{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "286485ce",
   "metadata": {},
   "source": [
    "# Hybrid vs Disjoint Contextual Bandits with LipschitzContextualAgent\n",
    "\n",
    "In this tutorial, we'll explore the concept of hybrid contextual bandits as introduced by Li et al. (2010) in their LinUCB paper, and demonstrate how `LipschitzContextualAgent` enables efficient feature sharing across arms.\n",
    "\n",
    "## Key Concepts\n",
    "\n",
    "- **Disjoint bandits**: Each arm has completely separate parameters with no sharing of learned information\n",
    "- **Hybrid bandits**: Arms share some of their parameters, allowing for more efficient learning and generalization across similar arms\n",
    "- **Benefits**: Better sample efficiency, faster learning, and knowledge transfer between arms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2539ef5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import Any, List\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from numpy.typing import NDArray\n",
    "from scipy.sparse import csc_array\n",
    "\n",
    "# Sklearn imports for feature transformation\n",
    "from sklearn.compose import ColumnTransformer\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.preprocessing import FunctionTransformer, OneHotEncoder\n",
    "\n",
    "# Bayesian Bandits imports\n",
    "from bayesianbandits import (\n",
    "    Arm,\n",
    "    ArmColumnFeaturizer,\n",
    "    ContextualAgent,\n",
    "    LipschitzContextualAgent,\n",
    "    NormalRegressor,\n",
    "    ThompsonSampling,\n",
    ")\n",
    "\n",
    "# Import LearnerPipeline for preprocessing\n",
    "from bayesianbandits.pipelines import LearnerPipeline\n",
    "\n",
    "rng = np.random.default_rng(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52fb63f8",
   "metadata": {},
   "source": [
    "## Block Sparse Hybrid Bandits = Disjoint Bandits\n",
    "\n",
    "Here's the key insight: **disjoint bandits are just a special case of hybrid bandits with block-sparse features**.\n",
    "\n",
    "### The Equivalence\n",
    "\n",
    "**Disjoint Bandit**: Each arm $a$ has its own parameter vector $\\theta_a \\in \\mathbb{R}^d$\n",
    "$$\\mathbb{E}[r_t | x_t, a] = x_t^T \\theta_a$$\n",
    "\n",
    "**Block-Sparse Hybrid Bandit**: Single parameter vector $\\theta \\in \\mathbb{R}^{Kd}$ where $K$ is the number of arms\n",
    "$$\\mathbb{E}[r_t | x_t, a] = z_{t,a}^T \\theta$$\n",
    "\n",
    "The trick is in how we construct $z_{t,a}$:\n",
    "\n",
    "```\n",
    "For arm a, create a vector of length Kd:\n",
    "z_{t,a} = [0...0 | x_t | 0...0]\n",
    "           ↑       ↑     ↑\n",
    "        (a-1)d    d   (K-a)d\n",
    "        \n",
    "Example with K=3 arms, d=2 dimensions:\n",
    "Arm 1: z = [x_t | 0 | 0]\n",
    "Arm 2: z = [0 | x_t | 0]  \n",
    "Arm 3: z = [0 | 0 | x_t]\n",
    "```\n",
    "\n",
    "This places the context $x_t$ in the $a$-th block and zeros everywhere else.\n",
    "\n",
    "### Why They're Equivalent\n",
    "\n",
    "When we multiply $z_{t,a}^T \\theta$:\n",
    "- Only the $a$-th block of $\\theta$ matters (all other blocks multiply by zero)\n",
    "- This block acts exactly like $\\theta_a$ in the disjoint formulation\n",
    "- We get: $z_{t,a}^T \\theta = x_t^T \\theta_{[ad:(a+1)d]}$ where $\\theta_{[ad:(a+1)d]}$ is the $a$-th block\n",
    "\n",
    "**Result**: The hybrid formulation with block-sparse features recovers the disjoint bandit exactly. Each block of $\\theta$ learns independently, just like separate $\\theta_a$ vectors.\n",
    "\n",
    "### Practical Implication\n",
    "\n",
    "This equivalence means:\n",
    "- **Disjoint bandits** = No parameter sharing between arms\n",
    "- **Hybrid bandits** = Flexible parameter sharing (can range from full sharing to no sharing)\n",
    "- By controlling the sparsity pattern of $z_{t,a}$, we control how much arms share information\n",
    "\n",
    "## Content Personalization Example: Partial Feature Sharing\n",
    "\n",
    "Now let's see why hybrid bandits outperform disjoint bandits in practice. We'll simulate a content recommendation system where **some user features affect all articles, while others only matter for specific categories**.\n",
    "\n",
    "### The Setup\n",
    "\n",
    "Consider recommending articles to users where:\n",
    "- **Shared features** affect all articles:\n",
    "  - `reading_level`: A user's comprehension level impacts enjoyment of any article\n",
    "  - `general_interest`: Overall engagement tendency applies universally\n",
    "  \n",
    "- **Category-specific features** only matter within their domain:\n",
    "  - `tech_interest`: Only relevant for tech articles\n",
    "  - `sports_interest`: Only relevant for sports articles  \n",
    "  - `politics_interest`: Only relevant for politics articles\n",
    "\n",
