# Towards Order Fairness: Mitigating LLMs Order Sensitivity through Dual Group Advantage Optimization

arXiv: https://arxiv.org/abs/2605.11974 · HTML: https://mlsanity.com/paper/2605.11974/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 51 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 30 of 34)

- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Fantastically Ordered Prompts and Where to Find Them: Overcoming Few-Shot Prompt Order Sensitivity](https://mlsanity.com/paper/2104.08786/) (2021)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [SearchQA: A New Q&A Dataset Augmented with Context from a Search Engine](https://mlsanity.com/paper/1704.05179/) (2017)
- [RankRAG: Unifying Context Ranking with Retrieval-Augmented Generation in LLMs](https://mlsanity.com/paper/2407.02485/) (2024)
- [In-Context Learning with Long-Context Models: An In-Depth Exploration](https://mlsanity.com/paper/2405.00200/) (2024)
- [Direct Preference Optimization with an Offset](https://mlsanity.com/paper/2402.10571/) (2024)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (2024)
- [Data-efficient Fine-tuning for LLM-based Recommendation](https://mlsanity.com/paper/2401.17197/) (2024)
- [An Information-theoretic Approach to Prompt Engineering Without Ground Truth Labels](https://mlsanity.com/paper/2203.11364/) (2022)
- [AceReason-Nemotron: Advancing Math and Code Reasoning through Reinforcement Learning](https://mlsanity.com/paper/2505.16400/) (2025)
- [Split and Merge: Aligning Position Biases in LLM-based Evaluators](https://mlsanity.com/paper/2310.01432/) (2023)
- [Step-level Value Preference Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2406.10858/) (2024)
- [Eliminating Position Bias of Language Models: A Mechanistic Approach](https://mlsanity.com/paper/2407.01100/) (2024)
- [Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks](https://mlsanity.com/paper/2107.01431/) (2021)
- [UniBias: Unveiling and Mitigating LLM Bias through Internal Attention and FFN Manipulation](https://mlsanity.com/paper/2405.20612/) (2024)
- [Qwen Look Again: Guiding Vision-Language Reasoning Models to Re-attention Visual Information](https://mlsanity.com/paper/2505.23558/) (2025)
- [Towards AI Search Paradigm](https://mlsanity.com/paper/2506.17188/) (2025)
- [IRCoCo: Immediate Rewards-Guided Deep Reinforcement Learning for Code Completion](https://mlsanity.com/paper/2401.16637/) (2024)
- [ARM-Thinker: Reinforcing Multimodal Generative Reward Models with Agentic Tool Use and Visual Reasoning](https://mlsanity.com/paper/2512.05111/) (2025)
- [Domaino1s: Guiding LLM Reasoning for Explainable Answers in High-Stakes Domains](https://mlsanity.com/paper/2501.14431/) (2025)

## Built on by (most cited first, 1 of 1)

- [FOCUS: Decoupling Expert Personas in LLMs to Enhance Domain Expert Capabilities](https://mlsanity.com/paper/2608.05611/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) suffer from order bias, where their performance is affected by the arrangement order of input elements. This unfairness limits the model's applications in scenarios such as in-context learning and Retrieval-Augmented Generation (RAG). Recent studies attempt to obtain optimal or suboptimal arrangements based on statistical results or using dataset-based search, but these methods increase inference overhead while leaving the model's inherent order bias unresolved. Other studies mitigate order sensitivity through supervised fine-tuning using augmented training sets with multiple order variants, but often at the cost of accuracy, trapping the model in consistent yet incorrect hallucinations. In this paper, we propose Dual Group Advantage Optimization (DGAO), which aims to improve model accuracy and order stability simultaneously. DGAO calculates and balances intra-group relative accuracy advantage and inter-group relative stability advantage, rewarding the policy model for generating order-stable and correct outputs while penalizing order-sensitive or incorrect responses. This marks the first time reinforcement learning has been used to mitigate LLMs' order sensitivity. We also propose two new metrics, Consistency Rate and Overconfidence Rate, to reveal the pseudo-stability of previous methods and guide more comprehensive evaluation. Extensive experiments demonstrate that DGAO achieves superior order fairness while improving performance on RAG, mathematical reasoning, and classification tasks. Our code is available at: https://github.com/Hyalinesky/DGAO.