# Discriminative Policy Optimization for Token-Level Reward Models

arXiv: https://arxiv.org/abs/2505.23363 · HTML: https://mlsanity.com/paper/2505.23363/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 31 of its 39 references that are in the map.
- First posted on arXiv 29 May 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 30 of 31)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [Fine-Grained Human Feedback Gives Better Rewards for Language Model Training](https://mlsanity.com/paper/2306.01693/) (2023)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)
- [HelpSteer2: Open-source dataset for training top-performing reward models](https://mlsanity.com/paper/2406.08673/) (2024)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems](https://mlsanity.com/paper/2412.09413/) (2024)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [DPO Meets PPO: Reinforced Token Optimization for RLHF](https://mlsanity.com/paper/2404.18922/) (2024)
- [O1 Replication Journey -- Part 2: Surpassing O1-preview through Simple Distillation, Big Progress or Bitter Lesson?](https://mlsanity.com/paper/2411.16489/) (2024)
- [Dense Reward for Free in Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2402.00782/) (2024)
- [What Makes a Reward Model a Good Teacher? An Optimization Perspective](https://mlsanity.com/paper/2503.15477/) (2025)

## Built on by (most cited first, 16 of 16)

- [A Survey of Process Reward Models: From Outcome Signals to Process Supervisions for Large Language Models](https://mlsanity.com/paper/2510.08049/) (2025)
- [Reward Hacking in the Era of Large Models: Mechanisms, Emergent Misalignment, Challenges](https://mlsanity.com/paper/2604.13602/) (2026)
- [Learning to Deliberate: Meta-policy Collaboration for Agentic LLMs with Multi-agent Reinforcement Learning](https://mlsanity.com/paper/2509.03817/) (2025)
- [Asymmetric Proximal Policy Optimization: mini-critics boost LLM reasoning](https://mlsanity.com/paper/2510.01656/) (2025)
- [STRIDE: Strategic Trajectory Reasoning via Discriminative Estimation for Verifiable Reinforcement Learning](https://mlsanity.com/paper/2606.15866/) (2026)
- [Reward Modeling for Reinforcement Learning-Based LLM Reasoning: Design, Challenges, and Evaluation](https://mlsanity.com/paper/2602.09305/) (2026)
- [CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2507.15698/) (2025)
- [ShapE-GRPO: Shapley-Enhanced Reward Allocation for Multi-Candidate LLM Training](https://mlsanity.com/paper/2603.29871/) (2026)
- [Skip-Connected Policy Optimization for Implicit Advantage](https://mlsanity.com/paper/2604.08690/) (2026)
- [MetaResearcher: Scaling Deep Research via Self-Reflective Reinforcement Learning in Adversarial Virtual Environments](https://mlsanity.com/paper/2606.19893/) (2026)
- [Difference Feedback: Generating Multimodal Process-Level Supervision for VLM Reinforcement Learning](https://mlsanity.com/paper/2603.27482/) (2026)
- [ARCA: Adapter-Residual Credit Assignment When Token Signals Degenerate](https://mlsanity.com/paper/2606.00257/) (2026)
- [BALTO: Balanced Token-Level Policy Optimization for Hallucination Mitigation](https://mlsanity.com/paper/2606.15893/) (2026)
- [Se-DPO: Self-Evolving Token Credit for Direct Preference Optimization](https://mlsanity.com/paper/2608.09568/) (2026)
- [Training-Free Inference-Time Self-Reflection and Cost-Bounded Early Stopping for Large Language Models](https://mlsanity.com/paper/2608.18884/) (2026)
- [Beyond Outcome Feedback: Trajectory-Quality-Guided Experience-based Learning](https://mlsanity.com/paper/2610.14877/) (2026)

## Abstract (arXiv)

Process reward models (PRMs) provide more nuanced supervision compared to outcome reward models (ORMs) for optimizing policy models, positioning them as a promising approach to enhancing the capabilities of LLMs in complex reasoning tasks. Recent efforts have advanced PRMs from step-level to token-level granularity by integrating reward modeling into the training of generative models, with reward scores derived from token generation probabilities. However, the conflict between generative language modeling and reward modeling may introduce instability and lead to inaccurate credit assignments. To address this challenge, we revisit token-level reward assignment by decoupling reward modeling from language generation and derive a token-level reward model through the optimization of a discriminative policy, termed the Q-function Reward Model (Q-RM). We theoretically demonstrate that Q-RM explicitly learns token-level Q-functions from preference data without relying on fine-grained annotations. In our experiments, Q-RM consistently outperforms all baseline methods across various benchmarks. For example, when integrated into PPO/REINFORCE algorithms, Q-RM enhances the average Pass@1 score by 5.85/4.70 points on mathematical reasoning tasks compared to the ORM baseline, and by 4.56/5.73 points compared to the token-level PRM counterpart. Moreover, reinforcement learning with Q-RM significantly enhances training efficiency, achieving convergence 12 times faster than ORM on GSM8K and 11 times faster than step-level PRM on MATH. Code and data are available at https://github.com/homzer/Q-RM.