    "This structure naturally fits a hybrid bandit: we want to learn that reading level matters universally, while tech interest should only influence tech article predictions.\n",
    "\n",
    "### Simulation Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "98d89507",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generated 1000 users with 5 features each\n",
      "Feature means: [-0.04567877  0.00916249  0.00311432 -0.02441159 -0.04157164]\n",
      "Feature stds: [1.00050872 1.03588143 0.96737206 1.01884787 0.97369746]\n"
     ]
    }
   ],
   "source": [
    "# Simulation parameters\n",
    "n_users = 1000\n",
    "n_articles = 100\n",
    "n_rounds = 2000\n",
    "\n",
    "# User features with clear semantics\n",
    "# - reading_level: affects ALL articles (truly shared)\n",
    "# - general_interest: affects ALL articles (truly shared)\n",
    "# - tech_interest: only matters for tech articles\n",
    "# - sports_interest: only matters for sports articles\n",
    "# - politics_interest: only matters for politics articles\n",
    "n_shared_features = 2  # reading_level, general_interest\n",
    "n_interest_features = 3  # tech, sports, politics\n",
    "n_features = n_shared_features + n_interest_features\n",
    "\n",
    "# Generate user features as DataFrame\n",
    "feature_names = [\n",
    "    \"reading_level\",\n",
    "    \"general_interest\",\n",
    "    \"tech_interest\",\n",
    "    \"sports_interest\",\n",
    "    \"politics_interest\",\n",
    "]\n",
    "X_users_array = rng.standard_normal((n_users, n_features))\n",
    "X_users = pd.DataFrame(X_users_array, columns=feature_names)\n",
    "\n",
    "print(f\"Generated {n_users} users with {n_features} features each\")\n",
    "print(f\"Feature means: {X_users.mean().values}\")\n",
    "print(f\"Feature stds: {X_users.std().values}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8866246",
   "metadata": {},
   "source": [
    "## Define true reward model\n",
    "\n",
    "We'll create a realistic model where:\n",
    "- Some features (reading_level, general_interest) affect ALL articles\n",
    "- Some features (tech_interest, sports_interest, etc.) only affect their respective categories\n",
    "- Each article also has small random variations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "41ac6d48",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1000x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Key insights from the true model:\n",
      "1. Reading level and general interest affect ALL articles similarly\n",
      "2. Tech interest only affects tech articles (articles 0-4)\n",
      "3. Sports interest only affects sports articles (articles 5-9)\n",
      "4. Politics interest only affects politics articles (articles 10-14)\n",
      "5. Lifestyle articles (15-19) only use shared features\n"
     ]
    }
   ],
   "source": [
    "# Shared effects: reading_level and general_interest affect ALL articles\n",
    "theta_shared_all = np.array([0.8, 0.5])  # Only for truly shared features\n",
    "\n",
    "# Article categories\n",
    "article_categories = (\n",
    "    [\"tech\"] * 25 + [\"sports\"] * 25 + [\"politics\"] * 25 + [\"lifestyle\"] * 25\n",
    ")\n",
    "\n",
    "# Create true parameters for each article\n",
    "# Each article has:\n",
    "# - Shared effects from reading_level and general_interest\n",
    "# - Category-specific effect from the relevant interest feature\n",
    "# - Small random variations\n",
    "theta_articles_full = []\n",
    "\n",
    "for i, category in enumerate(article_categories):\n",
    "    # Start with zeros for all features\n",
    "    theta = np.zeros(n_features)\n",
    "\n",
    "    # Add shared effects (these apply to ALL articles)\n",
    "    theta[:n_shared_features] = theta_shared_all\n",
    "\n",
    "    # Add category-specific interest effects\n",
    "    if category == \"tech\":\n",
    "        theta[2] = 1.2  # tech_interest matters for tech articles\n",
    "    elif category == \"sports\":\n",
    "        theta[3] = 1.2  # sports_interest matters for sports articles\n",
    "    elif category == \"politics\":\n",
    "        theta[4] = 1.2  # politics_interest matters for politics articles\n",
    "    # lifestyle articles don't have a specific interest feature\n",
    "\n",
    "    # Add small random variations\n",
    "    theta += rng.standard_normal(n_features) * 0.1\n",
    "\n",
    "    theta_articles_full.append(theta)\n",
    "\n",
    "theta_articles_full = np.array(theta_articles_full)\n",
    "\n",
    "\n",
    "# True reward function\n",
    "def true_reward(user_features, article_id: int, noise_std: float = 0.5) -> float:\n",
    "    \"\"\"Generate true reward for a user-article pair.\"\"\"\n",
    "    # Convert to numpy if DataFrame\n",
    "    if hasattr(user_features, \"values\"):\n",
    "        user_features = user_features.values\n",
    "    if user_features.ndim > 1:\n",
    "        user_features = user_features.flatten()\n",
    "\n",
