diff --git a/book/_toc.yml b/book/_toc.yml
index e50fadd..4b59776 100644
--- a/book/_toc.yml
+++ b/book/_toc.yml
@@ -24,3 +24,6 @@ parts:
       - file: scm/backdoor_criterion.ipynb
       - file: scm/frontdoor_criterion.ipynb
       - file: scm/causal_discovery.ipynb
+    - file: prescriptive_analytics/overview.md
+      sections:
+      - file: prescriptive_analytics/heterogeneous_causal_learning_for_effectiveness_optimization.ipynb
\ No newline at end of file
diff --git a/book/prescriptive_analytics/heterogeneous_causal_learning_for_effectiveness_optimization.ipynb b/book/prescriptive_analytics/heterogeneous_causal_learning_for_effectiveness_optimization.ipynb
new file mode 100644
index 0000000..c5b0644
--- /dev/null
+++ b/book/prescriptive_analytics/heterogeneous_causal_learning_for_effectiveness_optimization.ipynb
@@ -0,0 +1,1344 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "d6b70f64",
+   "metadata": {},
+   "source": [
+    "# Heterogeneous Causal Learning for Effectiveness Optimization"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b841ee2c",
+   "metadata": {},
+   "source": [
+    "- 기존 uplift 모델은 이질적 처치 효과를 추정할 수 있지만, 비용 대비 이익을 충분히 반영하지 못합니다.\n",
+    "\n",
+    "- 마케팅처럼 예산이 제한된 환경에서는, 비용을 고려하면서 효과를 최대화하는 처치 효과 최적화(treatment effect optimization) 접근이 필요합니다.\n",
+    "\n",
+    "- 이를 위해 다음 알고리즘들을 활용합니다.\n",
+    "  - Duality R-learner\n",
+    "  - Direct Ranking Model (DRM)\n",
+    "  - Constrained Ranking Models"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "21447276",
+   "metadata": {},
+   "source": [
+    "## Setup"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "0f91658c",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\u001b[33mWARNING: There was an error checking the latest version of pip.\u001b[0m\u001b[33m\n",
+      "\u001b[0mNote: you may need to restart the kernel to use updated packages.\n"
+     ]
+    }
+   ],
+   "source": [
+    "%pip -q install scikit-uplift"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "9114f7da",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.linear_model import Ridge, LogisticRegression\n",
+    "from sklearn.metrics import r2_score, roc_auc_score\n",
+    "\n",
+    "from sklift.datasets import fetch_hillstrom\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "RANDOM_STATE = 42\n",
+    "pd.set_option(\"display.max_columns\", 50)\n",
+    "\n",
+    "import warnings\n",
+    "warnings.filterwarnings(\"ignore\")\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "57cbb979",
+   "metadata": {},
+   "source": [
+    "### Hillstrom E-mail Test Dataset\n",
+    "\n",
+    "Kevin Hillstrom E-mail Test Dataset을 사용합니다.  \n",
+    "이 데이터는 e-mail 마케팅 A/B/n 테스트 로그입니다.\n",
+    "\n",
+    "- **Treatment**: ${T}$\n",
+    "  - `Mens E-Mail`, `Womens E-Mail`  $\\Rightarrow$  ${T = 1}$ (이메일 발송)\n",
+    "  - `No E-Mail`  $\\Rightarrow$  ${T = 0}$ (대조군)\n",
+    "\n",
+    "- **Gain outcome**: ${Y^r}$\n",
+    "  - 2주간 지출 금액 `spend`\n",
+    "  - “이메일을 보내면 spend가 얼마나 증가하는가?” 가 관심\n",
+    "\n",
+    "- **Cost outcome**: ${Y^c}$\n",
+    "  - 이메일 발송 1회당 비용을 1 단위로 단순화\n",
+    "  - 따라서 $Y^c = T \\in \\{0,1\\}$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "b2b3d7a2",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "data shape: (64000, 8)\n",
+      "\n",
+      "spend (target) describe:\n",
+      "count    64000.000000\n",
+      "mean         1.050908\n",
+      "std         15.036448\n",
+      "min          0.000000\n",
+      "25%          0.000000\n",
+      "50%          0.000000\n",
+      "75%          0.000000\n",
+      "max        499.000000\n",
+      "Name: spend, dtype: float64\n",
+      "\n",
+      "segment (treatment_raw) 분포:\n",
+      "segment\n",
+      "Womens E-Mail    0.334172\n",
+      "Mens E-Mail      0.332922\n",
+      "No E-Mail        0.332906\n",
+      "Name: proportion, dtype: float64\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>recency</th>\n",
+       "      <th>history_segment</th>\n",
+       "      <th>history</th>\n",
+       "      <th>mens</th>\n",
+       "      <th>womens</th>\n",
+       "      <th>zip_code</th>\n",
+       "      <th>newbie</th>\n",
+       "      <th>channel</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>10</td>\n",
+       "      <td>2) $100 - $200</td>\n",
+       "      <td>142.44</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>Surburban</td>\n",
+       "      <td>0</td>\n",
+       "      <td>Phone</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>6</td>\n",
+       "      <td>3) $200 - $350</td>\n",
+       "      <td>329.08</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>Rural</td>\n",
+       "      <td>1</td>\n",
+       "      <td>Web</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>7</td>\n",
