# Reinforcement Learning with Verifiable Rewards for Small Search Agents

arXiv: https://arxiv.org/abs/2609.28765 · HTML: https://mlsanity.com/paper/2609.28765/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 51 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 30 of 42)

- [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)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [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)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [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)
- [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)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Interleaving Retrieval with Chain-of-Thought Reasoning for Knowledge-Intensive Multi-Step Questions](https://mlsanity.com/paper/2212.10509/) (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)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [Small Language Models are the Future of Agentic AI](https://mlsanity.com/paper/2506.02153/) (2025)
- [FlashRAG: A Modular Toolkit for Efficient Retrieval-Augmented Generation Research](https://mlsanity.com/paper/2405.13576/) (2024)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) performs well on problems with clear rewards, such as mathematics and coding, but whether it also works where the reward is less clear remains open. The reason-over-search recipe applies RLVR to open-domain question answering, where retrieval grounds the answer and a match against the reference supplies the reward. So far it has been demonstrated on large models, and below one billion parameters only with distillation from a larger teacher. We test the recipe on a small model. We train Qwen3.5-0.8B with Group Relative Policy Optimization (GRPO) and an interleaved Wikipedia-search tool on MuSiQue, varying only the reward across three shapes over three seeds each, and we evaluate every checkpoint held-out on a seven-benchmark question-answering suite. The recipe works: the best run reaches 0.352 average exact match against a 0.092 untrained floor, a 3.8-fold gain, with no distillation step in the training loop. The reward shape also matters. The Search-R1-faithful exact-match-only reward is the worst of the three at every seed at the matched training horizon, and it is worst even on exact match, the metric it directly optimises. We conclude that the sparse exact-match reward, RLVR's default in mathematics and code, is the wrong starting point for models of this size. The reason-over-search setting can supply a suitable reward for RLVR on small models, but small-model RLVR needs its own reward-design study rather than a scaled-down copy of a large-model recipe.