    "    # Reward is just the dot product with article's parameters\n",
    "    reward = user_features @ theta_articles_full[article_id]\n",
    "    noise = rng.normal(0, noise_std)\n",
    "    return reward + noise\n",
    "\n",
    "\n",
    "# Visualize true parameters\n",
    "fig, ax = plt.subplots(1, 1, figsize=(10, 6))\n",
    "\n",
    "im = ax.imshow(theta_articles_full.T, cmap=\"RdBu_r\", aspect=\"auto\")\n",
    "ax.set_xlabel(\"Article ID\")\n",
    "ax.set_ylabel(\"Feature\")\n",
    "ax.set_title(\"True Parameters for Each Article\")\n",
    "ax.set_yticks(range(n_features))\n",
    "ax.set_yticklabels(feature_names)\n",
    "\n",
    "# Add category labels\n",
    "for i in range(0, n_articles, 25):\n",
    "    ax.axvline(x=i - 0.5, color=\"black\", linewidth=1)\n",
    "    if i < n_articles:\n",
    "        ax.text(i + 12.5, -1, article_categories[i], ha=\"center\", va=\"top\")\n",
    "\n",
    "plt.colorbar(im, ax=ax)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Key insights from the true model:\")\n",
    "print(\"1. Reading level and general interest affect ALL articles similarly\")\n",
    "print(\"2. Tech interest only affects tech articles (articles 0-4)\")\n",
    "print(\"3. Sports interest only affects sports articles (articles 5-9)\")\n",
    "print(\"4. Politics interest only affects politics articles (articles 10-14)\")\n",
    "print(\"5. Lifestyle articles (15-19) only use shared features\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "410dee6a",
   "metadata": {},
   "source": [
    "## Approach 1: Disjoint Bandits\n",
    "\n",
    "First, let's implement the traditional approach where each article has its own completely separate model.\n",
    "\n",
    "### Implicit Model Structure\n",
    "\n",
    "In the disjoint case, we **ONLY** need to provide user-specific (exogenous) features since there's no possibility of learning across arms. Each article learns its own separate parameter vector $\\theta_a \\in \\mathbb{R}^d$ independently:\n",
    "\n",
    "$$\\mathbb{E}[r_t | x_t, a] = x_t^T \\theta_a$$\n",
    "\n",
    "Key characteristics:\n",
    "- **No parameter sharing**: Each article's $\\theta_a$ is estimated using only data from that specific article\n",
    "- **Cold start problem**: New articles have no prior knowledge and must learn from scratch  \n",
    "- **Data inefficiency**: Universal patterns (like \"reading level affects all articles\") must be learned separately for each article\n",
    "- **Simple feature engineering**: We can directly use raw user features since each arm learns independently"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "23853f7d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Created disjoint agent with 100 independent arms\n"
     ]
    }
   ],
   "source": [
    "disjoint_arms: List[Arm[NDArray[Any] | csc_array, int]] = []\n",
    "for i in range(n_articles):\n",
    "    arm = Arm(\n",
    "        action_token=i,\n",
    "        learner=NormalRegressor(\n",
    "            alpha=1.0,  # Prior precision\n",
    "            beta=1.0,  # Noise precision\n",
    "        ),\n",
    "    )\n",
    "    disjoint_arms.append(arm)\n",
    "\n",
    "# Create agent with Thompson Sampling policy\n",
    "disjoint_agent = ContextualAgent(arms=disjoint_arms, policy=ThompsonSampling())\n",
    "\n",
    "print(f\"Created disjoint agent with {len(disjoint_arms)} independent arms\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df339526",
   "metadata": {},
   "source": [
    "## Approach 2: Hybrid Bandits with LipschitzContextualAgent\n",
    "\n",
    "Now let's implement the hybrid approach using a single shared model with arm-specific features.\n",
    "\n",
    "### Implicit Model Structure\n",
    "\n",
    "In the hybrid case, we want to add **category-specific features** to provide some shrinkage to a \"category mean\" on each article, and then we also have a **per-article intercept** to capture the variation between articles. The single shared parameter vector $\\theta \\in \\mathbb{R}^p$ captures multiple types of effects:\n",
    "\n",
    "$$\\mathbb{E}[r_t | z_{t,a}] = z_{t,a}^T \\theta$$\n",
    "\n",
    "Where $z_{t,a}$ contains:\n",
    "1. **Shared effects**: Features like `reading_level` that affect ALL articles identically\n",
    "2. **Category interactions**: Features like `tech_interest × is_tech_article` that only activate for relevant categories  \n",
    "3. **Article-specific intercepts**: One-hot encoded article IDs to capture unique article effects\n",
    "\n",
    "### \"Poor Man's Hierarchical Model\"\n",
    "\n",
    "Because we're doing **Bayesian ridge regression**, the regularization automatically puts more weight on the shared and category-level effects (which have more data) compared to article-specific effects (which have less data). This creates a natural hierarchy:\n",
    "\n",
    "- **Level 1 (Global)**: Shared effects like reading level get the most weight (learned from all data)\n",
