---
id: wiki-2026-0508-policy-optimization
title: Policy Optimization
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [policy-gradient, ppo, trpo, grpo, dpo, rlhf-optimization]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [reinforcement-learning, ppo, grpo, dpo, rlhf]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: PyTorch / TRL
---

# Policy Optimization

## 매 한 줄
> **"매 policy π_θ 의 reward expectation 의 직접 maximize"**. 매 vanilla PG (REINFORCE) → A2C/A3C → 매 TRPO (trust region) → 매 PPO (clip surrogate, 2017) → 매 GRPO (group-relative, DeepSeek 2024) → 매 DPO (preference, 2023). 매 modern LLM RLHF 의 backbone.

## 매 핵심

### 매 algorithm 계보
- **매 REINFORCE (1992)**: ∇J = E[∇log π · R]. 매 high variance.
- **매 A2C/A3C (2016)**: actor-critic, advantage A = Q - V. 매 lower variance.
- **매 TRPO (2015)**: trust region — KL constraint. 매 monotonic improvement guarantee. 매 expensive (Fisher).
- **매 PPO (2017, Schulman)**: clipped surrogate r·A vs clip(r, 1-ε, 1+ε)·A. 매 first-order, 매 simple, 매 dominant 2017-2023.
- **매 GRPO (2024, DeepSeek)**: PPO 의 critic 의 제거 — 매 group-relative advantage (mean of K samples). 매 efficient for LLM RL.
- **매 DPO (2023, Rafailov)**: 매 reward model 의 우회 — 매 preference data 의 closed-form policy update. 매 RLHF simplified.
- **매 GSPO, KTO, ORPO** (2024): DPO variants.

### 매 PPO clip objective
```
L_CLIP(θ) = E[ min( r·A, clip(r, 1-ε, 1+ε)·A ) ]
where r = π_θ(a|s) / π_old(a|s)
```

### 매 GRPO (DeepSeek-Math/R1)
```
A_i = (R_i - mean(R)) / std(R)   # group-relative
L = E[ min(r·A, clip(r, 1-ε, 1+ε)·A) - β·KL(π||π_ref) ]
```
매 critic 의 사용 X — 매 sample group 의 baseline 으로.

### 매 DPO objective
```
L_DPO = -E[ log σ( β·log(π(y_w|x)/π_ref(y_w|x)) - β·log(π(y_l|x)/π_ref(y_l|x)) ) ]
```
매 chosen y_w + rejected y_l 의 directly optimize.

### 매 응용
1. 매 LLM RLHF (PPO → GRPO → DPO).
2. 매 robot control (PPO).
3. 매 game-playing (OpenAI Five, AlphaStar).
4. 매 LLM reasoning (R1-style RL).

## 💻 패턴

### PPO — minimal (CleanRL-style)
```python
import torch, torch.nn as nn
import torch.nn.functional as F

class ActorCritic(nn.Module):
    def __init__(self, obs_dim, act_dim):
        super().__init__()
        self.actor = nn.Sequential(nn.Linear(obs_dim, 64), nn.Tanh(),
                                   nn.Linear(64, 64), nn.Tanh(),
                                   nn.Linear(64, act_dim))
        self.critic = nn.Sequential(nn.Linear(obs_dim, 64), nn.Tanh(),
                                    nn.Linear(64, 64), nn.Tanh(),
                                    nn.Linear(64, 1))

def ppo_update(net, opt, obs, acts, old_logp, advs, returns, eps=0.2, c_v=0.5, c_e=0.01):
    logits = net.actor(obs)
    dist = torch.distributions.Categorical(logits=logits)
    logp = dist.log_prob(acts)
    ratio = (logp - old_logp).exp()
    surr1 = ratio * advs
    surr2 = ratio.clamp(1-eps, 1+eps) * advs
    pg_loss = -torch.min(surr1, surr2).mean()
    v = net.critic(obs).squeeze(-1)
    v_loss = F.mse_loss(v, returns)
    ent = dist.entropy().mean()
    loss = pg_loss + c_v * v_loss - c_e * ent
    opt.zero_grad(); loss.backward()
    nn.utils.clip_grad_norm_(net.parameters(), 0.5); opt.step()
```

### GAE (Generalized Advantage Estimation)
```python
def gae(rewards, values, dones, last_v, gamma=0.99, lam=0.95):
    advs = torch.zeros_like(rewards)
    g = 0
    for t in reversed(range(len(rewards))):
        next_v = last_v if t == len(rewards)-1 else values[t+1]
        delta = rewards[t] + gamma * next_v * (1 - dones[t]) - values[t]
        g = delta + gamma * lam * (1 - dones[t]) * g
        advs[t] = g
    return advs, advs + values
```