+       "      <td>2) $100 - $200</td>\n",
+       "      <td>180.65</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>Surburban</td>\n",
+       "      <td>1</td>\n",
+       "      <td>Web</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>9</td>\n",
+       "      <td>5) $500 - $750</td>\n",
+       "      <td>675.83</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>Rural</td>\n",
+       "      <td>1</td>\n",
+       "      <td>Web</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>2</td>\n",
+       "      <td>1) $0 - $100</td>\n",
+       "      <td>45.34</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>Urban</td>\n",
+       "      <td>0</td>\n",
+       "      <td>Web</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   recency history_segment  history  mens  womens   zip_code  newbie channel\n",
+       "0       10  2) $100 - $200   142.44     1       0  Surburban       0   Phone\n",
+       "1        6  3) $200 - $350   329.08     1       1      Rural       1     Web\n",
+       "2        7  2) $100 - $200   180.65     0       1  Surburban       1     Web\n",
+       "3        9  5) $500 - $750   675.83     1       0      Rural       1     Web\n",
+       "4        2    1) $0 - $100    45.34     1       0      Urban       0     Web"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dataset = fetch_hillstrom(target_col=\"spend\", return_X_y_t=False)\n",
+    "\n",
+    "data = dataset.data.copy()                # X (features, 아직 전처리 전)\n",
+    "y_gain = dataset.target.copy()            # Y^r = spend\n",
+    "treatment_raw = dataset.treatment.copy()  # 'Mens E-Mail', 'Womens E-Mail', 'No E-Mail'\n",
+    "\n",
+    "print(\"data shape:\", data.shape)\n",
+    "print(\"\\nspend (target) describe:\")\n",
+    "print(y_gain.describe())\n",
+    "\n",
+    "print(\"\\nsegment (treatment_raw) 분포:\")\n",
+    "print(treatment_raw.value_counts(normalize=True))\n",
+    "\n",
+    "data.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "2ff956f2",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Treatment 비율 (T=1): 0.66709375\n",
+      "\n",
+      "Y_gain (spend) 요약:\n",
+      "count    64000.000000\n",
+      "mean         1.050908\n",
+      "std         15.036448\n",
+      "min          0.000000\n",
+      "25%          0.000000\n",
+      "50%          0.000000\n",
+      "75%          0.000000\n",
+      "max        499.000000\n",
+      "Name: spend, dtype: float64\n",
+      "\n",
+      "Y_cost 분포:\n",
+      "segment\n",
+      "1.0    0.667094\n",
+      "0.0    0.332906\n",
+      "Name: proportion, dtype: float64\n"
+     ]
+    }
+   ],
+   "source": [
+    "T = (treatment_raw != \"No E-Mail\").astype(int)  # 이메일 받았으면 1, 아니면 0\n",
+    "\n",
+    "Y_gain = y_gain.astype(float)   # spend (float)\n",
+    "Y_cost = T.astype(float)        # 이메일 발송 비용 (0/1)\n",
+    "\n",
+    "print(\"Treatment 비율 (T=1):\", T.mean())\n",
+    "print(\"\\nY_gain (spend) 요약:\")\n",
+    "print(pd.Series(Y_gain).describe())\n",
+    "\n",
+    "print(\"\\nY_cost 분포:\")\n",
+    "print(pd.Series(Y_cost).value_counts(normalize=True).rename(\"proportion\"))\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bfdbc4fd",
+   "metadata": {},
+   "source": [
+    "### Feature 전처리\n",
+    "\n",
+    "Hillstrom의 주요 feature 예시:\n",
+    "\n",
+    "- `recency`, `history`, `mens`, `womens`, `newbie` 등: 숫자/0-1 변수\n",
+    "- `history_segment`, `zip_code`, `channel`: 범주형\n",
+    "\n",
+    "R-learner / Propensity 모델에 넣기 위해\n",
+    "\n",
+    "- 숫자형 컬럼은 그대로 사용하고,\n",
+    "- 범주형 컬럼(`history_segment`, `zip_code`, `channel`)은 one-hot 인코딩으로 변환합니다.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "e286adf5",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "원본 feature columns:\n",
+      "['recency', 'history_segment', 'history', 'mens', 'womens', 'zip_code', 'newbie', 'channel']\n",
+      "\n",
+      "Numeric columns:\n",
+      "['recency', 'history', 'mens', 'womens', 'newbie']\n",
+      "\n",
+      "Categorical columns (one-hot 대상):\n",
+      "['history_segment', 'zip_code', 'channel']\n",
+      "\n",
+      "전처리 후 feature shape: (64000, 15)\n",
+      "전처리된 feature columns:\n",
+      "Index(['recency', 'history', 'mens', 'womens', 'newbie',\n",
+      "       'history_segment_2) $100 - $200', 'history_segment_3) $200 - $350',\n",
+      "       'history_segment_4) $350 - $500', 'history_segment_5) $500 - $750',\n",
+      "       'history_segment_6) $750 - $1,000', 'history_segment_7) $1,000 +',\n",
+      "       'zip_code_Surburban', 'zip_code_Urban', 'channel_Phone', 'channel_Web'],\n",
+      "      dtype='object')\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"원본 feature columns:\")\n",
+    "print(data.columns.tolist())\n",
+    "\n",
+    "# one-hot 대상 범주형 컬럼\n",