    "- **Level 2 (Category)**: Category interactions get moderate weight (learned from category subsets)  \n",
    "- **Level 3 (Article)**: Article intercepts get less weight (learned from individual article data)\n",
    "\n",
    "Key advantages:\n",
    "- **Knowledge transfer**: Learning about tech articles helps with other tech articles\n",
    "- **Automatic shrinkage**: Bayesian priors naturally shrink article-specific effects toward category and global means\n",
    "- **Cold start solution**: New articles immediately benefit from category-level knowledge\n",
    "- **Data efficiency**: Universal patterns are learned once using all available data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c718b80c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Created hybrid agent with 100 arms sharing a single learner\n",
      "Feature engineering:\n",
      "- Shared features: reading_level, general_interest (affect all articles)\n",
      "- Interaction features: tech_interest × is_tech_article, etc.\n",
      "- One-hot encoded article IDs for article-specific adjustments\n"
     ]
    }
   ],
   "source": [
    "arm_featurizer = ArmColumnFeaturizer(column_name=\"article_id\")\n",
    "\n",
    "\n",
    "# Create a more sophisticated feature engineering pipeline\n",
    "# This will create:\n",
    "# 1. Shared features that affect all arms\n",
    "# 2. Interaction features between interests and article categories\n",
    "def create_interaction_features(df):\n",
    "    \"\"\"Vectorized interaction feature creation - exact match to original.\"\"\"\n",
    "    # Direct boolean masks using vectorized operations\n",
    "    is_tech = (df[\"article_id\"] < 25).astype(float)\n",
    "    is_sports = ((df[\"article_id\"] >= 25) & (df[\"article_id\"] < 50)).astype(float)\n",
    "    is_politics = ((df[\"article_id\"] >= 50) & (df[\"article_id\"] < 75)).astype(float)\n",
    "\n",
    "    # Start with columns that are kept\n",
    "    result = df[[\"reading_level\", \"general_interest\", \"article_id\"]].copy()\n",
    "\n",
    "    # Add interaction features in the same order as original\n",
    "    result[\"tech_x_is_tech\"] = df[\"tech_interest\"] * is_tech\n",
    "    result[\"sports_x_is_sports\"] = df[\"sports_interest\"] * is_sports\n",
    "    result[\"politics_x_is_politics\"] = df[\"politics_interest\"] * is_politics\n",
    "\n",
    "    return result\n",
    "\n",
    "\n",
    "# Create preprocessing pipeline\n",
    "preprocessor = make_pipeline(\n",
    "    FunctionTransformer(create_interaction_features),\n",
    "    ColumnTransformer(\n",
    "        [\n",
    "            (\"shared\", \"passthrough\", [\"reading_level\", \"general_interest\"]),\n",
    "            (\n",
    "                \"interactions\",\n",
    "                \"passthrough\",\n",
    "                [\"tech_x_is_tech\", \"sports_x_is_sports\", \"politics_x_is_politics\"],\n",
    "            ),\n",
    "            (\"article_id\", OneHotEncoder(sparse_output=True), [\"article_id\"]),\n",
    "        ]\n",
    "    ),\n",
    ")\n",
    "\n",
    "# Pre-fit the preprocessor on dummy data, as our online learning framework will never call fit.\n",
    "# This only benefits one-hot encoding, as the other transformations are stateless. In practice,\n",
    "# we'd use something like FeatureHasher instead of OneHotEncoder for scalability.\n",
    "dummy_contexts = pd.DataFrame(np.random.randn(100, n_features), columns=feature_names)\n",
    "dummy_arms = list(range(n_articles))\n",
    "dummy_X_transformed = arm_featurizer.transform(dummy_contexts, action_tokens=dummy_arms)\n",
    "preprocessor.fit(dummy_X_transformed)\n",
    "\n",
    "# Create a single shared learner wrapped in LearnerPipeline\n",
    "learner_pipeline = LearnerPipeline(\n",
    "    steps=[(\"preprocessor\", preprocessor)],\n",
    "    learner=NormalRegressor(\n",
    "        alpha=1.0,  # Prior precision\n",
    "        beta=1.0,  # Noise precision\n",
    "        sparse=True,  # Use sparse matrices for efficiency\n",
    "    ),\n",
    ")\n",
    "\n",
    "# Create arms for hybrid agent\n",
    "hybrid_arms = [Arm(action_token=i) for i in range(n_articles)]\n",
    "\n",
    "# Create hybrid agent\n",
    "hybrid_agent = LipschitzContextualAgent(\n",
    "    arms=hybrid_arms,\n",
    "    learner=learner_pipeline,\n",
    "    policy=ThompsonSampling(),\n",
    "    arm_featurizer=arm_featurizer,\n",
    ")\n",
    "\n",
    "print(f\"Created hybrid agent with {n_articles} arms sharing a single learner\")\n",
    "print(\"Feature engineering:\")\n",
    "print(\"- Shared features: reading_level, general_interest (affect all articles)\")\n",
    "print(\"- Interaction features: tech_interest × is_tech_article, etc.\")\n",
    "print(\"- One-hot encoded article IDs for article-specific adjustments\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34b22b6f",
