# Exploiting Tree Structure for Credit Assignment in RL Training of LLMs

arXiv: https://arxiv.org/abs/2509.18314 · HTML: https://mlsanity.com/paper/2509.18314/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 39 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)
- [Unpacking DPO and PPO: Disentangling Best Practices for Learning from Preference Feedback](https://mlsanity.com/paper/2406.09279/) (2024)
- [RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-Fold](https://mlsanity.com/paper/2406.14532/) (2024)
- [TreeRL: LLM Reinforcement Learning with On-Policy Tree Search](https://mlsanity.com/paper/2506.11902/) (2025)
- [Dense Reward for Free in Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2402.00782/) (2024)
- [Step-level Value Preference Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2406.10858/) (2024)
- [TreePO: Bridging the Gap of Policy Optimization and Efficacy and Inference Efficiency with Heuristic Tree-based Modeling](https://mlsanity.com/paper/2508.17445/) (2025)
- [The N+ Implementation Details of RLHF with PPO: A Case Study on TL;DR Summarization](https://mlsanity.com/paper/2403.17031/) (2024)
- [TreeRPO: Tree Relative Policy Optimization](https://mlsanity.com/paper/2506.05183/) (2025)
- [TLCR: Token-Level Continuous Reward for Fine-grained Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2407.16574/) (2024)
- [Self-Explore: Enhancing Mathematical Reasoning in Language Models with Fine-grained Rewards](https://mlsanity.com/paper/2404.10346/) (2024)

## Built on by (most cited first, 27 of 27)

- [From Reasoning to Agentic: Credit Assignment in Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2604.09459/) (2026)
- [RTMC: Step-Level Credit Assignment via Rollout Trees](https://mlsanity.com/paper/2604.11037/) (2026)
- [MatchTIR: Fine-Grained Supervision for Tool-Integrated Reasoning via Bipartite Matching](https://mlsanity.com/paper/2601.10712/) (2026)
- [Generate, Filter, Control, Replay: A Comprehensive Survey of Rollout Strategies for LLM Reinforcement Learning](https://mlsanity.com/paper/2605.02913/) (2026)
- [Where Hindsight Credit Can Reside: A Signed-Capacity View of Token Updates in RLVR](https://mlsanity.com/paper/2604.11056/) (2026)
- [CARL: Criticality-Aware Agentic Reinforcement Learning](https://mlsanity.com/paper/2512.04949/) (2025)
- [TreePS-RAG: Tree-based Process Supervision for Reinforcement Learning in Agentic RAG](https://mlsanity.com/paper/2601.06922/) (2026)
- [Execution-Grounded Credit Assignment for GRPO in Code Generation](https://mlsanity.com/paper/2603.16158/) (2026)
- [TaoSR-AGRL: Adaptive Guided Reinforcement Learning Framework for E-commerce Search Relevance](https://mlsanity.com/paper/2510.08048/) (2025)
- [TopoCurate:Modeling Interaction Topology for Tool-Use Agent Training](https://mlsanity.com/paper/2603.01714/) (2026)
- [Self-Induced Outcome Potential: Turn-Level Credit Assignment for Agents without Verifiers](https://mlsanity.com/paper/2605.04984/) (2026)
- [IAPO: Information-Aware Policy Optimization for Token-Efficient Reasoning](https://mlsanity.com/paper/2602.19049/) (2026)
- [MICA: Multi-granularity Intertemporal Credit Assignment for Long-Horizon Emotional Support Dialogue](https://mlsanity.com/paper/2603.06194/) (2026)
- [Structured Role-Aware Policy Optimization for Multimodal Reasoning](https://mlsanity.com/paper/2605.07274/) (2026)
- [Modularized Reinforcement Learning on LLMs: From MDP Creation to Exploration and Learning](https://mlsanity.com/paper/2606.21943/) (2026)
- [Difficulty-Adaptive Tree-Structured Policy Optimization for Expanding Reasoning Coverage in RLVR](https://mlsanity.com/paper/2609.08650/) (2026)
- [Rethinking Critic Learning in PPO: Understanding and Mitigating Value Flattening](https://mlsanity.com/paper/2609.18708/) (2026)
- [Teaching the Way, Not the Answer: Privileged Tutoring Distillation for Multimodal Policy Optimization](https://mlsanity.com/paper/2606.07000/) (2026)
- [When Implausible Tokens Get Reinforced: Tail-Aware Credit Calibration for LLM Reinforcement Learning](https://mlsanity.com/paper/2607.07976/) (2026)
- [Graph-Based Chain-of-Thought Pruning for Reducing Redundant Reflections in Reasoning LLMs](https://mlsanity.com/paper/2604.05643/) (2026)
- [Reinforcing 3D Understanding in Point-VLMs via Geometric Reward Credit Assignment](https://mlsanity.com/paper/2604.21160/) (2026)
- [ARCA: Adapter-Residual Credit Assignment When Token Signals Degenerate](https://mlsanity.com/paper/2606.00257/) (2026)
- [LEAF: Growing Trees Without Branching for Speech-Aware Large Language Model Post-Training](https://mlsanity.com/paper/2606.07610/) (2026)
- [Learning with a Single Rollout via Pass@k Policy Optimization](https://mlsanity.com/paper/2606.25451/) (2026)
- [RP-OPSD: Reasoning-Pivot-Guided On-Policy Self-Distillation for Multilingual Reasoning Transfer](https://mlsanity.com/paper/2608.06347/) (2026)
- [Let Credit Follow Computation: Architecture-Aware Credit Transport for Large Language Model Reinforcement Learning](https://mlsanity.com/paper/2608.21501/) (2026)
- [Advancing Entropy-Level Credit Assignment in RLVR via Proximal Entropy Policy Optimization](https://mlsanity.com/paper/2609.39402/) (2026)

## Abstract (arXiv)

Reinforcement learning improves LLM reasoning, yet sparse delayed reward over long sequences makes token-level credit assignment the key bottleneck. We study the verifiable-reward setting, where the final answer is checkable and multiple responses can be drawn per prompt. Reasoning tasks in math and medical QA align with this setup, where only a few decision tokens significantly impact the outcome. PPO offers token-level advantages with a learned value model, but it is complex to train both the actor and critic models simultaneously, and it is not easily generalizable, as the token-level values from the critic model can make training prone to overfitting. GRPO is critic-free and supports verifiable rewards, but spreads a single sequence-level return across tokens and ignores branching. We introduce Prefix-to-Tree (P2T), a simple procedure that converts a group of responses into a prefix tree and computes nonparametric prefix values (V(s)) by aggregating descendant outcomes. Built on P2T, we propose TEMPO (emphTree-Estimated Mean Prefix Value for Policy Optimization), a critic-free algorithm that augments the group-relative outcome signal of GRPO with branch-gated temporal-difference corrections derived from the tree. At non-branch tokens, the temporal-difference (TD) term is zero, so TEMPO reduces to GRPO; at branching tokens, it supplies precise token-level credit without a learned value network or extra judges/teachers. On Qwen3-1.7B/4B, TEMPO outperforms PPO and GRPO on in-distribution (MATH, MedQA) and out-of-distribution (GSM-HARD, AMC23, MedMCQA, MMLU-Medical) benchmarks, and reaches higher validation accuracy with roughly the same wall-clock time.