# Scaling of Search and Learning: A Roadmap to Reproduce o1 from Reinforcement Learning Perspective

arXiv: https://arxiv.org/abs/2412.14135 · HTML: https://mlsanity.com/paper/2412.14135/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 97 of its 229 references that are in the map.
- First posted on arXiv 18 Dec 2024.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 97)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [Scalable agent alignment via reward modeling: a research direction](https://mlsanity.com/paper/1811.07871/) (2018)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [InternLM2 Technical Report](https://mlsanity.com/paper/2403.17297/) (2024)
- [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)
- [Navigation World Models](https://mlsanity.com/paper/2412.03572/) (2024)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)
- [Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning](https://mlsanity.com/paper/2405.00451/) (2024)
- [Emergent Analogical Reasoning in Large Language Models](https://mlsanity.com/paper/2212.09196/) (2022)
- [Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategies](https://mlsanity.com/paper/2308.03188/) (2023)
- [Secrets of RLHF in Large Language Models Part I: PPO](https://mlsanity.com/paper/2307.04964/) (2023)

## Built on by (most cited first, 30 of 50)

- [Search-o1: Agentic Search-Enhanced Large Reasoning Models](https://mlsanity.com/paper/2501.05366/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [HuatuoGPT-o1, Towards Medical Complex Reasoning with LLMs](https://mlsanity.com/paper/2412.18925/) (2024)
- [DAST: Difficulty-Adaptive Slow-Thinking for Large Reasoning Models](https://mlsanity.com/paper/2503.04472/) (2025)
- [LLM Post-Training: A Deep Dive into Reasoning Large Language Models](https://mlsanity.com/paper/2502.21321/) (2025)
- [A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyond](https://mlsanity.com/paper/2503.21614/) (2025)
- [A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systems](https://mlsanity.com/paper/2504.09037/) (2025)
- [An Empirical Study on Eliciting and Improving R1-like Reasoning Models](https://mlsanity.com/paper/2503.04548/) (2025)
- [Revisiting the Test-Time Scaling of o1-like Models: Do they Truly Possess Test-Time Scaling Capabilities?](https://mlsanity.com/paper/2502.12215/) (2025)
- [RedStar: Does Scaling Long-CoT Data Unlock Better Slow-Reasoning Systems?](https://mlsanity.com/paper/2501.11284/) (2025)
- [InftyThink: Breaking the Length Limits of Long-Context Reasoning in Large Language Models](https://mlsanity.com/paper/2503.06692/) (2025)
- [MARFT: Multi-Agent Reinforcement Fine-Tuning](https://mlsanity.com/paper/2504.16129/) (2025)
- [MT-R1-Zero: Advancing LLM-based Machine Translation via R1-Zero-like Reinforcement Learning](https://mlsanity.com/paper/2504.10160/) (2025)
- [PonderLM: Pretraining Language Models to Ponder in Continuous Space](https://mlsanity.com/paper/2505.20674/) (2025)
- [Deconstructing Long Chain-of-Thought: A Structured Reasoning Optimization Framework for Long CoT Distillation](https://mlsanity.com/paper/2503.16385/) (2025)
- [Reasoning Language Models: A Blueprint](https://mlsanity.com/paper/2501.11223/) (2025)
- [VisuoThink: Empowering LVLM Reasoning with Multimodal Tree Search](https://mlsanity.com/paper/2504.09130/) (2025)
- [Beyond Distillation: Pushing the Limits of Medical LLM Reasoning with Minimalist Rule-Based RL](https://mlsanity.com/paper/2505.17952/) (2025)
- [Two Heads are Better Than One: Test-time Scaling of Multi-agent Collaborative Reasoning](https://mlsanity.com/paper/2504.09772/) (2025)
- [Incentivizing Dual Process Thinking for Efficient Large Language Model Reasoning](https://mlsanity.com/paper/2505.16315/) (2025)
- [A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Law](https://mlsanity.com/paper/2505.02665/) (2025)
- [On the Effect of Sampling Diversity in Scaling LLM Inference](https://mlsanity.com/paper/2502.11027/) (2025)
- [Direct Reasoning Optimization: Token-Level Reasoning Reflectivity Meets Rubric Gates for Unverifiable Tasks](https://mlsanity.com/paper/2506.13351/) (2025)
- [Agent models: Internalizing Chain-of-Action Generation into Reasoning models](https://mlsanity.com/paper/2503.06580/) (2025)
- [Learning from Peers in Reasoning Models](https://mlsanity.com/paper/2505.07787/) (2025)
- [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025)
- [Enhancing Latent Computation in Transformers with Latent Tokens](https://mlsanity.com/paper/2505.12629/) (2025)
- [Generating Symbolic World Models via Test-time Scaling of Large Language Models](https://mlsanity.com/paper/2502.04728/) (2025)
- [A Survey on Feedback-based Multi-step Reasoning for Large Language Models on Mathematics](https://mlsanity.com/paper/2502.14333/) (2025)

## Abstract (arXiv)

OpenAI o1 represents a significant milestone in Artificial Inteiligence, which achieves expert-level performances on many challanging tasks that require strong reasoning ability.OpenAI has claimed that the main techinique behinds o1 is the reinforcement learining. Recent works use alternative approaches like knowledge distillation to imitate o1's reasoning style, but their effectiveness is limited by the capability ceiling of the teacher model. Therefore, this paper analyzes the roadmap to achieving o1 from the perspective of reinforcement learning, focusing on four key components: policy initialization, reward design, search, and learning. Policy initialization enables models to develop human-like reasoning behaviors, equipping them with the ability to effectively explore solution spaces for complex problems. Reward design provides dense and effective signals via reward shaping or reward modeling, which is the guidance for both search and learning. Search plays a crucial role in generating high-quality solutions during both training and testing phases, which can produce better solutions with more computation. Learning utilizes the data generated by search for improving policy, which can achieve the better performance with more parameters and more searched data. Existing open-source projects that attempt to reproduce o1 can be seem as a part or a variant of our roadmap. Collectively, these components underscore how learning and search drive o1's advancement, making meaningful contributions to the development of LLM.