---
id: wiki-2026-0508-grpo
title: GRPO (Group Relative Policy Optimization)
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [GRPO, group relative policy optimization, DeepSeek R1, RL fine-tune]
duplicate_of: none
source_trust_level: A
confidence_score: 0.92
verification_status: applied
tags: [rl, grpo, deepseek, reasoning, llm-fine-tune, ppo-alternative]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: TRL / DeepSeek
---

# GRPO (Group Relative Policy Optimization)

## 매 한 줄
> **"매 PPO 의 critic-free variant — 매 group 의 sample 의 의 의 baseline"**. DeepSeek 2024-2025. 매 R1 reasoning 의 enable. 매 reward model 의 의 의 X (rule-based reward 의 충분). 매 modern RLHF / reasoning 의 popular.

## 매 핵심

### 매 vs PPO
- **PPO**: 매 critic (value network).
- **GRPO**: 매 group sample 의 mean 의 baseline.
- **Result**: 매 simpler, 매 reasoning 의 strong.

### 매 algorithm
1. 매 prompt → 매 G rollouts (different responses).
2. 매 reward 의 매 rollout 의 score.
3. 매 advantage = (reward - group_mean) / group_std.
4. 매 PPO-style clipped objective.

### 매 famous
- **DeepSeek-Math** (2024).
- **DeepSeek-R1** (2025): 매 reasoning emerge.

### 매 응용
1. **Math reasoning**.
2. **Code generation**.
3. **Tool use**.
4. **Long CoT**.

## 💻 패턴

### Basic GRPO loop
```python
import torch
import torch.nn.functional as F

def grpo_step(policy, ref_policy, prompts, reward_fn, group_size=8, beta=0.04, eps=0.2):
    advantages_all = []
    log_probs_old_all = []
    log_probs_ref_all = []
    responses_all = []
    
    for prompt in prompts:
        # 매 G rollouts
        rollouts = []
        rewards = []
        for _ in range(group_size):
            response = policy.generate(prompt, do_sample=True)
            r = reward_fn(prompt, response)
            rollouts.append(response); rewards.append(r)
        
        rewards = torch.tensor(rewards)
        # 매 group baseline
        adv = (rewards - rewards.mean()) / (rewards.std() + 1e-8)
        advantages_all.extend(adv.tolist())
        
        # 매 log prob
        for resp in rollouts:
            log_probs_old_all.append(policy.log_prob(prompt, resp).detach())
            log_probs_ref_all.append(ref_policy.log_prob(prompt, resp).detach())
            responses_all.append((prompt, resp))
    
    # 매 PPO-style update
    for _ in range(4):  # 매 ppo epochs
        for (prompt, resp), adv, log_old, log_ref in zip(responses_all, advantages_all, log_probs_old_all, log_probs_ref_all):
            log_new = policy.log_prob(prompt, resp)
            ratio = (log_new - log_old).exp()
            
            obj1 = ratio * adv
            obj2 = ratio.clamp(1 - eps, 1 + eps) * adv
            policy_loss = -torch.min(obj1, obj2).mean()
            
            # 매 KL penalty (vs ref)
            kl = log_new - log_ref
            kl_loss = beta * kl.mean()
            
            loss = policy_loss + kl_loss
            loss.backward()
            optim.step(); optim.zero_grad()
```

### Rule-based reward (math)
```python
def math_reward(prompt, response):
    """매 deepseek-style: extract answer, verify."""
    answer = extract_answer(response)
    expected = extract_answer(prompt['solution'])
    
    correctness = 1.0 if answer == expected else 0.0
    format_bonus = 0.1 if has_required_format(response) else 0
    
    return correctness + format_bonus
```

### TRL implementation
```python
from trl import GRPOTrainer, GRPOConfig

trainer = GRPOTrainer(
    model='Qwen/Qwen2.5-7B',
    reward_funcs=[correctness_reward, format_reward],
    args=GRPOConfig(
        output_dir='out',
        num_generations=8,  # 매 group size
        per_device_train_batch_size=1,
        gradient_accumulation_steps=8,
        learning_rate=5e-6,
        max_prompt_length=512,
        max_completion_length=1024,
        beta=0.04,
    ),
    train_dataset=ds,
)
trainer.train()
```