+    "categorical_cols = [\"history_segment\", \"zip_code\", \"channel\"]\n",
+    "\n",
+    "# 나머지는 숫자/0-1 컬럼으로 그대로 사용\n",
+    "numeric_cols = [c for c in data.columns if c not in categorical_cols]\n",
+    "\n",
+    "print(\"\\nNumeric columns:\")\n",
+    "print(numeric_cols)\n",
+    "print(\"\\nCategorical columns (one-hot 대상):\")\n",
+    "print(categorical_cols)\n",
+    "\n",
+    "# one-hot 인코딩\n",
+    "X_cat = pd.get_dummies(data[categorical_cols], drop_first=True)\n",
+    "X_num = data[numeric_cols].reset_index(drop=True)\n",
+    "\n",
+    "X_df = pd.concat([X_num, X_cat], axis=1)\n",
+    "\n",
+    "print(\"\\n전처리 후 feature shape:\", X_df.shape)\n",
+    "print(\"전처리된 feature columns:\")\n",
+    "print(X_df.columns)\n",
+    "\n",
+    "# numpy array로 변환\n",
+    "X = X_df.values.astype(np.float32)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eeb08865",
+   "metadata": {},
+   "source": [
+    "데이터 세트는 각각 60%, 20%, 20%의 비율로 학습, 검증 및 테스트 세트의 3부분으로 나뉩니다."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "3d964183",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Train shape: (38400, 15)\n",
+      "Val   shape: (12800, 15)\n",
+      "Test  shape: (12800, 15)\n",
+      "\n",
+      "Treatment 비율 (Train/Val/Test):\n",
+      "Train: 0.6670833333333334\n",
+      "Val  : 0.667109375\n",
+      "Test : 0.667109375\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Train / Validation / Test 분할\n",
+    "X_train_val, X_test, T_train_val, T_test, Yg_train_val, Yg_test, Yc_train_val, Yc_test = train_test_split(\n",
+    "    X, T, Y_gain, Y_cost,\n",
+    "    test_size=0.2,\n",
+    "    random_state=RANDOM_STATE,\n",
+    "    stratify=T,\n",
+    ")\n",
+    "\n",
+    "X_train, X_val, T_train, T_val, Yg_train, Yg_val, Yc_train, Yc_val = train_test_split(\n",
+    "    X_train_val, T_train_val, Yg_train_val, Yc_train_val,\n",
+    "    test_size=0.25,  # 0.25 * 0.8 = 0.2\n",
+    "    random_state=RANDOM_STATE,\n",
+    "    stratify=T_train_val,\n",
+    ")\n",
+    "\n",
+    "print(\"Train shape:\", X_train.shape)\n",
+    "print(\"Val   shape:\", X_val.shape)\n",
+    "print(\"Test  shape:\", X_test.shape)\n",
+    "\n",
+    "print(\"\\nTreatment 비율 (Train/Val/Test):\")\n",
+    "print(\"Train:\", T_train.mean())\n",
+    "print(\"Val  :\", T_val.mean())\n",
+    "print(\"Test :\", T_test.mean())\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "576b8d00",
+   "metadata": {},
+   "source": [
+    "## Duality R-learner\n",
+    "\n",
+    "Duality R-learner는 다음 두 단계를 결합한 방식입니다.\n",
+    "\n",
+    "1. R-learner로 Gain/Cost CATE 추정\n",
+    "   - $\\tau_r(x)$: gain uplift (예: spend uplift)\n",
+    "   - $\\tau_c(x)$: cost uplift (예: 이메일 발송 비용 증가량)\n",
+    "\n",
+    "2. 예산 제약(budget constraint)을 듀얼 형태로 최적화\n",
+    "   - 라그랑지 승수 $\\lambda$ 를 학습하여 최적 정책을 찾습니다.\n",
+    "\n",
+    "우리가 풀고 싶은 문제는 다음과 같습니다.\n",
+    "\n",
+    "- 예산 $B$ 하에서\n",
+    "\n",
+    "  $$\n",
+    "  \\max_{z_i \\in \\{0,1\\}} \\sum_i \\tau_r(x^{(i)}) z_i\n",
+    "  \\quad \\text{s.t.} \\quad\n",
+    "  \\sum_i \\tau_c(x^{(i)}) z_i \\le B\n",
+    "  $$\n",
+    "  \n",
+    "- $z_i = 1$ 이면 고객 $i$ 에게 이메일 발송, $z_i = 0$ 이면 미발송\n",
+    "\n",
+    "Duality R-learner 핵심 단계:\n",
+    "\n",
+    "1. Nuisance models: $m_r(x)$, $e(x)$ 학습  \n",
+    "2. Gain / Cost R-learner: $\\tau_r(x)$, $\\tau_c(x)$ 추정  \n",
+    "3. Duality: $\\lambda$ 를 gradient ascent 로 최적화  \n",
+    "4. 정책 생성: $s(x) = \\tau_r(x) - \\lambda^* \\tau_c(x)$\n",
+    "5. Cost Curve / AUCC 로 정책 성능 평가  "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5d9e213b",
+   "metadata": {},
+   "source": [
+    "### 1. Nuisance Models: $m_r(x)$ 와 $e(x)$\n",
+    "\n",
+    "R-learner는 아래 식을 기반으로 합니다.\n",
+    "\n",
+    "$$\n",
+    "Y - m^*(X)\n",
+    "= (T - e^*(X))\\,\\tau^*(X) + \\epsilon\n",
+    "$$\n",
+    "\n",
+    "여기서  \n",
+    "- $m^*(X) = \\mathbb{E}[Y \\mid X]$: outcome 평균  \n",
+    "- $e^*(X) = \\mathbb{P}(T=1 \\mid X)$: propensity score  \n",
+    "\n",
+    "Gain outcome에 대한 nuisance 모델은 다음과 같이 구성합니다.\n",
+    "\n",
+    "- $m_r(x)$: Ridge 회귀  \n",
+    "- $e(x)$: Logistic 회귀  \n",
+    "\n",
+    "Cost outcome은 $Y^c = T$ 이므로\n",
+    "$m_c(x) = e(x)$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "3e718594",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "== m_r(x) 성능 (R^2: spend 회귀) ==\n",
+      "Train R^2: 0.0011321804124860835\n",
+      "Val   R^2: 0.0006200906912602333\n",
+      "\n",
+      "예측값 분포 (Val):\n",
+      "count    12800.000000\n",
+      "mean         0.998539\n",
+      "std          0.499257\n",
+      "min         -4.757108\n",
+      "25%          0.690851\n",
+      "50%          0.961950\n",
+      "75%          1.234435\n",
+      "max          4.417754\n",
