Understanding the Performance Gap in Preference Learning: A Dichotomy of RLHF and DPO (2505.19770v1)

Abstract: We present a fine-grained theoretical analysis of the performance gap between reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO) under a representation gap. Our study decomposes this gap into two sources: an explicit representation gap under exact optimization and an implicit representation gap under finite samples. In the exact optimization setting, we characterize how the relative capacities of the reward and policy model classes influence the final policy qualities. We show that RLHF, DPO, or online DPO can outperform one another depending on the type of model mis-specifications. Notably, online DPO can outperform both RLHF and standard DPO when the reward and policy model classes are isomorphic and both mis-specified. In the approximate optimization setting, we provide a concrete construction where the ground-truth reward is implicitly sparse and show that RLHF requires significantly fewer samples than DPO to recover an effective reward model -- highlighting a statistical advantage of two-stage learning. Together, these results provide a comprehensive understanding of the performance gap between RLHF and DPO under various settings, and offer practical insights into when each method is preferred.

• The paper analyzes the performance gap between RLHF and DPO, showing differences arise primarily from explicit and implicit representation gaps when reward or policy models are mis-specified.
• Under policy model mis-specification, RLHF outperforms DPO by leveraging accurately modeled rewards, whereas DPO performs better with reward model mis-specification by optimizing solely based on preferences.
• RLHF demonstrates better statistical efficiency than DPO when reward functions are sparse, requiring fewer samples for accurate estimation in large-scale data settings.

Performance Gap in Preference-Based Policy Learning: RLHF vs DPO

The paper entitled Understanding the Performance Gap in Preference Learning: A Dichotomy of RLHF and DPO meticulously investigates the complex interaction between reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO) in preference-based policy learning. The central focus of the paper is the performance discrepancies between RLHF and DPO, arising predominantly from representation gaps when model specifications deviate from their ideal forms.

Analytical Insights

The authors dissect the performance gap into two primary sources: explicit and implicit representation gaps. The explicit gap arises under exact optimization conditions, in which the representation capabilities of reward and policy model classes are crucial. Here, both RLHF and DPO are thoroughly examined to determine their respective advantages and deficiencies under various model mis-specifications.

1. Exact Optimization with No Mis-specification: The paper confirms that when both the reward and policy models are perfectly specified (realizable ground truth), RLHF and DPO converge upon the same optimal policy. This equivalence suggests that under ideal conditions, the choice between RLHF and DPO is largely a matter of procedural preference rather than performance.
2. Policy Model Mis-specification: When the policy model cannot realize the optimal solution, RLHF demonstrates superiority by optimizing the reward model first, thereby achieving better policy outcomes than DPO. This reflects RLHF’s proficiency in leveraging accurately modeled rewards to enhance policy learning.
3. Reward Model Mis-specification: Conversely, when the reward model is mis-specified, DPO can still achieve an optimal policy defined solely by preferences, outperforming RLHF which might be constrained by its sub-optimal reward model.
4. Double Mis-specification: The interplay between reward and policy classes becomes complex in scenarios of mutual mis-specification. When reward and policy model classes are isomorphic, RLHF and DPO exhibit similar performance, yet online DPO may offer improved outcomes. The findings stress the importance of model architecture choice, advocating for scenarios where DPO’s iterative refinements can leverage feedback loops.

The paper also explores approximate optimization settings, highlighting statistical efficiency gaps between RLHF and DPO. Particularly, it demonstrates RLHF’s ability to capitalize on sparse representations of the reward function, notably reducing sample complexity compared to DPO. This advantage becomes pronounced when handling large-scale, sparse data where reward model sparsity allows RLHF to achieve accurate estimations with fewer samples.

Empirical Substantiation

Empirical results reinforce theoretical claims, indicating that RLHF’s structured two-stage approach can consistently outperform DPO when reward learning is efficiently integrated, especially in realistic settings where computational constraints prevail. Experimental data illustrate the robustness of RLHF in adapting to various preference learning contexts, while emphasizing the pitfalls DPO faces when policy models are inaccurately specified.

Implications and Future Directions

The paper presents invaluable insights into the conditions under which RLHF or DPO should be adopted. Practitioners in AI and machine learning now have a clearer understanding of the strategic deployment of RLHF over DPO in contexts where reward realizability is uncertain or computational resources are limited. The theoretical frameworks introduced not only clarify current methodological choices but also encourage future advancements in preference-based policy learning algorithms, particularly in developing models that deftly manage sparse and mis-specified conditions.

Future research might explore the potential of hybrid models that combine the strengths of RLHF and DPO, crafting algorithms capable of dynamically selecting reward and policy optimization pathways based on the model specifications and environment constraints. The findings could also inform the development of more adaptive frameworks that leverage the inherent strengths of RLHF’s two-stage learning, enhancing statistical efficiency and policy accuracy in broader applications.