen as special cases or approximations of REBEL under certain conditions. - Quality: - The paper provides a thorough theoretical analysis comparing REBEL with existing RL approaches. - Clarity: - The paper is well-written and easy to understand, with a clear logical flow from motivation to theoretical analysis to empirical validation. The authors do an good job of explaining the intuition behind REBEL and highlighting its connections to prior work. - Significance: - The paper tackles the important problem of developing simpler and more efficient RL algorithms that can scale to large-scale generative model fine-tuning.

Weaknesses

1. Insufficient experimental validation and limited baseline comparisons: - While the paper presents empirical results on language modeling and image generation tasks, the experimental validation of REBEL could be more comprehensive. The authors should consider including a wider range of benchmarks and datasets to demonstrate the generality and robustness of their approach. - The comparison with baseline algorithms like PPO and DPO is somewhat limited. The authors should provide more details on the hyperparameter settings and training procedures for the baselines to ensure a fair comparison. Moreover, the poor performance of DPO compared to PPO in the experiments raises questions about the implementation or hyperparameter choices. - The authors claim that REBEL matches the strongest known theoretical guarantees in terms of convergence and sample complexity. However, the experiments only compare performance at a specific epoch without demonstrating improved sample efficiency. Convergence plots showing the performance of REBEL and baselines over the course of training would provide a clearer picture of the sample efficiency and convergence properties. 2. Lack of support for certain claims and limited exploration of key aspects: - The paper makes several claims regarding the advantages of REBEL, such as its ability to handle intransitive preferences, incorporate offline datasets, and apply to deterministic MDPs. However, there is a lack of corresponding experimental evidence or theoretical analysis to substantiate these claims. - The relationship between the regressor's performance and the quality of the dataset used for training is not explored in depth. Insights or experiments that investigate how dataset quality and diversity affect the regressor's ability to capture an improved policy would strengthen the paper. - The choice of base distribution \mu is mentioned as a determining factor for whether REBEL is hybrid or fully online. However, the paper does not provide experimental results comparing different forms of \mu across various tasks or practical guidelines for choosing \mu in real-world applications. 3. Inconsistencies and potential conflicts with previous statements: - The authors mention that critic-based variance reduction might be necessary for high-variance trajectory-level rewards in stochastic MDPs, which seems to contradict the criticism of PPO's complexity in the introductory section. The lack of experimental support for REBEL's performance in stochastic MDPs is a significant limitation, and the authors should provide preliminary results or theoretical insights to support their claims.

Questions

1. Sample efficiency and convergence guarantees: - The authors claim that REBEL matches the strongest known theoretical guarantees in terms of convergence and sample complexity. However, the experiments only compare performance at a specific epoch without demonstrating improved sample efficiency. Can the authors provide experimental results that support their claim of improved sample efficiency compared to other algorithms? - It would be helpful to see convergence plots that show the performance of REBEL and baseline algorithms over the course of training, rather than just at a selected epoch. This would provide a clearer picture of the sample efficiency and convergence properties of REBEL. 2. Relationship between regressor performance and dataset quality: - The authors state that a regressor that can predict the difference in rewards between trajectories implicitly captures an improved policy. Is the performance of this regressor dependent on the quality of the dataset used for training? How does the quality of the dataset affect the regressor's ability to capture an improved policy? - Can the authors provide insights or experiments that explore the relationship between dataset quality and the effectiveness of REBEL? 3. Applicability to deterministic MDPs: - The authors mention that REBEL can be applied to any deterministic MDP where the initial state is x and the trajectory y consists of a sequence of actions. Is there any experimental or theoretical support for this claim? - It would strengthen the paper if the authors could provide empirical results or theoretical analysis that demonstrates the effectiveness of REBEL in deterministic MDPs beyond the bandit formulation. 4. Choice of base distribution \mu: - The authors state that the choice of base distribution \mu determines whether REBEL is hybrid or fully online. Can they provide experimental results that compare different forms of \mu across various types of tasks? What are the practical guidelines for choosing \mu in real-world applications? - Insights into the impact of different choices of \mu on the performance and behavior of REBEL would be valuable for practitioners looking to apply this algorithm. 5. Stochastic MDPs and the need for critic-based variance reduction: - The authors leave the experimental validation of REBEL in stochastic MDPs for future work but mention that trajectory-level rewards can be high-variance, potentially requiring critic-based variance reduction. In what practical situations would the transition dynamics be stochastic? If critic-based variance reduction is needed, how does this align with the introductory section's criticism of PPO's complexity? - The lack of experimental support for REBEL's performance in stochastic MDPs is a significant limitation. Can the authors provide any preliminary results or theoretical insights that support their claims about REBEL's applicability to stochastic environments? 6. Performance comparison with baselines: - In the experiments conducted by the authors, DPO performs significantly worse than PPO, especially in Table 1, where DPO is inferior in every case. Can the authors provide an explanation for this discrepancy? Is it due to differences in implementation or hyperparameter settings? - In Figure 3, the comparison between PPO and REBEL is made at an intermediate checkpoint where REBEL observes a higher reward under the reward model. Is it possible that PPO has already overfit at this selected epoch? How was this specific epoch number chosen for REBEL? What would the comparison look like if the best-performing epoch for each algorithm were considered? Additionally, why is the comparison limited to only PPO? It would be informative to include other state-of-the-art RL algorithms in the comparison to better understand the relative performance of REBEL.