+      "dtype: float64\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Gain outcome 평균 모델 m_r(x): Ridge 회귀\n",
+    "m_r = Ridge(alpha=1.0, random_state=RANDOM_STATE)\n",
+    "m_r.fit(X_train, Yg_train)\n",
+    "\n",
+    "Yg_pred_train = m_r.predict(X_train)\n",
+    "Yg_pred_val   = m_r.predict(X_val)\n",
+    "\n",
+    "r2_train = r2_score(Yg_train, Yg_pred_train)\n",
+    "r2_val   = r2_score(Yg_val,   Yg_pred_val)\n",
+    "\n",
+    "print(\"== m_r(x) 성능 (R^2: spend 회귀) ==\")\n",
+    "print(\"Train R^2:\", r2_train)\n",
+    "print(\"Val   R^2:\", r2_val)\n",
+    "\n",
+    "print(\"\\n예측값 분포 (Val):\")\n",
+    "print(pd.Series(Yg_pred_val).describe())\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "1aa8d52b",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "== e(x) 성능 (AUC: treatment 모델) ==\n",
+      "Train AUC: 0.5117265124259399\n",
+      "Val   AUC: 0.49799591470904553\n",
+      "\n",
+      "Propensity e(x) range:\n",
+      "Train: 0.633101626124968 → 0.8026040280233658\n",
+      "Val  : 0.6331449838328645 → 0.8183494704982611\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Propensity model e(x) = P(T=1 | X): Logistic 회귀\n",
+    "propensity = LogisticRegression(\n",
+    "    penalty=\"l2\",\n",
+    "    C=1.0,\n",
+    "    solver=\"lbfgs\",\n",
+    "    max_iter=1000,\n",
+    "    n_jobs=-1,\n",
+    ")\n",
+    "\n",
+    "propensity.fit(X_train, T_train)\n",
+    "\n",
+    "e_train = propensity.predict_proba(X_train)[:, 1]\n",
+    "e_val   = propensity.predict_proba(X_val)[:, 1]\n",
+    "e_test  = propensity.predict_proba(X_test)[:, 1]\n",
+    "\n",
+    "auc_train_e = roc_auc_score(T_train, e_train)\n",
+    "auc_val_e   = roc_auc_score(T_val,   e_val)\n",
+    "\n",
+    "print(\"== e(x) 성능 (AUC: treatment 모델) ==\")\n",
+    "print(\"Train AUC:\", auc_train_e)\n",
+    "print(\"Val   AUC:\", auc_val_e)\n",
+    "\n",
+    "print(\"\\nPropensity e(x) range:\")\n",
+    "print(\"Train:\", e_train.min(), \"→\", e_train.max())\n",
+    "print(\"Val  :\", e_val.min(),   \"→\", e_val.max())\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a2b17bd8",
+   "metadata": {},
+   "source": [
+    "여기서 얻은 ${e(x)}$ 는 이후에\n",
+    "\n",
+    "- Gain R-learner에서 ${T - e(x)}$ 항을 만들 때,\n",
+    "- Cost R-learner에서 ${m_c(x)}$ 로도 재사용합니다.  "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "06b5558e",
+   "metadata": {},
+   "source": [
+    "### 2. Gain R-learner: $\\tau_r(x)$\n",
+    "\n",
+    "Gain outcome $Y^r$ 에 대해 R-learner 구조는 다음과 같습니다.\n",
+    "\n",
+    "$$\n",
+    "Y^r - m_r(X)\n",
+    "= (T - e(X))\\,\\tau_r(X) + \\epsilon\n",
+    "$$\n",
+    "\n",
+    "선형 모델 $\\tau_r(x) = w_r^\\top x$ 를 사용하면 학습 절차는 다음과 같습니다.\n",
+    "\n",
+    "1. 잔차 계산  \n",
+    "\n",
+    "   $$\n",
+    "   r^Y = Y^r - \\hat m_r(X), \\quad r^T = T - \\hat e(X)\n",
+    "   $$\n",
+    "\n",
+    "2. 행별 스케일링  \n",
+    "\n",
+    "   $$\n",
+    "   Z = X \\odot r^T\n",
+    "   $$\n",
+    "\n",
+    "3. 회귀  \n",
+    "\n",
+    "   $$\n",
+    "   r^Y \\approx Z w_r\n",
+    "   $$\n",
+    "\n",
+    "4. 최종 CATE  \n",
+    "\n",
+    "   $$\n",
+    "   \\hat\\tau_r(x) = w_r^\\top x\n",
+    "   $$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "28eb5e7c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def fit_r_learner_linear(\n",
+    "    X_tr, X_val,\n",
+    "    T_tr, T_val,\n",
+    "    Y_tr, Y_val,\n",
+    "    m_tr, m_val,\n",
+    "    e_tr, e_val,\n",
+    "    alpha=1.0,\n",
+    "    name=\"R-learner\",\n",
+    "):\n",
+    "    \"\"\"\n",
+    "    선형 τ(x) = w^T x 를 R-learner 방식으로 학습.\n",
+    "    - X_tr, X_val: feature 행렬\n",
+    "    - T_tr, T_val: treatment (0/1)\n",
+    "    - Y_tr, Y_val: outcome\n",
+    "    - m_tr, m_val: m(x) = E[Y|X] 예측값\n",
+    "    - e_tr, e_val: e(x) = P(T=1|X) 예측값\n",
+    "    \"\"\"\n",
+    "    X_tr = np.asarray(X_tr)\n",
+    "    X_val = np.asarray(X_val)\n",
+    "    T_tr = np.asarray(T_tr).astype(float)\n",
+    "    T_val = np.asarray(T_val).astype(float)\n",
+    "    Y_tr = np.asarray(Y_tr).astype(float)\n",
+    "    Y_val = np.asarray(Y_val).astype(float)\n",
+    "    m_tr = np.asarray(m_tr).astype(float)\n",
+    "    m_val = np.asarray(m_val).astype(float)\n",
+    "    e_tr = np.asarray(e_tr).astype(float)\n",
+    "    e_val = np.asarray(e_val).astype(float)\n",
+    "\n",
+    "    # residuals\n",
+    "    rY_tr = Y_tr - m_tr\n",
+    "    rT_tr = T_tr - e_tr\n",
+    "\n",
+    "    # Z = X * rT (각 행을 rT로 스케일링)\n",
+    "    Z_tr = X_tr * rT_tr.reshape(-1, 1)\n",
+    "\n",
+    "    # 회귀: rY ~ Z\n",
+    "    tau_model = Ridge(alpha=alpha, fit_intercept=False, random_state=RANDOM_STATE)\n",
+    "    tau_model.fit(Z_tr, rY_tr)\n",
+    "\n",
+    "    # τ_hat(x) = w^T x\n",
+    "    tau_tr = tau_model.predict(X_tr)\n",