   "metadata": {},
   "source": [
    "## Running the Comparison Experiment\n",
    "\n",
    "Let's run both agents on the same sequence of users and compare their performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7d52d6b5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Running simulation...\n",
      "Round 500/2000\n",
      "Round 1000/2000\n",
      "Round 1500/2000\n",
      "Round 2000/2000\n",
      "Simulation complete!\n"
     ]
    }
   ],
   "source": [
    "# Initialize metrics storage\n",
    "rewards_disjoint = []\n",
    "rewards_hybrid = []\n",
    "regrets_disjoint = []\n",
    "regrets_hybrid = []\n",
    "arms_pulled_disjoint = []\n",
    "arms_pulled_hybrid = []\n",
    "\n",
    "# Run simulation\n",
    "print(\"\\nRunning simulation...\")\n",
    "for t in range(n_rounds):\n",
    "    if (t + 1) % 500 == 0:\n",
    "        print(f\"Round {t + 1}/{n_rounds}\")\n",
    "\n",
    "    # Sample a random user\n",
    "    user_idx = np.random.randint(n_users)\n",
    "    user_features = X_users.iloc[[user_idx]]  # DataFrame with shape: (1, n_features)\n",
    "\n",
    "    # Compute optimal reward for this user\n",
    "    user_array = X_users.iloc[user_idx].values\n",
    "    optimal_rewards = [\n",
    "        true_reward(user_array, a, noise_std=0) for a in range(n_articles)\n",
    "    ]\n",
    "    optimal_reward = max(optimal_rewards)\n",
    "    optimal_arm = np.argmax(optimal_rewards)\n",
    "\n",
    "    # Disjoint agent's turn\n",
    "    arms_disjoint = disjoint_agent.pull(user_features)\n",
    "    arm_disjoint = arms_disjoint[0]  # Get first (and only) arm from list\n",
    "    reward_disjoint = true_reward(user_array, arm_disjoint)\n",
    "    disjoint_agent.select_for_update(arm_disjoint).update(\n",
    "        user_features, np.array([reward_disjoint])\n",
    "    )\n",
    "\n",
    "    # Hybrid agent's turn\n",
    "    arms_hybrid = hybrid_agent.pull(user_features)\n",
    "    arm_hybrid = arms_hybrid[0]  # Get first (and only) arm from list\n",
    "    reward_hybrid = true_reward(user_array, arm_hybrid)\n",
    "    hybrid_agent.select_for_update(arm_hybrid).update(\n",
    "        user_features, np.array([reward_hybrid])\n",
    "    )\n",
    "\n",
    "    # Record metrics\n",
    "    rewards_disjoint.append(reward_disjoint)\n",
    "    rewards_hybrid.append(reward_hybrid)\n",
    "    regrets_disjoint.append(optimal_reward - reward_disjoint)\n",
    "    regrets_hybrid.append(optimal_reward - reward_hybrid)\n",
    "    arms_pulled_disjoint.append(arm_disjoint)\n",
    "    arms_pulled_hybrid.append(arm_hybrid)\n",
    "\n",
    "print(\"Simulation complete!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb8df3f4",
   "metadata": {},
   "source": [
    "## Analyzing the Results\n",
    "\n",
    "Let's visualize and analyze the performance of both approaches.\n",
    "\n",
    "### Key Performance Insights\n",
    "\n",
    "Looking at the results, we can see several important patterns:\n",
    "\n",
    "1. **Similar Final Performance**: Both models eventually reach similar average rewards (~1.15-1.22), suggesting they can both learn the underlying problem structure given enough data.\n",
    "\n",
    "2. **Dramatically Different Learning Speed**: The hybrid model reaches good performance much faster, achieving ~40% lower cumulative regret. This is the key advantage of cross-arm learning.\n",
    "\n",
    "3. **Early Learning Advantage**: The hybrid model starts performing well within the first few hundred rounds, while the disjoint model takes over 1000 rounds to reach comparable performance.\n",
    "\n",
    "4. **Cross-Arm Learning Effect**: The hybrid model's faster convergence is due to its ability to transfer knowledge across articles. When it learns that \"reading level matters for tech articles,\" it immediately knows this applies to all other articles too. The disjoint model must learn this pattern separately for each article."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "38e05910",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Performance Summary ===\n",
      "Total Cumulative Regret:\n",
      "  Disjoint: 1458.22\n",
      "  Hybrid: 853.17\n",
      "  Improvement: 41.5%\n",
      "\n",
      "Final Average Reward (last 100 rounds):\n",
      "  Disjoint: 1.128\n",
      "  Hybrid: 1.193\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate cumulative metrics\n",
    "cumulative_regret_disjoint = np.cumsum(regrets_disjoint)\n",
    "cumulative_regret_hybrid = np.cumsum(regrets_hybrid)\n",
    "cumulative_reward_disjoint = np.cumsum(rewards_disjoint)\n",
    "cumulative_reward_hybrid = np.cumsum(rewards_hybrid)\n",
    "\n",
    "# Create comprehensive visualization\n",
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "\n",
    "# 1. Cumulative Regret\n",
    "ax = axes[0]\n",
    "ax.plot(cumulative_regret_disjoint, label=\"Disjoint Bandits\", linewidth=2)\n",
