# Towards Analyzing and Understanding the Limitations of DPO: A Theoretical Perspective

arXiv: https://arxiv.org/abs/2404.04626 · HTML: https://mlsanity.com/paper/2404.04626/

## Key facts

- Cited by 69 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 15 of its 22 references that are in the map.
- First posted on arXiv 6 Apr 2024.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 15 of 15)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [Understanding Dataset Difficulty with V-Usable Information](https://mlsanity.com/paper/2110.08420/) (2021)
- [Smaug: Fixing Failure Modes of Preference Optimisation with DPO-Positive](https://mlsanity.com/paper/2402.13228/) (2024)
- [Implementation Matters in Deep Policy Gradients: A Case Study on PPO and TRPO](https://mlsanity.com/paper/2005.12729/) (2020)
- [Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints](https://mlsanity.com/paper/2309.16240/) (2023)
- [Direct Preference Optimization with an Offset](https://mlsanity.com/paper/2402.10571/) (2024)
- [The Numerics of GANs](https://mlsanity.com/paper/1705.10461/) (2017)
- [Reward Generalization in RLHF: A Topological Perspective](https://mlsanity.com/paper/2402.10184/) (2024)

## Built on by (most cited first, 30 of 69)

- [Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability](https://mlsanity.com/paper/2411.19943/) (2024)
- [Fin-R1: A Large Language Model for Financial Reasoning through Reinforcement Learning](https://mlsanity.com/paper/2503.16252/) (2025)
- [Unintentional Unalignment: Likelihood Displacement in Direct Preference Optimization](https://mlsanity.com/paper/2410.08847/) (2024)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [Cal-DPO: Calibrated Direct Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2412.14516/) (2024)
- [Anchored Preference Optimization and Contrastive Revisions: Addressing Underspecification in Alignment](https://mlsanity.com/paper/2408.06266/) (2024)
- [Improving LLM Safety Alignment with Dual-Objective Optimization](https://mlsanity.com/paper/2503.03710/) (2025)
- [TIS-DPO: Token-level Importance Sampling for Direct Preference Optimization With Estimated Weights](https://mlsanity.com/paper/2410.04350/) (2024)
- [A Survey of Direct Preference Optimization](https://mlsanity.com/paper/2503.11701/) (2025)
- [DenseDPO: Fine-Grained Temporal Preference Optimization for Video Diffusion Models](https://mlsanity.com/paper/2506.03517/) (2025)
- [A Comprehensive Survey of Direct Preference Optimization: Datasets, Theories, Variants, and Applications](https://mlsanity.com/paper/2410.15595/) (2024)
- [Modality-Fair Preference Optimization for Trustworthy MLLM Alignment](https://mlsanity.com/paper/2410.15334/) (2024)
- [3D-Properties: Identifying Challenges in DPO and Charting a Path Forward](https://mlsanity.com/paper/2406.07327/) (2024)
- [Bayesian scaling laws for in-context learning](https://mlsanity.com/paper/2410.16531/) (2024)
- [SPRec: Self-Play to Debias LLM-based Recommendation](https://mlsanity.com/paper/2412.09243/) (2024)
- [Towards a Unified View of Preference Learning for Large Language Models: A Survey](https://mlsanity.com/paper/2409.02795/) (2024)
- [Generalizing Alignment Paradigm of Text-to-Image Generation with Preferences through f-divergence Minimization](https://mlsanity.com/paper/2409.09774/) (2024)
- [SafeMobile: Chain-level Jailbreak Detection and Automated Evaluation for Multimodal Mobile Agents](https://mlsanity.com/paper/2507.00841/) (2025)
- [Dual-IPO: Dual-Iterative Preference Optimization for Text-to-Video Generation](https://mlsanity.com/paper/2502.02088/) (2025)
- [Understanding the Performance Gap in Preference Learning: A Dichotomy of RLHF and DPO](https://mlsanity.com/paper/2505.19770/) (2025)
- [Value Drifts: Tracing Value Alignment During LLM Post-Training](https://mlsanity.com/paper/2510.26707/) (2025)
- [Uni-DPO: A Unified Paradigm for Dynamic Preference Optimization of LLMs](https://mlsanity.com/paper/2506.10054/) (2025)
- [Length Desensitization in Direct Preference Optimization](https://mlsanity.com/paper/2409.06411/) (2024)
- [RefineCoder: Iterative Improving of Large Language Models via Adaptive Critique Refinement for Code Generation](https://mlsanity.com/paper/2502.09183/) (2025)
- [Not Everything is All You Need: Toward Low-Redundant Optimization for Large Language Model Alignment](https://mlsanity.com/paper/2406.12606/) (2024)
- [Enhancing Tool Learning in Large Language Models with Hierarchical Error Checklists](https://mlsanity.com/paper/2506.00042/) (2025)
- [SPACE: Noise Contrastive Estimation Stabilizes Self-Play Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2512.07175/) (2025)
- [Fine Tuning Large Language Models for Medicine: The Role and Importance of Direct Preference Optimization](https://mlsanity.com/paper/2409.12741/) (2024)
- [GDPO: Learning to Directly Align Language Models with Diversity Using GFlowNets](https://mlsanity.com/paper/2410.15096/) (2024)
- [CodeLutra: Boosting LLM Code Generation via Preference-Guided Refinement](https://mlsanity.com/paper/2411.05199/) (2024)

## Abstract (arXiv)

Direct Preference Optimization (DPO), which derives reward signals directly from pairwise preference data, has shown its effectiveness on aligning Large Language Models (LLMs) with human preferences. Despite its widespread use across various tasks, DPO has been criticized for its sensitivity to the SFT's effectiveness and its hindrance to the learning capacity towards human-preferred responses, leading to less satisfactory performance. To overcome those limitations, the theoretical understanding of DPO are indispensable but still lacking. To this end, we take a step towards theoretically analyzing and understanding the limitations of DPO. Specifically, we provide an analytical framework using the field theory to analyze the optimization process of DPO. By analyzing the gradient vector field of the DPO loss function, we find that the DPO loss function decreases the probability of producing human dispreferred data at a faster rate than it increases the probability of producing preferred data. This provides theoretical insights for understanding the limitations of DPO discovered in the related research experiments, thereby setting the foundation for its improvement.