bandit-icml24.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2316044c-3c54-442f-9942-7adaf4f95990",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.stats import entropy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "582bb5bb-8481-414d-b957-3bfa270b1960",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the given functions\n",
    "# PR(\\theta)\n",
    "def f(y):\n",
    "    #return x**4 * (1 + x**2)\n",
    "    return -y**2*(y - 1)**2 - (1-y**2)*(y)**2\n",
    "\n",
    "# PR(\\phi)\n",
    "def g(x):\n",
    "    #return y**2 * (1 + y)\n",
    "    return -x*(np.sqrt(x)-1)**2 - (1-x)*x\n",
    "\n",
    "# Function to calculate the KL divergence between two Gaussians\n",
    "# def kl_divergence(x_target, y):\n",
    "#     if y < 0:\n",
    "#         y = 0\n",
    "#     mu1, sigma1 = np.sqrt(y), 1\n",
    "#     mu2, sigma2 = x_target, 1\n",
    "#     return np.log(sigma2/sigma1) + (sigma1**2 + (mu1 - mu2)**2) / (2 * sigma2**2) - 0.5\n",
    "\n",
    "\n",
    "# for Bernoulli distribution\n",
    "def kl_divergence(p, q):\n",
    "    \"\"\"\n",
    "    Calculate the Kullback-Leibler divergence between two Bernoulli distributions with parameters p and q.\n",
    "    \n",
    "    Parameters:\n",
    "    p (float): parameter of the first Bernoulli distribution (0 <= p <= 1)\n",
    "    q (float): parameter of the second Bernoulli distribution (0 <= q <= 1)\n",
    "    \n",
    "    Returns:\n",
    "    float: the KL divergence between the two distributions\n",
    "    \"\"\"\n",
    "    # Ensure that the probabilities are valid and non-zero to avoid division by zero\n",
    "    if p == 0 or q == 0 or p == 1 or q == 1:\n",
    "        return np.inf\n",
    "    \n",
    "    # Use the formula for KL divergence between two Bernoulli distributions\n",
    "    return p * np.log(p / q) + (1 - p) * np.log((1 - p) / (1 - q))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "609245fb-022b-4bca-8b40-0231ed7e43b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# vanilla two_point_feedback\n",
    "\n",
    "def two_point_feedback_zeroth_order_optimization(func, dim, x0, alpha=0.01, beta=0.1, num_iterations=1000):\n",
    "    \"\"\"\n",
    "    Two-point feedback zeroth order optimization.\n",
    "\n",
    "    Parameters:\n",
    "    - func: The objective function to minimize.\n",
    "    - dim: Dimension of the input space.\n",
    "    - x0: Initial guess.\n",
    "    - alpha: Learning rate.\n",
    "    - beta: Magnitude of the finite difference approximation.\n",
    "    - num_iterations: Number of iterations.\n",
    "\n",
    "    Returns:\n",
    "    - x: The estimated minimum point.\n",
    "    - f_values: List of function values at each iteration.\n",
    "    \"\"\"\n",
    "    x = np.array(x0)\n",
    "    f_values = []\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        #print(\"x\", x)\n",
    "        # Generate a random direction\n",
    "        d = np.random.randn(dim)\n",
    "        d = d / np.linalg.norm(d)  # Normalize the direction\n",
    "        \n",
    "        # Estimate gradient using two-point feedback\n",
    "        f_plus = func(x + beta * d)\n",
    "        f_minus = func(x - beta * d)\n",
    "\n",
    "        # print(\"f_plus\", f_plus)\n",
    "        # print(\"f_minus\", f_minus)\n",
    "        \n",
    "        grad_est = (f_plus - f_minus) / (2 * beta) * d\n",
    "\n",
    "        # print(\"grad_est\", grad_est)\n",
    "        \n",
    "        # Update the solution using the estimated gradient\n",
    "        x = x - alpha * grad_est\n",
    "\n",
    "        # Project x back onto the [0, 1] interval\n",
    "        x = np.clip(x, 0.01, 0.95)\n",
    "        \n",
    "        # Store the function value\n",
    "        f_values.append(func(x))\n",
    "    \n",