    "ax.plot(cumulative_regret_hybrid, label=\"Hybrid Bandits\", linewidth=2)\n",
    "ax.set_xlabel(\"Round\")\n",
    "ax.set_ylabel(\"Cumulative Regret\")\n",
    "ax.set_title(\"Cumulative Regret Comparison\")\n",
    "ax.legend()\n",
    "ax.grid(True, alpha=0.3)\n",
    "\n",
    "# 2. Average Reward (Moving Average)\n",
    "ax = axes[1]\n",
    "window = 100\n",
    "avg_reward_disjoint = pd.Series(rewards_disjoint).rolling(window, min_periods=1).mean()\n",
    "avg_reward_hybrid = pd.Series(rewards_hybrid).rolling(window, min_periods=1).mean()\n",
    "ax.plot(avg_reward_disjoint, label=\"Disjoint Bandits\", linewidth=2)\n",
    "ax.plot(avg_reward_hybrid, label=\"Hybrid Bandits\", linewidth=2)\n",
    "ax.set_xlabel(\"Round\")\n",
    "ax.set_ylabel(f\"Average Reward ({window}-round MA)\")\n",
    "ax.set_title(\"Average Reward Over Time\")\n",
    "ax.legend()\n",
    "ax.grid(True, alpha=0.3)\n",
    "\n",
    "\n",
    "# Print summary statistics\n",
    "print(\"\\n=== Performance Summary ===\")\n",
    "print(\"Total Cumulative Regret:\")\n",
    "print(f\"  Disjoint: {cumulative_regret_disjoint[-1]:.2f}\")\n",
    "print(f\"  Hybrid: {cumulative_regret_hybrid[-1]:.2f}\")\n",
    "print(\n",
    "    f\"  Improvement: {(1 - cumulative_regret_hybrid[-1] / cumulative_regret_disjoint[-1]) * 100:.1f}%\"\n",
    ")\n",
    "print(\"\\nFinal Average Reward (last 100 rounds):\")\n",
    "print(f\"  Disjoint: {np.mean(rewards_disjoint[-100:]):.3f}\")\n",
    "print(f\"  Hybrid: {np.mean(rewards_hybrid[-100:]):.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b873110",
   "metadata": {},
   "source": [
    "## Examining Learned Parameters\n",
    "\n",
    "Let's look at what each approach actually learned about the problem structure.\n",
    "\n",
    "### Key Observations\n",
    "\n",
    "**Hybrid Model Success**: The hybrid model recovers the shared parameters almost perfectly:\n",
    "\n",
    "- Learned: [0.85, 0.50] vs True: [0.8, 0.5]\n",
    "- This uses data from all 20 articles to estimate these universal effects\n",
    "- Interaction effects (e.g., reading_level * tech_interest) are also learned effectively, because they are shared across articles of the same category\n",
    "\n",
    "**Disjoint Model Limitations**:\n",
    "\n",
    "- Only well-explored arms (200+ pulls) achieve good parameter recovery\n",
    "- The top 3 arms show excellent correlation (0.99+) but consumed 589 of 2000 rounds\n",
    "- The remaining 17 arms have far fewer samples and thus noisier estimates\n",
    "- Each arm learns `reading_level` and `general_interest` effects independently, wasting data\n",
    "\n",
    "**Hot Start for New Content**: By recognizing that some features affect all articles identically, the hybrid model:\n",
    "\n",
    "- Learns universal patterns faster using all available data\n",
    "- Provides better estimates for rarely-explored arms\n",
    "- Achieves lower regret by transferring knowledge across arms\n",
    "- **Handles new content gracefully**: If we added a 21st tech article, the hybrid model would immediately know that reading level matters (shared effect) and that tech interest is relevant (category effect). The disjoint model would start from zero knowledge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3819e601",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hybrid model learned 105 parameters\n",
      "\n",
      "Learned shared parameters (reading_level, general_interest): [0.80393868 0.49107121]\n",
      "True shared parameters: [0.8 0.5]\n",
      "\n",
      "Learned interaction effects (true was 1.2 for all of them): [1.26979812 1.21611846 1.27814446]\n",
      "(tech×is_tech, sports×is_sports, politics×is_politics)\n",
      "\n",
      "\n",
      "=== Parameter Recovery for Disjoint Model ===\n",
      "\n",
      "Arm 30 (sports): 47 pulls\n",
      "  Correlation with true params: 0.990\n",
      "  Learned: [ 0.94932237  0.48656529 -0.22143663  1.52547513  0.09135378]\n",
      "  True: [0.96272311 0.49166674 0.00466268 1.33543005 0.06614784]\n",
      "\n",
      "Arm 1 (tech): 33 pulls\n",
      "  Correlation with true params: 0.987\n",
      "  Learned: [ 0.49790706  0.13633767  1.20539449 -0.06415957 -0.061974  ]\n",
      "  True: [ 0.64093503  0.3348474   1.24246845 -0.08152864  0.03020412]\n",
      "\n",
      "Arm 49 (sports): 32 pulls\n",
      "  Correlation with true params: 0.988\n",
      "  Learned: [0.70755246 0.87787503 0.2576354  1.27130739 0.03088537]\n",
      "  True: [ 0.8140541   0.82412591  0.10545337  1.23248776 -0.08759244]\n"
     ]
    }
   ],
   "source": [
    "# Examining learned parameters\n",
    "# Extract learned parameters from hybrid model\n",
    "if hasattr(hybrid_agent.learner, \"learner\") and hasattr(\n",
    "    hybrid_agent.learner.learner, \"coef_\"\n",
    "):\n",
    "    hybrid_params = hybrid_agent.learner.learner.coef_\n",
