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Group Relative Policy Optimization (GRPO) is a reinforcement-learning method for updating a language model from rewards on its own sampled answers. It generates several answers to the same prompt, scores them, and uses each answer’s standing within that group as its learning signal. That group comparison supplies a baseline without a separately learned value critic, while a PPO-style clipped update constrains how much the policy changes.
How does GRPO work?
GRPO was introduced in the 2024 DeepSeekMath paper as a variant of Proximal Policy Optimization (PPO). It is an update method—not a complete recipe for teaching a model to reason. The prompts, model, reward design, and training settings all affect what it learns.
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- Generate a group. For each prompt in a batch, the current policy samples multiple completions.
- Score the answers. A reward function, reward model, or task feedback assigns a score to each completion.
- Compare within the prompt’s group. GRPO turns the scores into relative advantages. In a common formulation, it subtracts the group’s mean reward and divides by the group’s standard deviation. Other scaling choices are possible.
- Update the policy. Token-level probability ratios feed a PPO-style clipped objective. Completions with positive relative advantage are pushed toward higher probability; those with negative advantage are pushed toward lower probability. Clipping limits how far the update can move those ratios in a batch.
- Optionally constrain drift from a reference policy. The original objective includes a KL-divergence penalty. Whether that term is enabled depends on the implementation and settings.
For example, a math prompt could produce several sampled solutions, which a checker scores according to their final answers. A solution scoring above its group’s average receives a positive relative signal; one below it receives a negative signal. That illustrates the mechanics, not a universal GRPO reward: other tasks need different scoring, and not every application uses a binary checker.
GRPO is also an online learning method: it uses responses generated by the trained model during training, then updates the model iteratively. The current Hugging Face TRL GRPOTrainer documentation describes this setup and exposes configurable reward functions and training options.
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What changes compared with PPO?
In a typical PPO setup, a separately learned value function estimates the expected return and supplies a baseline for calculating advantages. GRPO replaces that learned baseline with the scores of multiple completions for the same prompt. This is the defining change; both approaches still use policy-gradient updates and depend on a meaningful reward signal.
| Aspect | PPO | GRPO |
|---|---|---|
| Baseline | Typically estimated by a separately learned value or critic model. | Estimated from the relative rewards of a group of completions for the same prompt. |
| Completions per prompt | Uses sampled responses; the exact count depends on the setup. | Samples a group of responses for each prompt so it can compare their rewards. |
| Reward source | Depends on the task and training design. | Also depends on the task: a reward model, function, or task feedback may score answers. |
| Advantage calculation | Uses the learned value estimate as its baseline. | Uses group-relative rewards; centering and scaling depend on the formulation. |
| Policy constraint | PPO-style clipping constrains policy ratios; reference-policy KL use depends on the setup. | Uses PPO-style clipping; the original formulation includes reference-policy KL, but implementations may configure it differently. |
| Sequence-length treatment | Depends on the PPO implementation and loss. | Depends on the selected loss and normalization; GRPO-related variants address response-length bias differently. |
Removing the critic can reduce memory use compared with PPO’s separate value approximation, which was part of GRPO’s original motivation. It does not remove the need to train the policy, generate multiple answers, compute rewards, or run the rest of the training stack. Group sampling and scoring have costs of their own.
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Why do reward and normalization choices matter?
A group comparison is only as useful as its scores
Relative ranking tells the model which answers scored better under the chosen reward; it does not establish that those answers are better in the sense a user cares about. If a reward function is weak or exploitable, GRPO can reinforce the wrong behavior. A checker for a verifiable math answer is one possible reward source, not a requirement for all tasks.
Reward scaling changes the signal
Centering rewards by the group mean and scaling by the group’s standard deviation is a common approach, not a universal rule. The current TRL documentation exposes choices including group-level and batch-level scaling, as well as no reward scaling. It also discusses how standard-deviation scaling can introduce question-level difficulty bias. The choice affects the learning signal, so the scaling method should be treated as part of the training design.
Loss choice affects response length
Different GRPO-related losses normalize sequence contributions differently. Current TRL documentation covers GRPO, DAPO, and Dr. GRPO loss options and discusses their approaches to response-length bias. A method’s name alone therefore does not tell you every detail of a particular training run.
KL settings depend on the implementation
The original GRPO objective includes a KL penalty against a reference policy. In the current TRL documentation, the KL coefficient, beta, defaults to zero, so the term is omitted unless enabled. That is a documented implementation default, not a property shared by every GRPO implementation.
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What do DeepSeekMath’s reported results show?
The DeepSeekMath authors reported 51.7% on the competition-level MATH benchmark without external toolkits or voting. They reported 60.9% using self-consistency over 64 samples. These are results for the DeepSeekMath model and its full training and evaluation setup—not a guarantee from GRPO alone or an isolated measurement of GRPO’s causal contribution. The authors also described a training context involving 120 billion math-related pretraining tokens; that figure is not a GRPO setting.
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Can you use GRPO in a training library?
Hugging Face TRL currently documents a GRPOTrainer, a quick start using a Qwen2.5 0.5B Instruct model, configurable reward functions, and multiple training options. Its documentation is live and may change across library releases, so check the current page for the settings and defaults applicable to your version rather than assuming one configuration is universal.
DeepSeek’s DeepSeekMath repository lists 7B base, instruct, and RL model variants and says commercial use is supported subject to the model license. The repository’s code license and the model’s license are distinct; check the current model license text before using a particular artifact.
GRPO has also been reported in connection with DeepSeek-R1-Zero and DeepSeek-R1. The Nature article titled “DeepSeek-R1 incentivizes reasoning in LLMs through reinforcement learning” is a reference for that connection; the specific reward setup and training stages are not detailed here.
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