Rating

5

Confidence

4

Soundness

3

Presentation

3

Contribution

2

Limitations

Yes.

Reviewer HFsB7/10 · confidence 3/52024-07-16

Summary

This work presents REBEL, a minimalist reinforcement learning algorithm that does policy optimization by solving a sequence of regression problems using relative rewards as targets. Theoretical analysis shows that Natural Policy Gradient (NPG) is a variant of REBEL, and thus theoretical guarantees for NPG can be applied to REBEL. Experimental results show that REBEL matches or outperforms existing baselines, most notably PPO and RLOO, on multiple tasks.

Strengths

- The paper is well-organized and technically sound. The general flow of the paper is smooth and proposed methods are explained adequately. The paper has an appropriate number of citations and properly details existing work in the related work section. - The method is simple to implement and has little engineering overhead. Given the minimalist implementation, the results are impressive, surpassing even PPO, which typically requires significant engineering.

Weaknesses

- There are no significant weaknesses in this work, barring some clarifying details. - I believe that at least a brief section on related work should be included in the main paper, the in-depth one can be deferred to the appendix. In terms of space, I personally do not think Section 2.2 adds much value to the main paper.

Questions

- The reward model becomes increasingly off-distribution as the policy is updated. Although it is standard practice to keep reward models fixed even with iterative methods, prior works generally use it to generate preference labels between pairs of outputs. Since this work uses the difference of scores as the regression target, the off-distribution reward scores might have a greater impact here. Concisely, how significant a problem is reward model over-optimization [1] for REBEL? - It would be interesting to see and understand the differences between reward-weighted regression baseline (RWR) and REBEL as they have some close connections. - Is there an optimal choice of $\mu$ ? What are the intuitive differences between using the $\mu= \pi_{ref}$ and $\mu= \pi_{t}$ ? As the policy improves, samples $y,y’ \sim \pi_{t}$ are in the high reward region, and it can be difficult to separate them since these might be off-distribution for the reward model. Given these constraints of the reward model, there might be better choices of $\mu$ that allow for better prediction of score differences. It would be interesting to see an ablation study on this, or a well-reasoned answer that explains the tradeoffs between different choices of $\mu$. - Why are datasets not aggregated? Instead, only the most recently collected dataset is used for training. [1] : Gao, L., Schulman, J., & Hilton, J. (2023, July). Scaling laws for reward model overoptimization. In International Conference on Machine Learning (pp. 10835-10866). PMLR.

Rating

7

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

N/A

Reviewer dEG58/10 · confidence 3/52024-07-20

Summary

The authors present REBEL, a method for solving contextual bandit problems (such as the alignment of language models) via regressing relative rewards. They first derive their objective by demonstrating that the use of paired responses means that you can get rid of the partition function, which is impossible to estimate. They then connect their method to previous methods in RL including detailing, but not . They demonstrate that under strong assumptions REBEL is equivalent to mirror descent, and that under assumptions of coverage by the reference policy, that REBEL produces returns close to an optimal policy. Finally the authors run experiments on summarisation, general chat and image alignment, demonstrating their method compares favourably to other methods.

