# Selective Expert Guidance for Effective and Diverse Exploration in Reinforcement Learning of LLMs

arXiv: https://arxiv.org/abs/2510.04140 · HTML: https://mlsanity.com/paper/2510.04140/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 41 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [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)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [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)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)
- [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [On-Policy RL Meets Off-Policy Experts: Harmonizing Supervised Fine-Tuning and Reinforcement Learning via Dynamic Weighting](https://mlsanity.com/paper/2508.11408/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [BREAD: Branched Rollouts from Expert Anchors Bridge SFT & RL for Reasoning](https://mlsanity.com/paper/2506.17211/) (2025)
- [Blending Supervised and Reinforcement Fine-Tuning with Prefix Sampling](https://mlsanity.com/paper/2507.01679/) (2025)
- [QuestA: Expanding Reasoning Capacity in LLMs via Question Augmentation](https://mlsanity.com/paper/2507.13266/) (2025)
- [GHPO: Adaptive Guidance for Stable and Efficient LLM Reinforcement Learning](https://mlsanity.com/paper/2507.10628/) (2025)
- [CER: Confidence Enhanced Reasoning in LLMs](https://mlsanity.com/paper/2502.14634/) (2025)

## Built on by (most cited first, 7 of 7)

- [Learning to Explore with Parameter-Space Noise: A Deep Dive into Parameter-Space Noise for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2602.02555/) (2026)
- [Experience Augmented Policy Optimization for LLM Reasoning](https://mlsanity.com/paper/2606.30420/) (2026)
- [Difficulty-Adaptive Tree-Structured Policy Optimization for Expanding Reasoning Coverage in RLVR](https://mlsanity.com/paper/2609.08650/) (2026)
- [ARMOR: Stabilizing On-Policy LLM RL with Off-Policy Anchor Samples](https://mlsanity.com/paper/2607.10481/) (2026)
- [MInTRL: Off-policy Intervention can boost On-policy RL](https://mlsanity.com/paper/2609.12419/) (2026)
- [Learning Beyond What You Sample: Off-Policy-Aware Cross-Model Trajectory Exchange for RLVR](https://mlsanity.com/paper/2609.37868/) (2026)
- [Guide, Then Let Go: Gap-Adaptive Teacher Scheduling for Sparse-Reward Agentic RL](https://mlsanity.com/paper/2609.37898/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has become a widely adopted technique for enhancing the reasoning ability of Large Language Models (LLMs). However, the effectiveness of RLVR strongly depends on the capability of base models. This issue arises because it requires the model to have sufficient capability to perform high-quality exploration, which involves both effectiveness and diversity. Unfortunately, existing methods address this issue by imitating expert trajectories, which improve effectiveness but neglect diversity. To address this, we argue that the expert only needs to provide guidance only at critical decision points rather than the entire reasoning path. Based on this insight, we propose MENTOR: Mixed-policy Expert Navigation for Token-level Optimization of Reasoning, a framework that provides expert guidance only at critical decision points to perform effective and diverse exploration in RLVR. Extensive experiments show that MENTOR enables models capture the essence of expert strategies rather than surface imitation, thereby performing high-quality exploration and achieving superior overall performance. Our code is available online.