# Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints

arXiv: https://arxiv.org/abs/2309.16240 · HTML: https://mlsanity.com/paper/2309.16240/

## Key facts

- Cited by 174 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 37 of its 48 references that are in the map.
- First posted on arXiv 28 Sep 2023.

## Placed in

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

## Builds on (most cited first, 30 of 37)

- [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)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [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)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [A Diversity-Promoting Objective Function for Neural Conversation Models](https://mlsanity.com/paper/1510.03055/) (2015)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [Red Teaming Language Models with Language Models](https://mlsanity.com/paper/2202.03286/) (2022)
- [Whose Opinions Do Language Models Reflect?](https://mlsanity.com/paper/2303.17548/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Improving alignment of dialogue agents via targeted human judgements](https://mlsanity.com/paper/2209.14375/) (2022)
- [Texygen: A Benchmarking Platform for Text Generation Models](https://mlsanity.com/paper/1802.01886/) (2018)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [Scalable agent alignment via reward modeling: a research direction](https://mlsanity.com/paper/1811.07871/) (2018)
- [AI safety via debate](https://mlsanity.com/paper/1805.00899/) (2018)
- [Pretraining Language Models with Human Preferences](https://mlsanity.com/paper/2302.08582/) (2023)

## Built on by (most cited first, 30 of 174)

- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [Rewards-in-Context: Multi-objective Alignment of Foundation Models with Dynamic Preference Adjustment](https://mlsanity.com/paper/2402.10207/) (2024)
- [Token-level Direct Preference Optimization](https://mlsanity.com/paper/2404.11999/) (2024)
- [Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systems](https://mlsanity.com/paper/2504.01990/) (2025)
- [Multi-IF: Benchmarking LLMs on Multi-Turn and Multilingual Instructions Following](https://mlsanity.com/paper/2410.15553/) (2024)
- [Decoding-Time Language Model Alignment with Multiple Objectives](https://mlsanity.com/paper/2406.18853/) (2024)
- [Test-time Alignment of Diffusion Models without Reward Over-optimization](https://mlsanity.com/paper/2501.05803/) (2025)
- [Human Alignment of Large Language Models through Online Preference Optimisation](https://mlsanity.com/paper/2403.08635/) (2024)
- [β-DPO: Direct Preference Optimization with Dynamic β](https://mlsanity.com/paper/2407.08639/) (2024)
- [Noise Contrastive Alignment of Language Models with Explicit Rewards](https://mlsanity.com/paper/2402.05369/) (2024)
- [Correcting the Mythos of KL-Regularization: Direct Alignment without Overoptimization via Chi-Squared Preference Optimization](https://mlsanity.com/paper/2407.13399/) (2024)
- [On the Algorithmic Bias of Aligning Large Language Models with RLHF: Preference Collapse and Matching Regularization](https://mlsanity.com/paper/2405.16455/) (2024)
- [wd1: Weighted Policy Optimization for Reasoning in Diffusion Language Models](https://mlsanity.com/paper/2507.08838/) (2025)
- [Towards Analyzing and Understanding the Limitations of DPO: A Theoretical Perspective](https://mlsanity.com/paper/2404.04626/) (2024)
- [Rethinking Kullback-Leibler Divergence in Knowledge Distillation for Large Language Models](https://mlsanity.com/paper/2404.02657/) (2024)
- [On Softmax Direct Preference Optimization for Recommendation](https://mlsanity.com/paper/2406.09215/) (2024)
- [JetMoE: Reaching Llama2 Performance with 0.1M Dollars](https://mlsanity.com/paper/2404.07413/) (2024)
- [Learn Your Reference Model for Real Good Alignment](https://mlsanity.com/paper/2404.09656/) (2024)
- [Towards Robust Alignment of Language Models: Distributionally Robustifying Direct Preference Optimization](https://mlsanity.com/paper/2407.07880/) (2024)
- [Online Iterative Reinforcement Learning from Human Feedback with General Preference Model](https://mlsanity.com/paper/2402.07314/) (2024)
- [Diverse Preference Optimization](https://mlsanity.com/paper/2501.18101/) (2025)
- [Cal-DPO: Calibrated Direct Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2412.14516/) (2024)
- [Correlated Proxies: A New Definition and Improved Mitigation for Reward Hacking](https://mlsanity.com/paper/2403.03185/) (2024)
- [Offline Regularised Reinforcement Learning for Large Language Models Alignment](https://mlsanity.com/paper/2405.19107/) (2024)
- [Model Merging and Safety Alignment: One Bad Model Spoils the Bunch](https://mlsanity.com/paper/2406.14563/) (2024)
- [Fine-tuning of diffusion models via stochastic control: entropy regularization and beyond](https://mlsanity.com/paper/2403.06279/) (2024)
- [NFT: Bridging Supervised Learning and Reinforcement Learning in Math Reasoning](https://mlsanity.com/paper/2505.18116/) (2025)
- [SafeDPO: A Simple Approach to Direct Preference Optimization with Enhanced Safety](https://mlsanity.com/paper/2505.20065/) (2025)
- [The Choice of Divergence: A Neglected Key to Mitigating Diversity Collapse in Reinforcement Learning with Verifiable Reward](https://mlsanity.com/paper/2509.07430/) (2025)

## Abstract (arXiv)

The increasing capabilities of large language models (LLMs) raise opportunities for artificial general intelligence but concurrently amplify safety concerns, such as potential misuse of AI systems, necessitating effective AI alignment. Reinforcement Learning from Human Feedback (RLHF) has emerged as a promising pathway towards AI alignment but brings forth challenges due to its complexity and dependence on a separate reward model. Direct Preference Optimization (DPO) has been proposed as an alternative, and it remains equivalent to RLHF under the reverse KL regularization constraint. This paper presents f-DPO, a generalized approach to DPO by incorporating diverse divergence constraints. We show that under certain f-divergences, including Jensen-Shannon divergence, forward KL divergences and α-divergences, the complex relationship between the reward and optimal policy can also be simplified by addressing the Karush-Kuhn-Tucker conditions. This eliminates the need for estimating the normalizing constant in the Bradley-Terry model and enables a tractable mapping between the reward function and the optimal policy. Our approach optimizes LLMs to align with human preferences in a more efficient and supervised manner under a broad set of divergence constraints. Empirically, adopting these divergences ensures a balance between alignment performance and generation diversity. Importantly, f-DPO outperforms PPO-based methods in divergence efficiency, and divergence constraints directly influence expected calibration error (ECE).