Strengths

* The idea of using relative rewards to remove the partition function is a nice and simple idea * The theoretical connections of their method to prior methods grounds their work nicely in existing RL approaches. * The empirical results seem to demonstrate their method is competitive or better than other approaches. * REBEL compares favourably in terms of runtime and memory usage with other, similarly performing methods. Overall the theoretical and empirical examinations of their method seems very thorough.

Weaknesses

See questions

Questions

* Do the authors have any idea why REBEL seems to have a slightly higher KL than the other methods? * Although in image alignment REBEL seems to do similarly to PPO, it also has higher variance. Do you know why that might be? * Are the results for the 6.8B model significant? It seems as though REBEL produces very similar performance to e.g. PPO. For the smaller models the separation seems larger, is there a reason why the separation in performance between REBEL and other methods is bigger for smaller models? * What are the error bars in Table 1? Is that standard deviation?

Rating

8

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors discuss the limitations throughout their work at relevant stages.

Reviewer HFsB2024-08-10

Reply to rebuttal

I thank the authors for the rebuttal. My doubts have been cleared and I have raised my score to reflect the same.

Reviewer ihUH2024-08-12

Thank the authors for the rebuttal. However, I still find some of the responses to my questions to be somewhat evasive, and I would appreciate more detailed explanations from the authors. I would also be happy to increase the score if all my concerns are adequately addressed. 1. Regarding DPO's performance: The authors mention that DPO performs better than reported in [3] for the TL;DR task. However, why is this improvement limited to the TL;DR task and not observed in other tasks? Could you provide a more comprehensive explanation for DPO's underwhelming performance in other areas? 2. On REBEL's convergence guarantee: While the plots empirically demonstrates REBEL's faster convergence, the paper's main argument centers on theoretical explanations. Could you provide a corresponding theoretical justification for this faster convergence to complement the empirical evidence? 3. Concerning stochastic MDPs: Given the limited analysis provided for stochastic MDPs, I'm curious about the rationale for including this section in the main text, since there are not sufficient empirical support to this added part.

Authorsrebuttal2024-08-13

We thank the reviewer for the response and address each of the points below. > Regarding DPO's performance: The authors mention that DPO performs better than reported in [3] for the TL;DR task. However, why is this improvement limited to the TL;DR task and not observed in other tasks? Could you provide a more comprehensive explanation for DPO's underwhelming performance in other areas? In our experiments, we only performed experiments with DPO on the TL;DR summarization task. The improvement in performance regarding summarization could be due to differences in prompt, test time model temperature, or other factors. In particular, [3] used a temperature of 1.0 during the evaluation, while we used a temperature of 0.9. We referenced [3] to demonstrate that our DPO results are consistent with those reported by other independent researchers, indicating that our findings of DPO are reasonable within the existing literature. > On REBEL's convergence guarantee: While the plots empirically demonstrates REBEL's faster convergence, the paper's main argument centers on theoretical explanations. Could you provide a corresponding theoretical justification for this faster convergence to complement the empirical evidence? We provide a detailed analysis of REBEL's convergence rate in lines 140-147 and 200-217 of our paper. Specifically, we show that REBEL achieves a fast $1/T$ convergence under the assumption that the least square regression optimization returns the exact Bayes optimal solution. We then relax this assumption using a regression generalization bound, resulting in an agnostic regret bound with a convergence rate of $1/\sqrt{T}$. This agnostic regret bound represents the strongest type of agnostic learning results known in the RL literature. On the other hand, to the best of our knowledge, we do not know if PPO — our baseline in the image generative model experiment, has provable convergence guarantees. One reason that PPO convergence can be slower than REBEL is that PPO uses clipping to approximately maintain conservative policy update and the clipping operator throws away a non-trivial amount of training data. REBEL on the other hand does not use clipping and thus does not waste any training data. > Concerning stochastic MDPs: Given the limited analysis provided for stochastic MDPs, I'm curious about the rationale for including this section in the main text, since there are not sufficient empirical support to this added part. This point was also raised by Reviewer HFsB. We fully agree with this feedback and will move this section to the appendix.

Reviewer dEG52024-08-12

Response

Thank you very much for the responses to my questions. I will maintain my score and continue to believe this is an excellent paper.

Reviewer zZ2j2024-08-13

Thank you for your response, my concerns have been addressed during the rebuttal and I decide to keep my score.

Program Chairsdecision2024-09-25

Decision

Accept (poster)

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