### Multi-objective reward
```python
def multi_reward(prompt, response):
    rewards = {}
    rewards['correctness'] = correctness(prompt, response)
    rewards['format'] = check_format(response)
    rewards['length'] = -abs(len(response) - 500) / 1000  # 매 prefer ~500 tokens
    rewards['cot_quality'] = check_reasoning_quality(response)
    
    weights = {'correctness': 1.0, 'format': 0.1, 'length': 0.05, 'cot_quality': 0.3}
    return sum(rewards[k] * weights[k] for k in rewards)
```

### Reasoning-focused (R1-style)
```python
THINK_FORMAT = """
<think>
{reasoning}
</think>
<answer>
{answer}
</answer>
"""

def r1_format_reward(response):
    has_think = '<think>' in response and '</think>' in response
    has_answer = '<answer>' in response and '</answer>' in response
    return 0.5 if (has_think and has_answer) else 0
```

### Self-consistency (best-of-N at eval)
```python
def best_of_n_eval(model, prompt, n=16):
    responses = [model.generate(prompt, do_sample=True) for _ in range(n)]
    answers = [extract_answer(r) for r in responses]
    # 매 majority vote
    from collections import Counter
    return Counter(answers).most_common(1)[0][0]
```

### KL control
```python
def adaptive_beta(target_kl, current_kl, beta):
    if current_kl > 1.5 * target_kl: return beta * 1.5
    if current_kl < 0.5 * target_kl: return beta / 1.5
    return beta
```

### Reward hacking detection
```python
def detect_reward_hacking(rollouts, rewards):
    """매 high reward 의 의 의 quality 의 X?"""
    high_reward = [r for r, score in zip(rollouts, rewards) if score > 0.9]
    quality = [llm_judge_quality(r) for r in high_reward]
    if np.mean(quality) < 0.5:
        return 'WARN: high reward but low quality — possibly hacking'
    return None
```

### Process reward (PRM)
```python
def process_reward(steps):
    """매 step-by-step verify."""
    return sum(prm_score(step) for step in steps) / len(steps)
```

### Iterative training (R1-style)
```python
def r1_pipeline(base_model, dataset):
    # 매 stage 1: reasoning data SFT
    sft_model = sft(base_model, reasoning_data)
    
    # 매 stage 2: GRPO
    grpo_model = grpo(sft_model, dataset, math_reward)
    
    # 매 stage 3: rejection sampling — 매 high-quality 의 SFT 다시
    rs_data = filter_high_quality(grpo_model.generate_many(dataset))
    final = sft(grpo_model, rs_data)
    
    return final
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Reasoning task | GRPO + rule reward |
| Preference align | DPO / PPO |
| Code | GRPO + execution reward |
| General chat | RLHF / DPO |
| Tool use | GRPO + success reward |
| Cost-aware | GRPO (no critic) |

**기본값**: 매 reasoning = GRPO + rule + format reward + iterative + KL control.

## 🔗 Graph
- 부모: [[RLHF]] · [[Reinforcement-Learning]]
- 변형: [[PPO]] · [[DPO]]
- 응용: [[DeepSeek-R1]]
- Adjacent: [[Fine-tuning]] · [[Foundation-Models]]

## 🤖 LLM 활용
**언제**: 매 reasoning, math, code. 매 verifiable reward.
**언제 X**: 매 subjective preference (use DPO).

## ❌ 안티패턴
- **No KL control**: 매 reward hack drift.
- **Tiny group**: 매 noisy advantage.
- **No rule for format**: 매 hack format.
- **Single-objective**: 매 hacking.

## 🧪 검증 / 중복
- Verified (DeepSeek-Math 2024, DeepSeek-R1 2025, TRL docs).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — GRPO + 매 TRL / R1 / multi-reward / pipeline code |