+    "    tau_val = tau_model.predict(X_val)\n",
+    "\n",
+    "    print(f\"== {name} 요약 ==\")\n",
+    "    print(\"Train τ_hat summary:\")\n",
+    "    print(pd.Series(tau_tr).describe())\n",
+    "    print(\"\\nVal τ_hat summary:\")\n",
+    "    print(pd.Series(tau_val).describe())\n",
+    "\n",
+    "    return tau_model, tau_tr, tau_val\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "03fc2e68",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "== Gain R-learner τ_r(x) 요약 ==\n",
+      "Train τ_hat summary:\n",
+      "count    38400.000000\n",
+      "mean         0.562616\n",
+      "std          0.454530\n",
+      "min         -2.669276\n",
+      "25%          0.265676\n",
+      "50%          0.528041\n",
+      "75%          0.837171\n",
+      "max          1.976344\n",
+      "dtype: float64\n",
+      "\n",
+      "Val τ_hat summary:\n",
+      "count    12800.000000\n",
+      "mean         0.567048\n",
+      "std          0.453703\n",
+      "min         -3.313805\n",
+      "25%          0.272715\n",
+      "50%          0.530470\n",
+      "75%          0.836859\n",
+      "max          1.944813\n",
+      "dtype: float64\n"
+     ]
+    }
+   ],
+   "source": [
+    "# m_r(x) 예측값\n",
+    "m_r_train = m_r.predict(X_train)\n",
+    "m_r_val   = m_r.predict(X_val)\n",
+    "\n",
+    "tau_r_model, tau_r_train, tau_r_val = fit_r_learner_linear(\n",
+    "    X_tr=X_train,\n",
+    "    X_val=X_val,\n",
+    "    T_tr=T_train,\n",
+    "    T_val=T_val,\n",
+    "    Y_tr=Yg_train,\n",
+    "    Y_val=Yg_val,\n",
+    "    m_tr=m_r_train,\n",
+    "    m_val=m_r_val,\n",
+    "    e_tr=e_train,\n",
+    "    e_val=e_val,\n",
+    "    alpha=1.0,\n",
+    "    name=\"Gain R-learner τ_r(x)\",\n",
+    ")\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e8ae0ccd",
+   "metadata": {},
+   "source": [
+    "### 3. Cost R-learner: $\\tau_c(x)$\n",
+    "\n",
+    "Cost outcome은 $Y^c = T$ 이므로  \n",
+    "nuisance model은 이미\n",
+    "\n",
+    "$$m_c(x) = e(x)$$\n",
+    "\n",
+    "입니다.\n",
+    "\n",
+    "Cost R-learner 식은\n",
+    "\n",
+    "$$\n",
+    "Y^c - m_c(X)\n",
+    "= (T - e(X))\\,\\tau_c(X)\n",
+    "$$\n",
+    "\n",
+    "Gain과 동일한 R-learner 구조로 $\\tau_c(x)$ 를 학습합니다."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "f40867a2",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "== Cost R-learner τ_c(x) 요약 ==\n",
+      "Train τ_hat summary:\n",
+      "count    38400.000000\n",
+      "mean         0.974710\n",
+      "std          0.156975\n",
+      "min          0.429515\n",
+      "25%          0.894193\n",
+      "50%          0.978889\n",
+      "75%          1.046973\n",
+      "max          2.098633\n",
+      "dtype: float64\n",
+      "\n",
+      "Val τ_hat summary:\n",
+      "count    12800.000000\n",
+      "mean         0.974875\n",
+      "std          0.157403\n",
+      "min          0.424263\n",
+      "25%          0.894096\n",
+      "50%          0.979144\n",
+      "75%          1.046372\n",
+      "max          2.265868\n",
+      "dtype: float64\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Cost outcome 평균 m_c(x)는 e(x)를 그대로 사용\n",
+    "m_c_train = e_train\n",
+    "m_c_val   = e_val\n",
+    "\n",
+    "tau_c_model, tau_c_train, tau_c_val = fit_r_learner_linear(\n",
+    "    X_tr=X_train,\n",
+    "    X_val=X_val,\n",
+    "    T_tr=T_train,\n",
+    "    T_val=T_val,\n",
+    "    Y_tr=Yc_train,\n",
+    "    Y_val=Yc_val,\n",
+    "    m_tr=m_c_train,\n",
+    "    m_val=m_c_val,\n",
+    "    e_tr=e_train,\n",
+    "    e_val=e_val,\n",
+    "    alpha=1.0,\n",
+    "    name=\"Cost R-learner τ_c(x)\",\n",
+    ")\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "48f3ae13",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "== τ_r(x) 요약 ==\n",
+      "[Train]\n",
+      "count    38400.000000\n",
+      "mean         0.562616\n",
+      "std          0.454530\n",
+      "min         -2.669276\n",
+      "25%          0.265676\n",
+      "50%          0.528041\n",
+      "75%          0.837171\n",
+      "max          1.976344\n",
+      "dtype: float64\n",
+      "\n",
+      "[Val]\n",
+      "count    12800.000000\n",
+      "mean         0.567048\n",
+      "std          0.453703\n",
+      "min         -3.313805\n",
+      "25%          0.272715\n",
+      "50%          0.530470\n",
+      "75%          0.836859\n",
+      "max          1.944813\n",
+      "dtype: float64\n",
+      "\n",
+      "[Test]\n",
+      "count    12800.000000\n",
+      "mean         0.568442\n",
+      "std          0.450854\n",
+      "min         -2.486865\n",
+      "25%          0.268170\n",
+      "50%          0.534959\n",
+      "75%          0.841292\n",
+      "max          1.970332\n",
+      "dtype: float64\n",