    "    print(f\"Hybrid model learned {len(hybrid_params)} parameters\")\n",
    "\n",
    "    # The first 2 parameters should be the shared effects\n",
    "    learned_shared = hybrid_params[:2]\n",
    "    print(\n",
    "        f\"\\nLearned shared parameters (reading_level, general_interest): {learned_shared}\"\n",
    "    )\n",
    "    print(f\"True shared parameters: {theta_shared_all}\")\n",
    "\n",
    "    # Next 3 are the interaction effects\n",
    "    learned_interactions = hybrid_params[2:5]\n",
    "    print(\n",
    "        f\"\\nLearned interaction effects (true was 1.2 for all of them): {learned_interactions}\"\n",
    "    )\n",
    "    print(\"(tech×is_tech, sports×is_sports, politics×is_politics)\")\n",
    "\n",
    "else:\n",
    "    print(\"Could not access learned parameters\")\n",
    "\n",
    "# Check parameter recovery for a few well-explored arms in disjoint model\n",
    "print(\"\\n\\n=== Parameter Recovery for Disjoint Model ===\")\n",
    "arm_counts_disjoint = pd.Series(arms_pulled_disjoint).value_counts().sort_index()\n",
    "well_explored = sorted(\n",
    "    [(arm, count) for arm, count in arm_counts_disjoint.items()],\n",
    "    key=lambda x: x[1],\n",
    "    reverse=True,\n",
    ")[:3]\n",
    "\n",
    "for arm_id, count in well_explored:\n",
    "    arm = disjoint_arms[arm_id]\n",
    "    if hasattr(arm.learner, \"coef_\"):\n",
    "        learned = arm.learner.coef_\n",
    "        true = theta_articles_full[arm_id]\n",
    "        if len(learned) == len(true):\n",
    "            corr = np.corrcoef(learned, true)[0, 1]\n",
    "            print(f\"\\nArm {arm_id} ({article_categories[arm_id]}): {count} pulls\")\n",
    "            print(f\"  Correlation with true params: {corr:.3f}\")\n",
    "            print(f\"  Learned: {learned}\")\n",
    "            print(f\"  True: {true}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "185297ca",
   "metadata": {},
   "source": [
    "## Computational Efficiency and Production Scale Considerations\n",
    "\n",
    "Real production systems face dramatically different scale challenges than our toy example:\n",
    "\n",
    "**Scale Characteristics:**\n",
    "- **Features**: 10⁶-10⁹ sparse features (user demographics, item attributes, interaction history)\n",
    "- **Arms**: 10³-10⁶ possible actions (products, ads, content items)  \n",
    "- **Latency**: <1ms inference time required for real-time serving\n",
    "- **Throughput**: 10⁵-10⁶ predictions per second\n",
    "\n",
    "### Production Challenges Beyond Scale\n",
    "\n",
    "Real systems must handle **biased feedback** that fundamentally corrupts the learning signal:\n",
    "- **Position bias**: On Google Search, users click on the first position 10x more than the tenth position¹\n",
    "- **Pseudo-exposure**: In recommendation scenarios, a list of items is recommended based on user and item information. Due to the limited screen size, at first glance, a user only sees certain items. To see the remaining items, the user has to swipe through the screen²\n",
    "- **Selection bias**: Only 0.1-1% CTR means 99%+ items lack explicit feedback\n",
    "\n",
    "### Scaling Challenges and How We Address Them\n",
    "\n",
    "**Yahoo's LinUCB (2010)** ³:\n",
    "- **Challenge**: Full covariance matrices were computationally intractable for 40M+ users\n",
    "- **Their solution**: Diagonal approximation, losing feature correlation information\n",
    "- **Our toolkit**: Sparse covariance matrices maintain correlations while reducing memory from O(d²) to O(s)\n",
    "\n",
    "**Microsoft's Decision Service (2016)** ⁴:\n",
    "- **Challenge**: Unbounded feature spaces from user-generated content and dynamic contexts\n",
    "- **Their solution**: features with more informantive ones. The Decision Service uses feature hashing to fixed-size representations\n",
    "- **Our toolkit**: `FeatureHasher` transformer provides the same capability with configurable hash sizes\n",
    "\n",
    "**Facebook's Ad Prediction (2014)** ⁵:\n",
    "- **Challenge**: With over 750 million daily active users and over 1 million active advertisers, predicting clicks on Facebook ads is a challenging machine learning task\n",
    "- **Their solution**: This paper introduces a model which combines decision trees with logistic regression, outperforming either of these methods on its own by over 3%\n",
    "- **Our toolkit**: Sparse matrix support throughout the pipeline handles high-dimensional features naturally\n",
    "\n",
    "**Alibaba's Taobao Recommendations (2020)** ⁶:\n",
    "- **Challenge**: If the user exits from the recommendation scenario before browsing through all the items, this phenomenon is referred to as pseudo exposure\n",
    "- **Their solution**: Used weighted updates to correct position/exposure bias\n",
    "- **Our toolkit**: `NormalRegressor` accepts sample weights, enabling the same bias correction\n",
    "\n",
