# RewardFlow: Topology-Aware Reward Propagation on State Graphs for Agentic RL with Large Language Models

arXiv: https://arxiv.org/abs/2603.18859 · HTML: https://mlsanity.com/paper/2603.18859/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 61 of its 79 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)
- 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 61)

- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [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)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [ALFRED: A Benchmark for Interpreting Grounded Instructions for Everyday Tasks](https://mlsanity.com/paper/1912.01734/) (2019)
- [UI-TARS: Pioneering Automated GUI Interaction with Native Agents](https://mlsanity.com/paper/2501.12326/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [LLM+P: Empowering Large Language Models with Optimal Planning Proficiency](https://mlsanity.com/paper/2304.11477/) (2023)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025)
- [Navigating the Digital World as Humans Do: Universal Visual Grounding for GUI Agents](https://mlsanity.com/paper/2410.05243/) (2024)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)

## Built on by (most cited first, 3 of 3)

- [TRCA: Transition-wise Rubric Credit Assignment for Long-horizon LLM Agents](https://mlsanity.com/paper/2608.16156/) (2026)
- [LOTAPO: Leave-One-Turn Attribution for Self-Generated Process Rewards in Multi-Turn Search Reasoning](https://mlsanity.com/paper/2607.13501/) (2026)
- [MoFlow: Multi-Objective Agentic Workflow Generation](https://mlsanity.com/paper/2609.38294/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) shows promise for enhancing LLM agentic reasoning, yet sparse terminal rewards hinder fine-grained optimization. Process reward modeling offers an alternative but incurs high computational costs, reward hacking risks, and annotation bottlenecks. We introduce RewardFlow, a lightweight method for estimating state-level rewards in agentic reasoning. By constructing state graphs that capture the intrinsic topological structure of trajectories, RewardFlow performs topology-aware propagation to estimate each state's contribution to success, yielding principled, annotation-free dense rewards. Used for RL optimization, RewardFlow substantially outperforms prior baselines across four agentic benchmarks: +6.2% average success rate on text-based tasks, +29.7% on visual reasoning over the strongest baseline across three model scales, and +10% accuracy on DeepResearch, with superior robustness and training efficiency. The implementation of RewardFlow is publicly available at https://github.com/tmlr-group/RewardFlow.