+      "\n",
+      "== τ_c(x) 요약 ==\n",
+      "[Train]\n",
+      "count    38400.000000\n",
+      "mean         0.974710\n",
+      "std          0.156975\n",
+      "min          0.429515\n",
+      "25%          0.894193\n",
+      "50%          0.978889\n",
+      "75%          1.046973\n",
+      "max          2.098633\n",
+      "dtype: float64\n",
+      "\n",
+      "[Val]\n",
+      "count    12800.000000\n",
+      "mean         0.974875\n",
+      "std          0.157403\n",
+      "min          0.424263\n",
+      "25%          0.894096\n",
+      "50%          0.979144\n",
+      "75%          1.046372\n",
+      "max          2.265868\n",
+      "dtype: float64\n",
+      "\n",
+      "[Test]\n",
+      "count    12800.000000\n",
+      "mean         0.975139\n",
+      "std          0.155813\n",
+      "min          0.436810\n",
+      "25%          0.895776\n",
+      "50%          0.978849\n",
+      "75%          1.045682\n",
+      "max          1.803177\n",
+      "dtype: float64\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Test set CATE 예측\n",
+    "tau_r_test = tau_r_model.predict(X_test)\n",
+    "tau_c_test = tau_c_model.predict(X_test)\n",
+    "\n",
+    "print(\"== τ_r(x) 요약 ==\")\n",
+    "print(\"[Train]\")\n",
+    "print(pd.Series(tau_r_train).describe())\n",
+    "print(\"\\n[Val]\")\n",
+    "print(pd.Series(tau_r_val).describe())\n",
+    "print(\"\\n[Test]\")\n",
+    "print(pd.Series(tau_r_test).describe())\n",
+    "\n",
+    "print(\"\\n== τ_c(x) 요약 ==\")\n",
+    "print(\"[Train]\")\n",
+    "print(pd.Series(tau_c_train).describe())\n",
+    "print(\"\\n[Val]\")\n",
+    "print(pd.Series(tau_c_val).describe())\n",
+    "print(\"\\n[Test]\")\n",
+    "print(pd.Series(tau_c_test).describe())\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e6e387a2",
+   "metadata": {},
+   "source": [
+    "### 4. Duality: 예산 제약 하에서 라그랑지안 기반 $\\lambda$ 최적화\n",
+    "\n",
+    "우리가 풀고자 하는 문제는 다음과 같습니다.\n",
+    "\n",
+    "$$\n",
+    "\\begin{aligned}\n",
+    "\\max_{z_i \\in \\{0,1\\}} &\\quad \\sum_i \\tau_r(x^{(i)}) z_i \\\\\n",
+    "\\text{s.t.} &\\quad \\sum_i \\tau_c(x^{(i)}) z_i \\le B.\n",
+    "\\end{aligned}\n",
+    "$$\n",
+    "\n",
+    "여기서 $z_i = 1$ 은 고객 $i$를 타겟팅하는 경우이며, $B$는 전체 예산입니다.  \n",
+    "이 제약을 다루기 위해 라그랑지 승수 $\\lambda \\ge 0$ 를 도입하면 라그랑지안은\n",
+    "\n",
+    "$$\n",
+    "L(z,\\lambda)\n",
+    "= -\\sum_i \\tau_r(x^{(i)}) z_i\n",
+    "+ \\lambda\\left(\\sum_i \\tau_c(x^{(i)}) z_i - B\\right)\n",
+    "$$\n",
+    "\n",
+    "으로 표현됩니다.\n",
+    "\n",
+    "고정된 $\\lambda$ 아래에서 고객 $i$의 효율성 점수는 다음과 같습니다.\n",
+    "\n",
+    "$$\n",
+    "s_i(\\lambda) = \\tau_r(x^{(i)}) - \\lambda\\, \\tau_c(x^{(i)}).\n",
+    "$$\n",
+    "\n",
+    "점수가 양수이면 타겟팅하는 것이 유리하므로  \n",
+    "$s_i(\\lambda) \\ge 0$ 이면 $z_i = 1$, 음수이면 $z_i = 0$ 을 선택합니다.  \n",
+    "즉, $\\lambda$가 주어지면 단순히 $s_i(\\lambda)$가 양수인 고객만 선택하면 됩니다.\n",
+    "\n",
+    "듀얼 목적함수의 기울기는\n",
+    "\n",
+    "$$\n",
+    "\\frac{\\partial g}{\\partial \\lambda}\n",
+    "\\approx \\sum_i z_i \\tau_c(x^{(i)}) - B\n",
+    "$$\n",
+    "\n",
+    "으로 근사할 수 있고, 이에 따른 gradient ascent 업데이트는\n",
+    "\n",
+    "$$\n",
+    "\\lambda \\leftarrow \\bigl[\\lambda + \\eta(\\text{cost\\_used} - B)\\bigr]_+\n",
+    "$$\n",
+    "\n",
+    "로 진행됩니다. 여기서 $[\\cdot]_+$ 는 $\\lambda$가 음수가 되지 않도록 하는 projection입니다.\n",
+    "\n",
+    "예산을 초과하면 $(\\text{cost\\_used} > B)$ $\\lambda$는 증가하여 비용 효과를 더 강하게 억제하고,  \n",
+    "예산보다 적게 사용하면 $\\lambda$는 감소하여 더 많은 고객이 선택될 수 있도록 조정됩니다.\n",
+    "\n",
+    "Train 데이터에서 양의 Cost CATE 합을 기반으로 예산 $B$를 설정하고,  \n",
+    "위 규칙을 반복 적용하여 최종 $\\lambda^*$와 정책을 학습합니다."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "5fe3e686",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def duality_learn_lambda(\n",
+    "    tau_r,\n",
+    "    tau_c,\n",
+    "    budget_fraction=0.3,\n",
+    "    lr=1e-5,\n",
+    "    n_iter=200,\n",
+    "    verbose_every=20,\n",
+    "):\n",
+    "    \"\"\"\n",
+    "    τ_r, τ_c 가 주어졌을 때 Duality gradient ascent로 λ 학습.\n",
+    "    - budget_fraction: 전체 양의 cost effect 합 중 몇 %를 예산으로 둘지\n",
+    "    \"\"\"\n",
+    "    tau_r = np.asarray(tau_r).astype(float)\n",
+    "    tau_c = np.asarray(tau_c).astype(float)\n",
+    "\n",
+    "    # 양의 cost effect만 예산 계산에 사용\n",
+    "    tau_c_pos = np.clip(tau_c, a_min=0.0, a_max=None)\n",
+    "    total_pos_cost = tau_c_pos.sum()\n",
+    "    B = budget_fraction * total_pos_cost\n",
+    "\n",
+    "    lam = 0.0\n",
+    "\n",
+    "    for it in range(n_iter + 1):\n",
+    "        # effectiveness score\n",
+    "        s = tau_r - lam * tau_c\n",
+    "\n",
+    "        # z_i: 선택 여부 (s_i >= 0 이면 선택)\n",
+    "        z = (s >= 0).astype(float)\n",
+    "\n",
+    "        cost_used = (tau_c_pos * z).sum()\n",
