# On Designing Effective RL Reward at Training Time for LLM Reasoning

arXiv: https://arxiv.org/abs/2410.15115 · HTML: https://mlsanity.com/paper/2410.15115/

## Key facts

- Cited by 87 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 39 of its 43 references that are in the map.
- First posted on arXiv 19 Oct 2024.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- 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 39)

- [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)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [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)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [A Long Way to Go: Investigating Length Correlations in RLHF](https://mlsanity.com/paper/2310.03716/) (2023)
- [Is DPO Superior to PPO for LLM Alignment? A Comprehensive Study](https://mlsanity.com/paper/2404.10719/) (2024)
- [Secrets of RLHF in Large Language Models Part I: PPO](https://mlsanity.com/paper/2307.04964/) (2023)
- [Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking](https://mlsanity.com/paper/2312.09244/) (2023)
- [Advancing LLM Reasoning Generalists with Preference Trees](https://mlsanity.com/paper/2404.02078/) (2024)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)
- [Teaching Large Language Models to Reason with Reinforcement Learning](https://mlsanity.com/paper/2403.04642/) (2024)
- [MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2310.03731/) (2023)

## Built on by (most cited first, 30 of 87)

- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Video-R1: Reinforcing Video Reasoning in MLLMs](https://mlsanity.com/paper/2503.21776/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [SFT or RL? An Early Investigation into Training R1-Like Reasoning Large Vision-Language Models](https://mlsanity.com/paper/2504.11468/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence](https://mlsanity.com/paper/2507.21046/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Act Only When It Pays: Efficient Reinforcement Learning for LLM Reasoning via Selective Rollouts](https://mlsanity.com/paper/2506.02177/) (2025)
- [A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systems](https://mlsanity.com/paper/2504.09037/) (2025)
- [PRMBench: A Fine-grained and Challenging Benchmark for Process-Level Reward Models](https://mlsanity.com/paper/2501.03124/) (2025)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [Nemotron-Research-Tool-N1: Exploring Tool-Using Language Models with Reinforced Reasoning](https://mlsanity.com/paper/2505.00024/) (2025)
- [Unlocking Multimodal Mathematical Reasoning via Process Reward Model](https://mlsanity.com/paper/2501.04686/) (2025)
- [ThetaEvolve: Test-time Learning on Open Problems](https://mlsanity.com/paper/2511.23473/) (2025)
- [Prosperity before Collapse: How Far Can Off-Policy RL Reach with Stale Data on LLMs?](https://mlsanity.com/paper/2510.01161/) (2025)
- [Reward Reasoning Model](https://mlsanity.com/paper/2505.14674/) (2025)
- [Spatial-SSRL: Enhancing Spatial Understanding via Self-Supervised Reinforcement Learning](https://mlsanity.com/paper/2510.27606/) (2025)
- [Trust, But Verify: A Self-Verification Approach to Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.13445/) (2025)
- [Position: Stop Anthropomorphizing Intermediate Tokens as Reasoning/Thinking Traces!](https://mlsanity.com/paper/2504.09762/) (2025)
- [Navigate the Unknown: Enhancing LLM Reasoning with Intrinsic Motivation Guided Exploration](https://mlsanity.com/paper/2505.17621/) (2025)
- [Metacognitive Reuse: Turning Recurring LLM Reasoning Into Concise Behaviors](https://mlsanity.com/paper/2509.13237/) (2025)
- [Stable Reinforcement Learning for Efficient Reasoning](https://mlsanity.com/paper/2505.18086/) (2025)
- [TritonRL: Training LLMs to Think and Code Triton Without Cheating](https://mlsanity.com/paper/2510.17891/) (2025)
- [Step-KTO: Optimizing Mathematical Reasoning through Stepwise Binary Feedback](https://mlsanity.com/paper/2501.10799/) (2025)
- [Imitation Learning for Multi-turn LM Agents via On-policy Expert Corrections](https://mlsanity.com/paper/2512.14895/) (2025)
- [Does Your Reasoning Model Implicitly Know When to Stop Thinking?](https://mlsanity.com/paper/2602.08354/) (2026)
- [Language Models Can Learn from Verbal Feedback Without Scalar Rewards](https://mlsanity.com/paper/2509.22638/) (2025)
- [Improving Multi-Step Reasoning Abilities of Large Language Models with Direct Advantage Policy Optimization](https://mlsanity.com/paper/2412.18279/) (2024)
- [IPO: Your Language Model is Secretly a Preference Classifier](https://mlsanity.com/paper/2502.16182/) (2025)

## Abstract (arXiv)

Reward models have been increasingly critical for improving the reasoning capability of LLMs. Existing research has shown that a well-trained reward model can substantially improve model performances at inference time via search. However, the potential of reward models during RL training time still remains largely under-explored. It is currently unclear whether these reward models can provide additional training signals to enhance the reasoning capabilities of LLMs in RL training that uses sparse success rewards, which verify the correctness of solutions. In this work, we evaluate popular reward models for RL training, including the Outcome-supervised Reward Model (ORM) and the Process-supervised Reward Model (PRM), and train a collection of LLMs for math problems using RL by combining these learned rewards with success rewards. Surprisingly, even though these learned reward models have strong inference-time performances, they may NOT help or even hurt RL training, producing worse performances than LLMs trained with the success reward only. Our analysis reveals that an LLM can receive high rewards from some of these reward models by repeating correct but unnecessary reasoning steps, leading to a severe reward hacking issue. Therefore, we introduce two novel reward refinement techniques, including Clipping and Delta. The key idea is to ensure the accumulative reward of any reasoning trajectory is upper-bounded to keep a learned reward model effective without being exploited. We evaluate our techniques with multiple reward models over a set of 1.5B and 7B LLMs on MATH and GSM8K benchmarks and demonstrate that with a carefully designed reward function, RL training without any additional supervised tuning can improve all the evaluated LLMs, including the state-of-the-art 7B LLM Qwen2.5-Math-7B-Instruct on MATH and GSM8K benchmarks.