# Can David Beat Goliath? On Multi-Hop Reasoning with Resource-Constrained Agents

arXiv: https://arxiv.org/abs/2601.21699 · HTML: https://mlsanity.com/paper/2601.21699/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 35 of its 89 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 30 of 35)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (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)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Active Retrieval Augmented Generation](https://mlsanity.com/paper/2305.06983/) (2023)
- [R1-Searcher: Incentivizing the Search Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2503.05592/) (2025)
- [PAQ: 65 Million Probably-Asked Questions and What You Can Do With Them](https://mlsanity.com/paper/2102.07033/) (2021)
- [APIGen-MT: Agentic Pipeline for Multi-Turn Data Generation via Simulated Agent-Human Interplay](https://mlsanity.com/paper/2504.03601/) (2025)
- [FlashRAG: A Modular Toolkit for Efficient Retrieval-Augmented Generation Research](https://mlsanity.com/paper/2405.13576/) (2024)
- [Answering Complex Open-Domain Questions with Multi-Hop Dense Retrieval](https://mlsanity.com/paper/2009.12756/) (2020)
- [Learning to Retrieve Reasoning Paths over Wikipedia Graph for Question Answering](https://mlsanity.com/paper/1911.10470/) (2019)
- [Synthetic QA Corpora Generation with Roundtrip Consistency](https://mlsanity.com/paper/1906.05416/) (2019)
- [StepSearch: Igniting LLMs Search Ability via Step-Wise Proximal Policy Optimization](https://mlsanity.com/paper/2505.15107/) (2025)
- [Hierarchical Graph Network for Multi-hop Question Answering](https://mlsanity.com/paper/1911.03631/) (2019)
- [ReST meets ReAct: Self-Improvement for Multi-Step Reasoning LLM Agent](https://mlsanity.com/paper/2312.10003/) (2023)
- [Tree Search for LLM Agent Reinforcement Learning](https://mlsanity.com/paper/2509.21240/) (2025)
- [An Empirical Study on Reinforcement Learning for Reasoning-Search Interleaved LLM Agents](https://mlsanity.com/paper/2505.15117/) (2025)
- [AntiLeakBench: Preventing Data Contamination by Automatically Constructing Benchmarks with Updated Real-World Knowledge](https://mlsanity.com/paper/2412.13670/) (2024)
- [Improving Retrieval-Augmented Generation through Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2501.15228/) (2025)

## Built on by (most cited first, 1 of 1)

- [Effective Reinforcement Learning for Agentic Search by Recycling Zero-Variance Queries During Training](https://mlsanity.com/paper/2606.10709/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) trains small language model agents to answer multi-hop questions by retrieving evidence over multiple turns, but reported gains typically rely on thousands of on-policy rollouts per update. We study RL for such agents on commodity GPUs, where each update samples only a few rollouts per question. Most sampled trajectories then retrieve none of the required evidence, so the outcome reward gives the policy little to learn from and small agents settle for answering without retrieval, a failure we call retrieval collapse. DAVID-GRPO addresses this with two mechanisms: (1) expert trajectory seeding places a handful of off-policy expert trajectories into the GRPO groups of the early updates, and (2) evidence-guided continuation rewards evidence coverage and resumes the most promising partial trajectory. The evidence for each training question is constructed from the corpus link graph, without annotated evidence. On six multi-hop QA benchmarks, DAVID-GRPO trained on four RTX 3090 GPUs with 144 rollouts per step brings Qwen2.5-1.5B to 22.6 average EM against 11.9 for the best baseline under the same budget, is comparable to Tree-GRPO trained with 20 times more rollouts, and, unlike the baselines that stop after at most one search, learns to retrieve across turns. The implementation is available at: https://github.com/AsadalJung/David-GRPO