+    "        gain_used = (np.clip(tau_r, 0.0, None) * z).sum()\n",
+    "\n",
+    "        # ∂g/∂λ ≈ cost_used - B\n",
+    "        grad = cost_used - B\n",
+    "\n",
+    "        # gradient ascent (λ >= 0 유지)\n",
+    "        lam = max(0.0, lam + lr * grad)\n",
+    "\n",
+    "        if it % verbose_every == 0:\n",
+    "            sel_ratio = z.mean()\n",
+    "            print(\n",
+    "                f\"[iter {it:03d}] λ={lam:.6f}, \"\n",
+    "                f\"cost_used={cost_used:.4f}, gain_used={gain_used:.4f}, \"\n",
+    "                f\"grad={grad:.4f}, selected={sel_ratio:.3f}\"\n",
+    "            )\n",
+    "\n",
+    "    print(\"\\n최종 λ*:\", lam)\n",
+    "    print(\"총 양의 cost effect 합:\", total_pos_cost)\n",
+    "    print(f\"예산 B (fraction={budget_fraction}):\", B)\n",
+    "    return lam, B\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "id": "233a6a45",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[iter 000] λ=0.228487, cost_used=34077.3618, gain_used=22363.6067, grad=22848.7019, selected=0.907\n",
+      "[iter 020] λ=0.784009, cost_used=11251.8179, gain_used=12501.7237, grad=23.1579, selected=0.298\n",
+      "[iter 040] λ=0.784586, cost_used=11228.2803, gain_used=12483.2661, grad=-0.3797, selected=0.297\n",
+      "[iter 060] λ=0.784587, cost_used=11228.2803, gain_used=12483.2661, grad=-0.3797, selected=0.297\n",
+      "[iter 080] λ=0.784587, cost_used=11228.2803, gain_used=12483.2661, grad=-0.3797, selected=0.297\n",
+      "[iter 100] λ=0.784587, cost_used=11228.2803, gain_used=12483.2661, grad=-0.3797, selected=0.297\n",
+      "[iter 120] λ=0.784588, cost_used=11228.2803, gain_used=12483.2661, grad=-0.3797, selected=0.297\n",
+      "[iter 140] λ=0.784588, cost_used=11229.1281, gain_used=12483.9314, grad=0.4682, selected=0.297\n",
+      "[iter 160] λ=0.784588, cost_used=11229.1281, gain_used=12483.9314, grad=0.4682, selected=0.297\n",
+      "[iter 180] λ=0.784589, cost_used=11229.1281, gain_used=12483.9314, grad=0.4682, selected=0.297\n",
+      "[iter 200] λ=0.784589, cost_used=11229.1281, gain_used=12483.9314, grad=0.4682, selected=0.297\n",
+      "\n",
+      "최종 λ*: 0.7845891317539325\n",
+      "총 양의 cost effect 합: 37428.86642372066\n",
+      "예산 B (fraction=0.3): 11228.659927116198\n"
+     ]
+    }
+   ],
+   "source": [
+    "lambda_star, B = duality_learn_lambda(\n",
+    "    tau_r=tau_r_train,\n",
+    "    tau_c=tau_c_train,\n",
+    "    budget_fraction=0.3,\n",
+    "    lr=1e-5,\n",
+    "    n_iter=200,\n",
+    "    verbose_every=20,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "a54ac8cf",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def selection_summary(tau_r, tau_c, lam, name=\"\"):\n",
+    "    tau_r = np.asarray(tau_r).astype(float)\n",
+    "    tau_c = np.asarray(tau_c).astype(float)\n",
+    "\n",
+    "    s = tau_r - lam * tau_c\n",
+    "    z = (s >= 0).astype(float)\n",
+    "\n",
+    "    gain_pos = np.clip(tau_r, 0.0, None)\n",
+    "    cost_pos = np.clip(tau_c, 0.0, None)\n",
+    "\n",
+    "    gain_used = (gain_pos * z).sum()\n",
+    "    cost_used = (cost_pos * z).sum()\n",
+    "    sel_ratio = z.mean()\n",
+    "\n",
+    "    ratio = gain_used / cost_used if cost_used > 0 else np.nan\n",
+    "\n",
+    "    print(f\"\\n== Selection summary ({name}) ==\")\n",
+    "    print(f\"λ = {lam:.6f}\")\n",
+    "    print(f\"선택 비율: {sel_ratio:.3f}  ({z.sum():.0f} / {len(z)})\")\n",
+    "    print(f\"총 gain (∑ τ_r^+ z): {gain_used:.4f}\")\n",
+    "    print(f\"총 cost (∑ τ_c^+ z): {cost_used:.4f}\")\n",
+    "    print(f\"gain / cost 비율: {ratio:.4f}\")\n",
+    "\n",
+    "    return {\n",
+    "        \"lambda\": lam,\n",
+    "        \"selected_ratio\": sel_ratio,\n",
+    "        \"gain_used\": gain_used,\n",
+    "        \"cost_used\": cost_used,\n",
+    "        \"gain_per_cost\": ratio,\n",
+    "    }\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "6947da6a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "== Selection summary (Train) ==\n",
+      "λ = 0.784589\n",
+      "선택 비율: 0.297  (11420 / 38400)\n",
+      "총 gain (∑ τ_r^+ z): 12483.2661\n",
+      "총 cost (∑ τ_c^+ z): 11228.2803\n",
+      "gain / cost 비율: 1.1118\n",
+      "\n",
+      "== Selection summary (Val) ==\n",
+      "λ = 0.784589\n",
+      "선택 비율: 0.293  (3753 / 12800)\n",
+      "총 gain (∑ τ_r^+ z): 4124.4445\n",
+      "총 cost (∑ τ_c^+ z): 3685.4466\n",
+      "gain / cost 비율: 1.1191\n",
+      "\n",
+      "== Selection summary (Test) ==\n",
+      "λ = 0.784589\n",
+      "선택 비율: 0.302  (3862 / 12800)\n",
+      "총 gain (∑ τ_r^+ z): 4210.7541\n",
+      "총 cost (∑ τ_c^+ z): 3794.4139\n",
+      "gain / cost 비율: 1.1097\n"
+     ]
+    }
+   ],
+   "source": [
