# WARP: On the Benefits of Weight Averaged Rewarded Policies

arXiv: https://arxiv.org/abs/2406.16768 · HTML: https://mlsanity.com/paper/2406.16768/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 117 of its 141 references that are in the map.
- First posted on arXiv 24 Jun 2024.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 30 of 117)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)

## Built on by (most cited first, 30 of 45)

- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [BOND: Aligning LLMs with Best-of-N Distillation](https://mlsanity.com/paper/2407.14622/) (2024)
- [RRM: Robust Reward Model Training Mitigates Reward Hacking](https://mlsanity.com/paper/2409.13156/) (2024)
- [What Matters for Model Merging at Scale?](https://mlsanity.com/paper/2410.03617/) (2024)
- [Rethinking Mixture-of-Agents: Is Mixing Different Large Language Models Beneficial?](https://mlsanity.com/paper/2502.00674/) (2025)
- [From Lists to Emojis: How Format Bias Affects Model Alignment](https://mlsanity.com/paper/2409.11704/) (2024)
- [GRPO-CARE: Consistency-Aware Reinforcement Learning for Multimodal Reasoning](https://mlsanity.com/paper/2506.16141/) (2025)
- [Calibrated Multi-Preference Optimization for Aligning Diffusion Models](https://mlsanity.com/paper/2502.02588/) (2025)
- [Activation-Informed Merging of Large Language Models](https://mlsanity.com/paper/2502.02421/) (2025)
- [Model Swarms: Collaborative Search to Adapt LLM Experts via Swarm Intelligence](https://mlsanity.com/paper/2410.11163/) (2024)
- [How to Merge Your Multimodal Models Over Time?](https://mlsanity.com/paper/2412.06712/) (2024)
- [WSM: Decay-Free Learning Rate Schedule via Checkpoint Merging for LLM Pre-training](https://mlsanity.com/paper/2507.17634/) (2025)
- [A Modular Approach for Clinical SLMs Driven by Synthetic Data with Pre-Instruction Tuning, Model Merging, and Clinical-Tasks Alignment](https://mlsanity.com/paper/2505.10717/) (2025)
- [NileChat: Towards Linguistically Diverse and Culturally Aware LLMs for Local Communities](https://mlsanity.com/paper/2505.18383/) (2025)
- [Real-Time Aligned Reward Model beyond Semantics](https://mlsanity.com/paper/2601.22664/) (2026)
- [Reward Model Overoptimisation in Iterated RLHF](https://mlsanity.com/paper/2505.18126/) (2025)
- [RL-finetuning LLMs from on- and off-policy data with a single algorithm](https://mlsanity.com/paper/2503.19612/) (2025)
- [Towards Reward Fairness in RLHF: From a Resource Allocation Perspective](https://mlsanity.com/paper/2505.23349/) (2025)
- [Subspace-Boosted Model Merging](https://mlsanity.com/paper/2506.16506/) (2025)
- [Bias Fitting to Mitigate Length Bias of Reward Model in RLHF](https://mlsanity.com/paper/2505.12843/) (2025)
- [Efficient Model Development through Fine-tuning Transfer](https://mlsanity.com/paper/2503.20110/) (2025)
- [Low-rank bias, weight decay, and model merging in neural networks](https://mlsanity.com/paper/2502.17340/) (2025)
- [Emergent Abilities of Large Language Models under Continued Pretraining for Language Adaptation](https://mlsanity.com/paper/2506.00288/) (2025)
- [A Systematic Study of In-the-Wild Model Merging for Large Language Models](https://mlsanity.com/paper/2511.21437/) (2025)
- [EMA Policy Gradient: Taming Reinforcement Learning for LLMs with EMA Anchor and Top-k KL](https://mlsanity.com/paper/2602.04417/) (2026)
- [Unifying Stable Optimization and Reference Regularization in RLHF](https://mlsanity.com/paper/2602.11523/) (2026)
- [Decoupled DiLoCo for Resilient Distributed Pre-training](https://mlsanity.com/paper/2604.21428/) (2026)
- [Parameter-Efficient Interventions for Enhanced Model Merging](https://mlsanity.com/paper/2412.17023/) (2024)

## Abstract (arXiv)

Reinforcement learning from human feedback (RLHF) aligns large language models (LLMs) by encouraging their generations to have high rewards, using a reward model trained on human preferences. To prevent the forgetting of pre-trained knowledge, RLHF usually incorporates a KL regularization; this forces the policy to remain close to its supervised fine-tuned initialization, though it hinders the reward optimization. To tackle the trade-off between KL and reward, in this paper we introduce a novel alignment strategy named Weight Averaged Rewarded Policies (WARP). WARP merges policies in the weight space at three distinct stages. First, it uses the exponential moving average of the policy as a dynamic anchor in the KL regularization. Second, it applies spherical interpolation to merge independently fine-tuned policies into a new enhanced one. Third, it linearly interpolates between this merged model and the initialization, to recover features from pre-training. This procedure is then applied iteratively, with each iteration's final model used as an advanced initialization for the next, progressively refining the KL-reward Pareto front, achieving superior rewards at fixed KL. Experiments with GEMMA policies validate that WARP improves their quality and alignment, outperforming other open-source LLMs.