    "**Netflix's Exploration (2018)** ⁷:\n",
    "- **Challenge**: Batch updates too slow for real-time personalization\n",
    "- **Their solution**: contextual bandits can learn to personalize UI elements to maximize each user's experience using Thompson sampling\n",
    "- **Our toolkit**: Efficient incremental Cholesky updates enable true online learning\n",
    "\n",
    "### Key Architectural Patterns\n",
    "\n",
    "Production systems repeatedly encounter similar scaling bottlenecks:\n",
    "\n",
    "1. **Memory explosion** → Addressed by sparse representations\n",
    "2. **Feature cardinality** → Addressed by feature hashing  \n",
    "3. **Biased feedback** → Addressed by weighted updates\n",
    "4. **Update latency** → Addressed by incremental algorithms\n",
    "5. **Cold start** → Addressed by hybrid parameter sharing\n",
    "\n",
    "### Performance Characteristics\n",
    "\n",
    "Our sparse Bayesian approach exhibits scaling properties suitable for production:\n",
    "\n",
    "**Memory Usage**: \n",
    "- Dense covariance: 8GB for 10K × 10K matrix\n",
    "- Sparse (1% density): 80MB for same effective capacity\n",
    "\n",
    "**Update Performance**:\n",
    "- Incremental Cholesky: O(s²) where s << d for sparse matrices\n",
    "- Batch processing: Vectorized operations across all arms simultaneously\n",
    "\n",
    "**Inference Speed**:\n",
    "- Sparse matrix-vector multiply: <0.1ms for 1M features with 0.1% density\n",
    "- Thompson sampling: Direct sampling from updated posterior\n",
    "\n",
    "The combination of sparse linear algebra, feature hashing, and weighted updates addresses the core scaling challenges that production recommender systems encounter, providing a foundation suitable for real-world deployment.\n",
    "\n",
    "---\n",
    "\n",
    "¹ Yan, Z. (2022). How to Measure and Mitigate Position Bias. eugeneyan.com.\n",
    "\n",
    "² He, X., et al. (2019). How to Remove \"Pseudo Exposure\" from Mobile E-commerce Platforms. Alibaba Cloud Community.\n",
    "\n",
    "³ Li, L., et al. \"A contextual-bandit approach to personalized news article recommendation.\" WWW 2010.\n",
    "\n",
    "⁴ Agarwal, A., et al. \"Making contextual decisions with low technical debt.\" arXiv:1606.03966, 2016.\n",
    "\n",
    "⁵ He, X., et al. \"Practical lessons from predicting clicks on ads at Facebook.\" ADKDD 2014.\n",
    "\n",
    "⁶ He, X., et al. \"Contextual User Browsing Bandits for Large-Scale Online Mobile Recommendation.\" RecSys 2020.\n",
    "\n",
    "⁷ Amat, F., et al. \"Artwork personalization at Netflix.\" RecSys 2018."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "12517747",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Computational Efficiency ===\n",
      "\n",
      "Time to make 1000 predictions one at a time:\n",
      "  Disjoint: 21.462 seconds (21.5 ms/prediction)\n",
      "  Hybrid: 2.632 seconds (2.6 ms/prediction)\n",
      "  Speedup: 8.2x\n",
      "\n",
      "=== Memory Efficiency ===\n",
      "Number of parameters to store:\n",
      "  Disjoint: 100 models × 6 params = 600 total\n",
      "  Hybrid: 1 model × (2 shared + 3 interactions + 100 one-hot) = 105 total\n",
      "  Memory reduction: 82.5%\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "# Measure prediction time for a batch of users\n",
    "n_test_users = 1000\n",
    "test_features = X_users.iloc[:n_test_users]\n",
    "\n",
    "# Disjoint timing\n",
    "start_time = time.time()\n",
    "for idx in range(n_test_users):\n",
    "    _ = disjoint_agent.pull(test_features.iloc[[idx]])\n",
    "disjoint_time = time.time() - start_time\n",
    "\n",
    "# Hybrid timing\n",
    "start_time = time.time()\n",
    "for idx in range(n_test_users):\n",
    "    _ = hybrid_agent.pull(test_features.iloc[[idx]])\n",
    "hybrid_time = time.time() - start_time\n",
    "\n",
    "print(\"=== Computational Efficiency ===\")\n",
    "print(f\"\\nTime to make {n_test_users} predictions one at a time:\")\n",
    "print(\n",
    "    f\"  Disjoint: {disjoint_time:.3f} seconds ({disjoint_time / n_test_users * 1000:.1f} ms/prediction)\"\n",
    ")\n",
    "print(\n",
    "    f\"  Hybrid: {hybrid_time:.3f} seconds ({hybrid_time / n_test_users * 1000:.1f} ms/prediction)\"\n",
    ")\n",
    "print(f\"  Speedup: {disjoint_time / hybrid_time:.1f}x\")\n",
    "\n",
    "print(\"\\n=== Memory Efficiency ===\")\n",
    "print(\"Number of parameters to store:\")\n",
    "print(\n",
    "    f\"  Disjoint: {n_articles} models × {n_features + 1} params = {n_articles * (n_features + 1)} total\"\n",
    ")\n",
    "print(\n",
    "    f\"  Hybrid: 1 model × (2 shared + 3 interactions + {n_articles} one-hot) = {2 + 3 + n_articles} total\"\n",
    ")\n",
    "print(\n",
    "    f\"  Memory reduction: {(1 - (2 + 3 + n_articles) / (n_articles * (n_features + 1))) * 100:.1f}%\"\n",
    ")"
   ]
  }
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