+    "_ = selection_summary(tau_r_train, tau_c_train, lambda_star, name=\"Train\")\n",
+    "_ = selection_summary(tau_r_val,   tau_c_val,   lambda_star, name=\"Val\")\n",
+    "_ = selection_summary(tau_r_test,  tau_c_test,  lambda_star, name=\"Test\")\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6ec8b309",
+   "metadata": {},
+   "source": [
+    "### 5. Cost Curve & AUCC\n",
+    "\n",
+    "Cost Curve 와 그 면적(AUCC, Area Under Cost Curve)로 비용 대비 uplift 모델을 평가합니다.\n",
+    "\n",
+    "Test 셋에서:\n",
+    "\n",
+    "1. Duality 점수 ${s(x) = \\tau_r(x) - \\lambda^* \\tau_c(x)}$ 기준으로 내림차순 정렬\n",
+    "2. 정렬된 순서대로\n",
+    "   - ${\\tau_r^+(x) = \\max(\\tau_r(x), 0)}$\n",
+    "   - ${\\tau_c^+(x) = \\max(\\tau_c(x), 0)}$\n",
+    "   의 누적합 계산\n",
+    "3. 누적 cost/gain 을 각각 최종값으로 나누어 ${[0,1]}$ 범위로 정규화\n",
+    "4. $(0,0)$ 에서 $(1,1)$ 까지 이어지는 곡선을 Cost Curve 로 사용\n",
+    "5. 수치 적분으로 AUCC 계산:\n",
+    "   $$\n",
+    "   \\text{AUCC} = \\int_0^1 \\text{gain}(x)\\,dx\n",
+    "   $$\n",
+    "\n",
+    "비교를 위해 랜덤 ranking 의 Cost Curve 와 AUCC 도 함께 계산합니다.\n",
+    "\n",
+    "- AUCC ${\\approx 0.5}$: 랜덤에 가까운 정책\n",
+    "- AUCC ${>} 0.5$: 효율적인 고객부터 잘 고르는 정책\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "56c9cc3e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "== Test set Cost Curve (τ 기반) ==\n",
+      "max_cost: 12481.778185597159\n",
+      "max_gain: 7511.766716461641\n",
+      "Normalized AUCC: 0.6946670819574676\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Duality R-learner 기반 effectiveness score (Test set)\n",
+    "s_test = tau_r_test - lambda_star * tau_c_test\n",
+    "\n",
+    "# score 기준 내림차순 정렬\n",
+    "order = np.argsort(-s_test)\n",
+    "tau_r_sorted = np.clip(tau_r_test[order], 0.0, None)  # gain은 양수 부분만\n",
+    "tau_c_sorted = np.clip(tau_c_test[order], 0.0, None)  # cost도 양수 부분만\n",
+    "\n",
+    "# 누적 cost / gain\n",
+    "cum_cost = np.cumsum(tau_c_sorted)\n",
+    "cum_gain = np.cumsum(tau_r_sorted)\n",
+    "\n",
+    "# 0 지점 포함\n",
+    "cum_cost = np.insert(cum_cost, 0, 0.0)\n",
+    "cum_gain = np.insert(cum_gain, 0, 0.0)\n",
+    "\n",
+    "# 정규화\n",
+    "max_cost = cum_cost[-1]\n",
+    "max_gain = cum_gain[-1]\n",
+    "\n",
+    "x = cum_cost / max_cost\n",
+    "y = cum_gain / max_gain\n",
+    "\n",
+    "# AUCC 계산\n",
+    "aucc = np.trapz(y, x)\n",
+    "\n",
+    "print(\"== Test set Cost Curve (τ 기반) ==\")\n",
+    "print(\"max_cost:\", max_cost)\n",
+    "print(\"max_gain:\", max_gain)\n",
+    "print(\"Normalized AUCC:\", aucc)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "3b6badd9",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Random ranking AUCC: 0.5006872435398204\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 600x500 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# 랜덤 베이스라인 Cost Curve\n",
+    "rng = np.random.default_rng(RANDOM_STATE)\n",
+    "perm = rng.permutation(len(tau_r_test))\n",
+    "\n",
+    "tau_r_rand = np.clip(tau_r_test[perm], 0.0, None)\n",
+    "tau_c_rand = np.clip(tau_c_test[perm], 0.0, None)\n",
+    "\n",
+    "cum_cost_rand = np.cumsum(tau_c_rand)\n",
+    "cum_gain_rand = np.cumsum(tau_r_rand)\n",
+    "\n",
+    "cum_cost_rand = np.insert(cum_cost_rand, 0, 0.0)\n",
+    "cum_gain_rand = np.insert(cum_gain_rand, 0, 0.0)\n",
+    "\n",
+    "x_rand = cum_cost_rand / cum_cost_rand[-1]\n",
+    "y_rand = cum_gain_rand / cum_gain_rand[-1]\n",
+    "\n",
+    "aucc_rand = np.trapz(y_rand, x_rand)\n",
+    "print(\"Random ranking AUCC:\", aucc_rand)\n",
+    "\n",
+    "# 플롯\n",
+    "plt.figure(figsize=(6, 5))\n",
+    "plt.plot(x,      y,      label=f\"Duality R-learner (AUCC={aucc:.3f})\")\n",
+    "plt.plot(x_rand, y_rand, linestyle=\"--\", label=f\"Random (AUCC={aucc_rand:.3f})\")\n",
+    "plt.plot([0, 1], [0, 1], alpha=0.4, linewidth=1, label=\"y=x reference\")\n",
+    "\n",
+    "plt.xlabel(\"Cumulative cost / max\")\n",
+    "plt.ylabel(\"Cumulative gain / max\")\n",
+    "plt.title(\"Cost curve on Test set (τ-based)\")\n",
+    "plt.legend()\n",
+    "plt.grid(alpha=0.3)\n",
+    "plt.tight_layout()\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "965eecec",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "  "
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": ".venv",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/book/prescriptive_analytics/overview.md b/book/prescriptive_analytics/overview.md
new file mode 100644
index 0000000..8bcc007
--- /dev/null
+++ b/book/prescriptive_analytics/overview.md
@@ -0,0 +1,5 @@
+# Prescriptive Analytics
+
+- Prescriptive Analytics는 데이터를 활용해 최적의 의사결정을 도출하는 분석 방식입니다.  
+- 접근 방식은 크게 **Prediction + Optimization**, **Causal Inference + Optimization** 으로 나눌 수 있습니다.  
+- 이 섹션에서는 **Causal Inference + Optimization** 에 집중하여, 개입의 인과효과(CATE)를 기반으로 **가장 효율적인 정책·전략을 선택하는 방법**을 다룹니다.