2nd/10_Wiki/Topics/AI_and_ML/Policy-Optimization.md

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

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

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)

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)

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)

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)

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)

# 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)

# 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