---
id: wiki-2026-0508-model-free-rl-vs-model-based-rl
title: Model-Free RL vs Model-Based RL
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [MFRL vs MBRL, Model-Based Reinforcement Learning, World Model]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [reinforcement-learning, machine-learning, planning, world-model]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: PyTorch/JAX
---

# Model-Free RL vs Model-Based RL

## 매 한 줄
> **"매 environment dynamics 의 learn 하나, 의 X 하나 — sample efficiency 의 vs simplicity 의 trade"**. Model-free (Q-learning, PPO) 매 reward signal 의 만으로 policy 의 update — simple 의 brittle. Model-based (Dreamer, MuZero) 매 world model 의 learn → 매 imagined rollout 의 train. 2026 의 Dreamer V3, EfficientZero, DayDreamer 의 robotics deployment — sample efficiency 의 1-2 orders.

## 매 핵심

### 매 dichotomy
- **Model-free**: $\pi(a|s)$ 또는 $Q(s,a)$ 의 직접 learn. 매 transition $p(s'|s,a)$ 의 access 의 X.
- **Model-based**: $\hat{p}(s'|s,a)$, $\hat{r}(s,a)$ 의 learn → 매 plan / imagined rollout / Dyna-style.

### 매 trade-off table
| Axis | Model-Free | Model-Based |
|---|---|---|
| Sample efficiency | Low | **High** (10-100×) |
| Compute per update | Low | **High** |
| Asymptotic perf | **Often higher** | Bounded by model error |
| Stability | **Stable** | Compounding model error |
| Transfer | Poor | **Better** (model 의 reuse) |
| Implementation | **Simple** | Complex |

### 매 modern flavors
- **Model-free**: PPO, SAC, DQN family, TD3.
- **Model-based**: Dreamer V3 (RSSM), MuZero (planning + value tree), TD-MPC2, PILCO (Gaussian process).
- **Hybrid**: MBPO (model-generated rollouts → SAC), Dyna-Q.

### 매 응용
1. Robotics (sample-efficient sim-to-real).
2. Atari/board game (MuZero).
3. Drug design (sample-efficient exploration).
4. Game NPC behavior (PPO 의 still default).

## 💻 패턴

### PPO — model-free policy gradient (gymnasium)
```python
import torch, torch.nn as nn, torch.nn.functional as F
from torch.distributions import Categorical

class ActorCritic(nn.Module):
    def __init__(self, obs_dim, n_act):
        super().__init__()
        self.shared = nn.Sequential(nn.Linear(obs_dim, 64), nn.Tanh(),
                                    nn.Linear(64, 64), nn.Tanh())
        self.pi = nn.Linear(64, n_act)
        self.v  = nn.Linear(64, 1)
    def forward(self, x):
        h = self.shared(x)
        return Categorical(logits=self.pi(h)), self.v(h).squeeze(-1)

def ppo_step(ac, opt, batch, clip=0.2, vf_c=0.5, ent_c=0.01):
    dist, v = ac(batch.obs)
    logp = dist.log_prob(batch.act)
    ratio = torch.exp(logp - batch.logp_old)
    surr1 = ratio * batch.adv
    surr2 = torch.clamp(ratio, 1-clip, 1+clip) * batch.adv
    pi_loss = -torch.min(surr1, surr2).mean()
    v_loss = F.mse_loss(v, batch.ret)
    ent = dist.entropy().mean()
    loss = pi_loss + vf_c * v_loss - ent_c * ent
    opt.zero_grad(); loss.backward(); opt.step()
    return loss.item()
```

