# Fishing Out Free Riders: Shapley-Based Reward Attribution for Parallel Reasoning via Reinforcement Learning

arXiv: https://arxiv.org/abs/2607.18979 · HTML: https://mlsanity.com/paper/2607.18979/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## 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, 25 of 25)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [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)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [MEM1: Learning to Synergize Memory and Reasoning for Efficient Long-Horizon Agents](https://mlsanity.com/paper/2506.15841/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Agentic Reinforced Policy Optimization](https://mlsanity.com/paper/2507.19849/) (2025)
- [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024)
- [Generative Reward Models](https://mlsanity.com/paper/2410.12832/) (2024)
- [A Survey of Reasoning with Foundation Models](https://mlsanity.com/paper/2312.11562/) (2023)
- [Agentic Entropy-Balanced Policy Optimization](https://mlsanity.com/paper/2510.14545/) (2025)
- [ParaThinker: Native Parallel Thinking as a New Paradigm to Scale LLM Test-time Compute](https://mlsanity.com/paper/2509.04475/) (2025)
- [Detecting Proxy Gaming in RL and LLM Alignment via Evaluator Stress Tests](https://mlsanity.com/paper/2507.05619/) (2025)
- [GPTVoiceTasker: Advancing Multi-step Mobile Task Efficiency Through Dynamic Interface Exploration and Learning](https://mlsanity.com/paper/2401.14268/) (2024)
- [Native Parallel Reasoner: Reasoning in Parallelism via Self-Distilled Reinforcement Learning](https://mlsanity.com/paper/2512.07461/) (2025)
- [ASPD: Unlocking Adaptive Serial-Parallel Decoding by Exploring Intrinsic Parallelism in LLMs](https://mlsanity.com/paper/2508.08895/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) excel at multi-step reasoning, yet current parallel reasoning approaches often fail to distinguish the contributions of individual reasoning paths. Many paths may be redundant, misleading, or even detrimental, but outcome-level rewards assign uniform reward, leading to ambiguous learning signals and unstable training. We propose Parallel Shapley, a reinforcement learning framework that attributes fine-grained, path-level contributions in multi-path reasoning. Treating each path as a player in a cooperative game, we leverage Shapley values to quantify marginal contributions, using a generative reward model to evaluate path utilities and Monte Carlo sampling for efficient approximation. Experiments on mathematical reasoning benchmarks show that Parallel Shapley outperforms existing baselines while providing more stable and interpretable training. Our framework effectively "fishes out the free riders," assigning reward proportionally and improving multi-path reasoning in LLMs.