mlsanityData to 14 Oct 2026

Hint-Guided Diversified Policy Optimization for LLM Reasoning

arXiv 2606.03021 ↗First posted 2 Jun 2026cs.CLcited by 2

On the map: LLM reasoning → Reinforcement learning for reasoning

Abstract (arXiv)

Recent developments in Large Language Models (LLMs) have showcased impressive reasoning capabilities, with Reinforcement Learning with Verifiable Rewards (RLVR) being a promising enhancement strategy. However, existing reward mechanisms are constrained to the outcome-level correctness and lack explicit signals to guide the model to consider diverse solutions. In contrast, human problem solving typically involves evaluating multiple potential approaches and selecting the most reliable solution, a cognitive process that current RLVR frameworks do not explicitly incentivize. Inspired by this, we propose Hint-Guided Diversified Policy Optimization (HDPO), allowing the model to first list all potential candidate solution outlines as hints and then select the most reliable one for further reasoning. HDPO comprises two stages of Cold Start for Structured Reasoning and Hint-Guided Diversified Reinforcement Learning to incentivize the model to generate diverse and reliable solutions following the ``propose-select-think'' trajectory. Experimental results show that HDPO effectively boosts LLM reasoning and enhances the diversity of candidate solutions as well as the LLM's ability to identify reliable solutions.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 24 of its 42 references that are in the map. First posted on arXiv 2 Jun 2026.

Builds on

24 of 42 references.

Closest ancestors · 10

Same direction, newest first

  1. 2025EDGE-GRPO: Entropy-Driven GRPO with Guided Error Correction for Advantage Diversity29 Jul
  2. 2025Critique-GRPO: Advancing LLM Reasoning with Natural Language and Numerical Feedback3 Jun
  3. 2025Learning to Reason under Off-Policy Guidance21 Apr
  4. 2025VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks7 Apr
  5. 2025Understanding R1-Zero-Like Training: A Critical Perspective26 Mar
  6. 2025SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild24 Mar
  7. 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scale18 Mar
  8. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning22 Jan
  9. 2025Kimi k1.5: Scaling Reinforcement Learning with LLMs22 Jan
  10. 2017Proximal Policy Optimization Algorithms20 Jul

Other references · 14

  1. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  2. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  3. 2025Qwen3 Technical Reportcited by 8,820
  4. 2021Evaluating Large Language Models Trained on Codecited by 8,320
  5. 2023GPQA: A Graduate-Level Google-Proof Q&A Benchmarkcited by 2,879
  6. 2025Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Modelscited by 1,261
  7. 2024OpenAI o1 System Cardcited by 1,244
  8. 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,090
  9. 2024M3-Embedding: Multi-Linguality, Multi-Functionality, Multi-Granularity Text Embeddings Through Self-Knowledge Distillationcited by 1,073
  10. 2025Group Sequence Policy Optimizationcited by 835
  11. 2025L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learningcited by 384
  12. 2025Beyond Distillation: Pushing the Limits of Medical LLM Reasoning with Minimalist Rule-Based RLcited by 36
2 more
  1. 2025Language Models Can Learn from Verbal Feedback Without Scalar Rewardscited by 18
  2. 2025ToTRL: Unlock LLM Tree-of-Thoughts Reasoning Potential through Puzzles Solvingcited by 8

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Strategically Diverse Sampling for Self-Trainingcited by 0
  2. 2026Learning from Evolving Errors: Adaptive Iterative Repair for On-Policy Distillationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Staying in the Sweet Spot: Responsive Reasoning Evolution via Capability-Adaptive Hint Scaffolding
  2. 2026SetPO: Set-Level Policy Optimization for Diversity-Preserving LLM Reasoning
  3. 2026Re2: Unlocking LLM Reasoning via Reinforcement Learning with Re-solving
  4. 2026Resource-Efficient Reinforcement for Reasoning Large Language Models via Dynamic One-Shot Policy Refinement
  5. 2026Back to Basics: Revisiting Exploration in Reinforcement Learning for LLM Reasoning via Generative Probabilities
  6. 2025Don't Tell the Answer, Truly Guide the Reasoning During RL Rollouts
  7. 2025Enhancing LLM Reasoning with Iterative DPO: A Comprehensive Empirical Investigation
  8. 2026Training LLMs for Divide-and-Conquer Reasoning Elevates Test-Time Scalability