# Beyond Correctness: Harmonizing Process and Outcome Rewards through RL Training

arXiv: https://arxiv.org/abs/2509.03403 · HTML: https://mlsanity.com/paper/2509.03403/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Placed in Process reward models for reasoning, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 43 of its 52 references that are in the map.
- First posted on arXiv 3 Sep 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 30 of 43)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Monitoring Reasoning Models for Misbehavior and the Risks of Promoting Obfuscation](https://mlsanity.com/paper/2503.11926/) (2025)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)
- [Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking](https://mlsanity.com/paper/2312.09244/) (2023)
- [Mitigating the Alignment Tax of RLHF](https://mlsanity.com/paper/2309.06256/) (2023)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [Process Reward Models That Think](https://mlsanity.com/paper/2504.16828/) (2025)
- [GenPRM: Scaling Test-Time Compute of Process Reward Models via Generative Reasoning](https://mlsanity.com/paper/2504.00891/) (2025)
- [Not All Rollouts are Useful: Down-Sampling Rollouts in LLM Reinforcement Learning](https://mlsanity.com/paper/2504.13818/) (2025)

## Built on by (most cited first, 29 of 29)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [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)
- [Cognitive Foundations for Reasoning and Their Manifestation in LLMs](https://mlsanity.com/paper/2511.16660/) (2025)
- [Reinforce-Ada: An Adaptive Sampling Framework under Non-linear RL Objectives](https://mlsanity.com/paper/2510.04996/) (2025)
- [TRACE: Turn-level Reward Assignment via Credit Estimation for Long-Horizon Agents](https://mlsanity.com/paper/2607.13988/) (2026)
- [Attention as a Compass: Efficient Exploration for Process-Supervised RL in Reasoning Models](https://mlsanity.com/paper/2509.26628/) (2025)
- [Beyond Majority Voting: Towards Fine-grained and More Reliable Reward Signal for Test-Time Reinforcement Learning](https://mlsanity.com/paper/2512.15146/) (2025)
- [Save the Good Prefix: Precise Error Penalization via Process-Supervised RL to Enhance LLM Reasoning](https://mlsanity.com/paper/2601.18984/) (2026)
- [HiPRAG: Hierarchical Process Rewards for Efficient Agentic Retrieval Augmented Generation](https://mlsanity.com/paper/2510.07794/) (2025)
- [Train at Moving Edge: Online-Verified Prompt Selection for Efficient RL Training of Large Reasoning Model](https://mlsanity.com/paper/2603.25184/) (2026)
- [SELAUR: Self Evolving LLM Agent via Uncertainty-aware Rewards](https://mlsanity.com/paper/2602.21158/) (2026)
- [Enhancing Large Language Model Reasoning with Reward Models: An Analytical Survey](https://mlsanity.com/paper/2510.01925/) (2025)
- [DGPO: Distribution Guided Policy Optimization for Fine Grained Credit Assignment](https://mlsanity.com/paper/2605.03327/) (2026)
- [TreeAdv: Tree-Structured Advantage Redistribution for Group-Based RL](https://mlsanity.com/paper/2601.03703/) (2026)
- [HeaPA: Difficulty-Aware Heap Sampling and On-Policy Query Augmentation for LLM Reinforcement Learning](https://mlsanity.com/paper/2601.22448/) (2026)
- [MulFeRL: Enhancing Reinforcement Learning with Verbal Feedback in a Multi-turn Loop](https://mlsanity.com/paper/2601.22900/) (2026)
- [Recycling Failures: Salvaging Exploration in RLVR via Fine-Grained Off-Policy Guidance](https://mlsanity.com/paper/2602.24110/) (2026)
- [LLM Reasoning with Process Rewards for Outcome-Guided Steps](https://mlsanity.com/paper/2604.02341/) (2026)
- [Process Supervision of Confidence Margin for Calibrated LLM Reasoning](https://mlsanity.com/paper/2604.23333/) (2026)
- [SAAS: Self-Aware Reinforcement Learning for Over-Search Mitigation in Agentic Search](https://mlsanity.com/paper/2605.29796/) (2026)
- [Process Advantage Signal Shaping: A Paradigm-Agnostic Middleware for Process-Supervised RL in LLM Reasoners](https://mlsanity.com/paper/2606.29296/) (2026)
- [Towards Generalizable Reasoning: Group Causal Counterfactual Policy Optimization for LLM Reasoning](https://mlsanity.com/paper/2602.06475/) (2026)
- [A Primer in Post-Training Reasoning Data: What We Know About How It Works](https://mlsanity.com/paper/2606.02113/) (2026)
- [Hi-TTRL: Regulating Consensus with Hints for Test-Time Reinforcement Learning](https://mlsanity.com/paper/2608.03545/) (2026)
- [Unlearnable, or Unmeasured? On the Reliability of Difficulty Labels in RLVR](https://mlsanity.com/paper/2609.40115/) (2026)
- [RLFR: Extending Reinforcement Learning for LLMs with Flow Environment](https://mlsanity.com/paper/2510.10201/) (2025)
- [PubSwap: Public-Data Off-Policy Coordination for Federated RLVR](https://mlsanity.com/paper/2604.12160/) (2026)
- [A Survey of Reinforcement Learning for Large Language Models under Data Scarcity: Challenges and Solutions](https://mlsanity.com/paper/2604.17312/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) improves final-answer accuracy on reasoning tasks, but it does not reliably improve reasoning quality. Because outcome rewards only assess final answers, they also reward spurious successes: flawed reasoning can still receive maximal reward when it accidentally reaches the correct outcome. This outcome reward hacking creates biased gradients, making current RLVR insufficient for learning faithful reasoning. Process Reward Models (PRMs) provide step-wise supervision, but directly optimizing PRMs or naively combining them with outcome rewards is unstable under distribution shift during RL training process. We introduce PRocess cOnsistency Filter (PROF), a data curation method that uses PRM--ORM consistency for sample selection rather than direct reward optimization. PROF keeps correct responses with strong process support and incorrect responses with weak process support while maintaining a balanced training ratio. Experiments show that PROF consistently improves both final-answer accuracy and intermediate reasoning quality over strong baselines, with less dependence on strong PRMs.