### Dreamer-style world model (RSSM skeleton)
```python
class RSSM(nn.Module):
    def __init__(self, obs_dim, act_dim, h=200, z=32):
        super().__init__()
        self.gru = nn.GRUCell(z + act_dim, h)
        self.prior = nn.Linear(h, 2 * z)         # μ, σ
        self.post  = nn.Linear(h + obs_dim, 2 * z)
        self.dec_obs = nn.Linear(h + z, obs_dim)
        self.dec_rew = nn.Linear(h + z, 1)

    def step(self, h, z, a, obs=None):
        h = self.gru(torch.cat([z, a], -1), h)
        pri_mu, pri_log = self.prior(h).chunk(2, -1)
        if obs is not None:
            po_mu, po_log = self.post(torch.cat([h, obs], -1)).chunk(2, -1)
            z = po_mu + torch.exp(po_log) * torch.randn_like(po_mu)
        else:
            z = pri_mu + torch.exp(pri_log) * torch.randn_like(pri_mu)
        return h, z, (pri_mu, pri_log)

    def imagine(self, h, z, policy, T=15):
        states = []
        for _ in range(T):
            a = policy(torch.cat([h, z], -1))
            h, z, _ = self.step(h, z, a)
            states.append((h, z))
        return states
```

### Dyna-Q (hybrid — tabular)
```python
def dyna_q(env, n_planning=10, episodes=500, alpha=0.1, gamma=0.99, eps=0.1):
    Q = defaultdict(lambda: np.zeros(env.action_space.n))
    model = {}                                          # (s,a) → (r, s')
    for _ in range(episodes):
        s, _ = env.reset()
        done = False
        while not done:
            a = np.random.randint(env.action_space.n) if np.random.random() < eps \
                else int(np.argmax(Q[s]))
            s2, r, done, *_ = env.step(a)
            Q[s][a] += alpha * (r + gamma * Q[s2].max() - Q[s][a])
            model[(s, a)] = (r, s2)
            for _ in range(n_planning):                 # 매 imagined step
                (sp, ap), (rp, sp2) = random.choice(list(model.items())), None
                rp, sp2 = model[(sp, ap)]
                Q[sp][ap] += alpha * (rp + gamma * Q[sp2].max() - Q[sp][ap])
            s = s2
```

### MuZero (planning sketch — value/policy net + MCTS)
```python
# 매 environment 의 black-box; learned (representation, dynamics, prediction) heads
# search 매 imagined trajectory 의 over MCTS — replay 매 (search policy, search value, n-step return)
# 의 train. (full impl 매 muzero_general repo)
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Lots of cheap simulation | **Model-free** (PPO/SAC) — simpler |
| Real-robot, expensive samples | **Model-based** (Dreamer V3, TD-MPC2) |
| Discrete board game | **MuZero** — planning 의 wins |
| Continuous control benchmark | SAC or DreamerV3 |
| Fast prototype | PPO — most stable, easiest to tune |
| Long-horizon planning | Model-based + planning |

**기본값**: prototype 매 PPO. Sample 매 expensive — Dreamer V3 / TD-MPC2.

## 🔗 Graph
- 부모: [[Reinforcement Learning]]
- 변형: [[PPO]]
- Adjacent: [[World Model]] · [[Planning]]

## 🤖 LLM 활용
**언제**: trade-off explanation, algorithm choice, pseudocode skeleton.
**언제 X**: 매 hyperparameter — paper-specific 의 cross-check (Dreamer V3 매 sensitivity 의 paper 의 careful).

## ❌ 안티패턴
- **MBRL 의 default 의 reach**: 매 cheap-sim 환경 의 PPO 의 win 매 simpler.
- **Imagined rollout 의 too-long horizon**: 매 model error compounds — 5-15 step 의 typical.
- **MFRL 의 sparse reward 의 hope**: 매 exploration 의 add (RND, ICM) — 또는 의 model-based 의 switch.
- **MuZero 의 small problem 의 use**: 매 overkill — tabular Q 의 enough.
- **Single-seed report**: 매 RL variance huge — 5+ seeds 의 IQM (Agarwal et al. 2021).

## 🧪 검증 / 중복
- Verified (Sutton & Barto 2nd ed. 2018; Hafner _DreamerV3_ 2023; Schrittwieser _MuZero_ Nature 2020).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — MFRL/MBRL trade-off + DreamerV3/MuZero 정리 |