### GRPO — DeepSeek-style (TRL)
```python
from trl import GRPOConfig, GRPOTrainer
from transformers import AutoModelForCausalLM, AutoTokenizer

model = AutoModelForCausalLM.from_pretrained("Qwen/Qwen2.5-7B-Instruct")
tok = AutoTokenizer.from_pretrained("Qwen/Qwen2.5-7B-Instruct")

def reward_fn(prompts, completions, **kwargs):
    # 매 e.g. correctness check for math problems
    return [1.0 if check_answer(c) else 0.0 for c in completions]

config = GRPOConfig(
    num_generations=8,    # 매 group size K
    learning_rate=1e-6,
    beta=0.04,            # KL penalty
    max_prompt_length=512, max_completion_length=512,
)
trainer = GRPOTrainer(model=model, reward_funcs=reward_fn, args=config,
                      train_dataset=ds, processing_class=tok)
trainer.train()
```

### DPO (TRL)
```python
from trl import DPOTrainer, DPOConfig

# Dataset: {"prompt": str, "chosen": str, "rejected": str}
config = DPOConfig(beta=0.1, learning_rate=5e-7, max_length=1024)
trainer = DPOTrainer(model=model, ref_model=ref_model, args=config,
                     train_dataset=preference_ds, processing_class=tok)
trainer.train()
```

### Reward shaping for GRPO (math + format)
```python
import re

def reward_correctness(completions, ground_truth, **k):
    return [1.0 if extract_answer(c) == gt else 0.0
            for c, gt in zip(completions, ground_truth)]

def reward_format(completions, **k):
    # 매 <think>...</think><answer>...</answer> 의 강요
    pat = re.compile(r"<think>.*?</think>\s*<answer>.*?</answer>", re.S)
    return [0.5 if pat.search(c) else 0.0 for c in completions]

# Combine in TRL: pass as list reward_funcs=[reward_correctness, reward_format]
```

### KL penalty (PPO-RLHF)
```python
# 매 reference model 매 anchor 의 사용 — 매 RLHF 의 stay close to SFT
log_ratio = logp_policy - logp_ref
kl = (log_ratio.exp() - 1 - log_ratio).mean()  # 매 unbiased k3 estimator
loss = pg_loss + beta * kl
```

### TRPO line-search (sketch)
```python
# 매 modern code 매 PPO 의 사용 — TRPO 매 reference only
# 1. compute natural gradient: F^-1 g (Fisher inverse via conjugate gradient)
# 2. line-search with KL ≤ δ constraint
# 3. accept step if surrogate improves and KL within budget
```

## 매 결정 기준
| 상황 | Algorithm |
|---|---|
| 매 standard RL benchmark (Atari, MuJoCo) | 매 PPO |
| 매 LLM RL with verifiable reward | 매 GRPO |
| 매 LLM preference data (no reward model) | 매 DPO |
| 매 LLM RLHF (with RM) | 매 PPO or GRPO |
| 매 sample-efficient continuous control | 매 SAC (off-policy) |
| 매 monotonic improvement guarantee | 매 TRPO (rare in practice) |

**기본값**: 매 PPO (RL benchmark) / GRPO (LLM RL) / DPO (LLM preference).

## 🔗 Graph
- 부모: [[Reinforcement-Learning]] · [[RLHF]]
- 변형: [[PPO]] · [[GRPO]] · [[DPO]] · [[TRPO]] · [[A2C]]

## 🤖 LLM 활용
**언제**: 매 PPO 매 baseline RL, 매 GRPO 매 LLM verifiable-reward task (math, code), 매 DPO 매 preference data only 매 사용.
**언제 X**: 매 sample-efficiency critical (off-policy: SAC, TD3), 매 ground-truth label exists (supervised 의 사용).

## ❌ 안티패턴
- **매 huge KL divergence allow**: 매 policy 매 ref 보다 collapse → 매 reward hacking.
- **매 advantage 의 normalize 안 함**: 매 PPO 매 batch advantage normalization 의 critical.
- **매 single epoch only**: 매 PPO 매 multiple epochs (3-10) 의 importance ratio 의 활용.
- **매 GRPO without group**: 매 group size 1 → 매 advantage = 0.

## 🧪 검증 / 중복
- Verified (PPO Schulman 2017, GRPO DeepSeek-Math 2024, DPO Rafailov 2023, TRL docs).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — PPO/GRPO/DPO + GAE + TRL patterns |
