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Antigravity Agent
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id: wiki-2026-0508-reward-shaping-in-rl
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title: Reward Shaping in RL
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [Reward Shaping, Shaped Reward, Dense Reward Design]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.95
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verification_status: applied
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tags: [reinforcement-learning, reward-design, RLHF, GRPO, sparse-reward]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: Python
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framework: PyTorch/Gymnasium/TRL
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---
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# Reward Shaping in RL
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## 매 한 줄
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> **"매 sparse reward → dense intermediate signal — without changing optimal policy."**. Ng, Harada, Russell 1999 ("Policy Invariance Under Reward Transformations") 의 prove 의 매 potential-based shaping F(s,s') = γΦ(s') − Φ(s) 가 optimal policy 의 preserve, 매 modern RLHF/GRPO/RLVR 의 reward design 의 foundation 의.
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## 매 핵심
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### 매 핵심 theorem (Ng et al. 1999)
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- Shaped reward: r'(s, a, s') = r(s, a, s') + F(s, s').
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- F(s, s') = γ·Φ(s') − Φ(s) (potential-based) → policy invariance guaranteed.
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- 의 X 가 well-defined Φ — 매 arbitrary bonus 의 optimal policy 의 distort 의 가능.
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### 매 shaping types
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- **Potential-based** (theory-safe): heuristic value Φ(s).
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- **Curiosity / intrinsic motivation**: ICM, RND — exploration bonus.
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- **Demonstrations (LfD)**: shaped reward from expert similarity.
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- **Curriculum**: progressively harder targets.
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- **RLHF reward model**: human-trained dense reward.
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- **RLVR (verifiable)**: rule-based pass/fail (math, code) — sparse but exact.
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- **GRPO advantages** (DeepSeek 2024-25): group-relative normalization replaces critic.
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### 매 응용
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1. Sparse-reward locomotion / manipulation.
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2. Game RL (StarCraft II, Atari hard-exploration).
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3. RLHF for LLM alignment.
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4. RLVR/GRPO for math/code (DeepSeek-R1, o1).
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5. Robotics imitation + RL hybrid.
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## 💻 패턴
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### Potential-Based Shaping (Ng 1999)
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```python
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def potential(state) -> float:
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"""매 heuristic 의 — e.g. 의 distance-to-goal."""
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return -goal_distance(state)
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def shaped_reward(r, s, s_next, gamma=0.99):
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return r + gamma * potential(s_next) - potential(s)
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```
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### Curiosity-Driven (RND)
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```python
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import torch
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import torch.nn as nn
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class RND(nn.Module):
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def __init__(self, obs_dim, feat_dim=128):
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super().__init__()
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self.target = nn.Sequential(nn.Linear(obs_dim, 256), nn.ReLU(),
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nn.Linear(256, feat_dim))
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for p in self.target.parameters(): p.requires_grad_(False)
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self.predictor = nn.Sequential(nn.Linear(obs_dim, 256), nn.ReLU(),
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nn.Linear(256, feat_dim))
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def intrinsic(self, obs):
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return ((self.predictor(obs) - self.target(obs)) ** 2).mean(-1)
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```
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### Curriculum Reward
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```python
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def curriculum_target(episode_idx, easy_target, hard_target, ramp_episodes=10000):
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t = min(episode_idx / ramp_episodes, 1.0)
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return easy_target + t * (hard_target - easy_target)
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```
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### RLHF Reward Model
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```python
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import torch.nn as nn
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from transformers import AutoModel
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class RewardModel(nn.Module):
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def __init__(self, base="meta-llama/Llama-3-8b"):
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super().__init__()
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self.backbone = AutoModel.from_pretrained(base)
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self.head = nn.Linear(self.backbone.config.hidden_size, 1)
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def forward(self, input_ids, attn):
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out = self.backbone(input_ids, attn).last_hidden_state
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last = out[:, -1]
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return self.head(last).squeeze(-1)
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# Bradley-Terry pairwise loss
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def bt_loss(r_chosen, r_rejected):
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return -torch.nn.functional.logsigmoid(r_chosen - r_rejected).mean()
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```
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### RLVR — Verifiable Rule Reward
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```python
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def rlvr_reward(generated: str, gold: str, task: str) -> float:
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if task == "math":
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return 1.0 if extract_answer(generated) == gold else 0.0
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elif task == "code":
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return float(run_unit_tests(generated))
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elif task == "format":
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return 1.0 if has_required_tags(generated) else 0.0
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```
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### GRPO Advantage (DeepSeek 2024)
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```python
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import numpy as np
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def grpo_advantages(group_rewards: np.ndarray) -> np.ndarray:
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"""매 group-relative normalization — critic 의 X."""
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mean = group_rewards.mean()
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std = group_rewards.std() + 1e-8
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return (group_rewards - mean) / std
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# Usage: sample G=8 outputs per prompt, compute rewards, normalize within group
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```
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### Combined Shaping
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```python
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def combined_reward(r_env, s, s_next, model, obs, gamma=0.99,
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pot_w=1.0, cur_w=0.1):
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pot = gamma * potential(s_next) - potential(s)
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cur = model.intrinsic(obs).item()
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return r_env + pot_w * pot + cur_w * cur
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```
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### Reward Hacking Detector
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```python
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def detect_hacking(rewards, true_returns, window=100):
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"""매 reward 의 up 의 X 의 true return 의 stagnant → hacking."""
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if len(rewards) < window: return False
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rew_trend = np.polyfit(range(window), rewards[-window:], 1)[0]
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ret_trend = np.polyfit(range(window), true_returns[-window:], 1)[0]
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return rew_trend > 0.01 and ret_trend < 0
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```
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## 매 결정 기준
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| 상황 | Approach |
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|---|---|
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| Sparse reward, known heuristic | Potential-based shaping |
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| Hard exploration | RND / ICM curiosity |
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| Have expert demos | LfD-shaped reward + BC pretrain |
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| LLM alignment, subjective | RLHF reward model |
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| LLM math/code | RLVR (rule-based) + GRPO |
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| Robotic manipulation | Combined: potential + curiosity + demo |
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**기본값**: Potential-based primary; RLVR + GRPO 의 LLM verifiable tasks 의; RLHF 의 subjective tasks 의.
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## 🔗 Graph
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- 부모: [[Reinforcement Learning]] · [[Reward Design]]
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- 변형: [[GRPO]] · [[RLHF]]
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- Adjacent: [[Reward Prediction Error]]
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## 🤖 LLM 활용
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**언제**: reward model training (RLHF), reward function code generation, reward hacking analysis from logs.
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**언제 X**: LLM 의 reward function 의 propose 의 hacking 의 prone 의 — verify 의 with controlled rollouts.
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## ❌ 안티패턴
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- **Non-potential bonus**: arbitrary +10 의 sub-goal 의 reach → optimal policy 의 distort.
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- **Reward hacking ignored**: cumulative reward up 의 task fail 의 monitor 의 X.
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- **Over-shaping**: dense bonus 의 overwhelm sparse signal → agent 의 task 의 ignore.
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- **Static curriculum**: agent 의 surpass 의 still serving easy targets.
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- **No baseline check**: shaping with vs without 의 ablation 의 X — actual gain unknown.
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## 🧪 검증 / 중복
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- Verified (Ng/Harada/Russell 1999 ICML; DeepSeek-R1 paper 2025; Sutton & Barto Ch 17).
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — potential-based + RND + RLHF + GRPO + RLVR |
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