# APLOT: Robust Reward Modeling via Adaptive Preference Learning with Optimal Transport

arXiv: https://arxiv.org/abs/2510.10963 · HTML: https://mlsanity.com/paper/2510.10963/

## Key facts

- Cited by 6 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 35 of its 53 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## 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 35)

- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [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)
- [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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [Skywork-Reward: Bag of Tricks for Reward Modeling in LLMs](https://mlsanity.com/paper/2410.18451/) (2024)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Sampling Matters in Deep Embedding Learning](https://mlsanity.com/paper/1706.07567/) (2017)
- [Reward Model Ensembles Help Mitigate Overoptimization](https://mlsanity.com/paper/2310.02743/) (2023)
- [Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking](https://mlsanity.com/paper/2312.09244/) (2023)
- [RM-Bench: Benchmarking Reward Models of Language Models with Subtlety and Style](https://mlsanity.com/paper/2410.16184/) (2024)
- [Rewards-in-Context: Multi-objective Alignment of Foundation Models with Dynamic Preference Adjustment](https://mlsanity.com/paper/2402.10207/) (2024)
- [Regularizing Hidden States Enables Learning Generalizable Reward Model for LLMs](https://mlsanity.com/paper/2406.10216/) (2024)
- [RRM: Robust Reward Model Training Mitigates Reward Hacking](https://mlsanity.com/paper/2409.13156/) (2024)
- [PsycoLLM: Enhancing LLM for Psychological Understanding and Evaluation](https://mlsanity.com/paper/2407.05721/) (2024)
- [Graph Enhanced Contrastive Learning for Radiology Findings Summarization](https://mlsanity.com/paper/2204.00203/) (2022)
- [Learning to Re-weight Examples with Optimal Transport for Imbalanced Classification](https://mlsanity.com/paper/2208.02951/) (2022)

## Built on by (most cited first, 6 of 6)

- [Eliminating Inductive Bias in Reward Models with Information-Theoretic Guidance](https://mlsanity.com/paper/2512.23461/) (2025)
- [Mitigating Reward Hacking in RLHF via Bayesian Non-negative Reward Modeling](https://mlsanity.com/paper/2602.10623/) (2026)
- [MARCH: Multi-Agent Reinforced Self-Check for LLM Hallucination](https://mlsanity.com/paper/2603.24579/) (2026)
- [AnomSeer: Reinforcing Multimodal LLMs to Reason for Time-Series Anomaly Detection](https://mlsanity.com/paper/2602.08868/) (2026)
- [VisCache: Visual KV Cache Pruning for Efficient Vision Large Language Model Inference](https://mlsanity.com/paper/2608.24063/) (2026)
- [From Soft Targets to Reward Signals: How Assignment and Reward Objectives Interact](https://mlsanity.com/paper/2609.34850/) (2026)

## Abstract (arXiv)

The reward model (RM) plays a crucial role in aligning Large Language Models (LLMs) with human preferences through Reinforcement Learning, where the Bradley-Terry (BT) objective has been recognized as simple yet powerful, specifically for pairwise preference learning. However, BT-based RMs often struggle to effectively distinguish between similar preference responses, leading to insufficient separation between preferred and non-preferred outputs. Consequently, they may easily overfit easy samples and cannot generalize well to Out-Of-Distribution (OOD) samples, resulting in suboptimal performance. To address these challenges, this paper introduces an effective enhancement to BT-based RMs through an adaptive margin mechanism. Specifically, we design to dynamically adjust the RM focus on more challenging samples through margins, based on both semantic similarity and model-predicted reward differences, which is approached from a distributional perspective solvable with Optimal Transport (OT). By incorporating these factors into a principled OT cost matrix design, our adaptive margin enables the RM to better capture distributional differences between chosen and rejected responses, yielding significant improvements in performance, convergence speed, and generalization capabilities. Experimental results across multiple benchmarks demonstrate that our method outperforms several existing RM techniques, showcasing enhanced performance in both In-Distribution (ID) and OOD settings. Moreover, RLHF experiments support our practical effectiveness in better aligning LLMs with human preferences. Our code is available at https://github.com/BIRlz/APLOT