Reinforcement Learning for Hierarchical Reasoning Rewards: Minimax-Optimal Rates with Transformers

arXiv:2610.08561 · cs.LG, stat.ML · Submitted 2026-10-06 · Read on arXiv

cs.LG, stat.ML

Submitted: 2026-10-06

Updated: 2026-10-06

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence
• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• Kimi k1.5: Scaling Reinforcement Learning with LLMs
• Proximal Policy Optimization Algorithms
• Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning
• When Greedy Sampling Explores: KL-Regularized Contextual Bandits without Eluder-Dimension Dependence
• Fine-Tuning Language Models from Human Preferences

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