Reinforcement Learning for Reasoning (RLVR and GRPO)

What is it?

Instead of asking people which answer they prefer, you can reward a model when its answer can be checked automatically — the maths result is right, the code passes its tests. Training a model this way pushes it to find reasoning strategies that work, and is a key ingredient behind many reasoning models.

GRPO is one algorithm used for this; it compares several answers to the same question against each other.

Also known as: RLVR, GRPO, group relative policy optimization, reinforcement learning from verifiable rewards, RL with verifiable rewards, rule-based rewards, R1 style training, reasoning RL.

Technical definition

RL with verifiable rewards (RLVR) uses programmatic reward functions on tasks with ground truth. Group Relative Policy Optimization (GRPO; introduced in DeepSeekMath, Shao et al., 2024) samples a group of outputs per prompt and uses within-group reward normalisation as the advantage, removing the learned critic used by PPO (Proximal Policy Optimization (PPO)). Reported outcomes include longer reasoning traces and self-verification behaviours (DeepSeek-R1 report). It is a reinforcement-learning method on verifiable tasks, distinct from preference optimisation methods like Direct Preference Optimization (DPO).

Entity type: technique · Freshness class: volatile.

When should I use it?

Relevant if you train or fine-tune models on tasks with automatic checkers. Most application teams consume such models rather than train them.

Prerequisites and related concepts

Understand these first: Reinforcement Learning, Proximal Policy Optimization (PPO), Outcome Reward Model (ORM).

Related concepts: Reasoning Models, Process Reward Model (PRM), Reward Hacking and Over-Optimization, Preference Optimization (Aligning Models from Human or AI Preferences), Direct Preference Optimization (DPO), RLHF (Reinforcement Learning from Human Feedback).

Implementation patterns

• Sample a group of G completions per prompt, score each with a verifier, normalise within the group, update the policy.
• Add a format reward so the final answer is parseable.
• Curriculum: start with solvable problems, increase difficulty.
• KL penalty or reference model to limit drift.

Technologies and frameworks

Commonly associated: TRL (Hugging Face), verl, OpenRLHF, unit-test sandboxes, math answer checkers. Names are examples of what exists, not recommendations, and projects change quickly.

Practical guide

1. Assemble prompts with exact, trustworthy verifiers.
2. Establish a supervised baseline.
3. Run small-scale RL and inspect samples regularly.
4. Track held-out and out-of-domain performance.
5. Defend verifiers against hacking.

Common failure modes

• Reward hacking: the model learns to exploit the checker (format tricks, test special-casing).
• Unstable training or collapsing output length.
• Gains confined to verifiable domains; poor transfer to open-ended tasks.
• Weak or leaky verifiers (answers present in the prompt).

Troubleshooting

• Rewards rise but real quality does not — Audit samples; harden the verifier (hidden tests, held-out checks).
• Output length explodes or collapses — Add length-aware rewards, or adjust KL / sampling settings.
• No learning signal (all rewards equal) — Adjust problem difficulty so some samples pass and some fail.

Contrasted with

• RLHF (Reinforcement Learning from Human Feedback) — RLHF learns rewards from human preferences; RLVR uses programmatic, verifiable rewards.
• Direct Preference Optimization (DPO) — DPO optimises directly on preference pairs without an RL loop; RLVR/GRPO is online RL with checkable rewards.
• Proximal Policy Optimization (PPO) — PPO uses a learned value function; GRPO uses group-relative advantages.

Questions this page answers

• What is GRPO?
• What is RLVR?
• How are reasoning models trained with reinforcement learning?
• How is GRPO different from PPO?
• Is DPO the same as reinforcement learning?

Typical goals: understand how reasoning models are trained; compare GRPO and PPO; choose reward signals for reasoning training.

Sources and verification

Status: not independently verified. This entry was authored on 2026-10-06 from general technical knowledge, without live checking of the sources below. Treat every source as a lead to confirm (identifier, title, authorship, current version) before publication or citation.

Freshness class: volatile — Products, versions, protocols, benchmarks, leaderboards, regulations and dates. Verify against the primary source before relying on specifics; re-review every 3 months.

Time-sensitive claims to verify before relying on them:

• Which production models were trained with RLVR/GRPO and how.
• Specific claims about emergent behaviours from RL training.
• Algorithm variants and best-practice hyperparameters, which change quickly.

Canonical sources (unverified leads):

• Shao et al., DeepSeekMath (introduces GRPO) (2024) — arXiv:2402.03300
• DeepSeek-AI, DeepSeek-R1 (2025) — arXiv:2501.12948
• Lambert et al., Tulu 3 (introduces RLVR naming) (2024) — arXiv:2411.15124

Related concepts