    "    return x, f_values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4dab5876-cd4a-447d-acfb-1ef59f893917",
   "metadata": {},
   "source": [
    "### reparametrization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "1440ca90-e11e-47fa-b8d3-9d04c9eb274c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# goal of LearnModel is to find a \\theta (y) such that \\varphi(\\theta) \\approx \\phi (x_target)through minimizing the KL divergence\n",
    "def LearnModel(x_target, initial_y, alpha=0.01, beta=0.1, num_iterations=10):\n",
    "    y_current = initial_y\n",
    "    \n",
    "    for _ in range(num_iterations):\n",
    "        # Perturbation for gradient estimation, ensuring float type for operations\n",
    "        d = np.random.randn(dim)\n",
    "        d = d / np.linalg.norm(d)  # Normalize the direction\n",
    "\n",
    "        # print(\"perturbation\", perturbation)\n",
    "    \n",
    "        y_plus = y_current + beta * d\n",
    "        y_minus = y_current - beta * d\n",
    "\n",
    "        # print(\"y_plus\", y_plus)\n",
    "        # print(\"y_minus\", y_minus)       \n",
    "        \n",
    "        # Calculate KL divergence for both perturbed points, ensuring all operations are float-compatible\n",
    "        kl_plus = kl_divergence(x_target, y_plus**2)\n",
    "        kl_minus = kl_divergence(x_target, y_minus**2)\n",
    "\n",
    "        # print(\"kl_plus\", kl_plus)\n",
    "        # print(\"kl_minus\", kl_minus)\n",
    "        \n",
    "        # Approximate the gradient of KL divergence\n",
    "        grad_kl = (kl_plus - kl_minus) / (2.0 * beta) * d  # Use 2.0 to ensure float operation\n",
    "\n",
    "        # print(\"grad_kl\", grad_kl)\n",
    "        \n",
    "        # Update y using the approximate gradient, adjust with float operation\n",
    "        y_current =  y_current - alpha * grad_kl\n",
    "\n",
    "\n",
    "        # Project y_current back onto the [0, 1] interval\n",
    "        y_current = np.clip(y_current, 0.01, 0.95)\n",
    "\n",
    "        if np.abs(grad_kl) <=10e-5:\n",
    "            print(\"here\")\n",
    "            break\n",
    "\n",
    "    # print(\"y_current**2\", y_current**2)\n",
    "    # print(\"x_target\", x_target)\n",
    "    return y_current"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec68602e-79a7-4bde-ba41-c68b5dd5ae83",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "628cc375-1193-4262-b302-11a8bc415d93",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "bd61d69d-a029-4de5-99d3-3de0f4d6d593",
   "metadata": {},
   "outputs": [],
   "source": [
    "def modified_two_point_feedback_optimization(func, dim, x0, alpha=0.001, beta=0.1, num_iterations=100):\n",
    "    x = np.array(x0)\n",
    "    f_values = []\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        # Generate a random direction\n",
    "        d = np.random.randn(dim)\n",
    "        d = d / np.linalg.norm(d)  # Normalize the direction\n",
    "\n",
    "        # print(d)\n",
    "        \n",
    "        # Use LearnModel to approximate y_plus and y_minus\n",
    "        y_plus = LearnModel(x + beta * d, x)\n",
    "        y_minus = LearnModel(x - beta * d, x)\n",
    "\n",
    "        # print(\"y_plus, y_minus\", y_plus, y_minus)\n",
    "        # print(\"func(y_plus**2)\", func(y_plus**2))\n",
    "        # print(\"func(y_minus**2)\", func(y_plus**2))\n",
    "\n",
    "        \n",
    "        # Estimate gradient using two-point feedback\n",
    "        grad_est = (func(y_plus) - func(y_minus)) / (2 * beta) * d\n",
    "\n",
    "        # print(\"grad_est\", grad_est)\n",
    "\n",
    "        # if np.abs(grad_est) <=10e-3:\n",
    "        #     print(\"here\")\n",
    "        #     break\n",
    "        \n",
    "        # Update the solution using the estimated gradient\n",
    "        x = x - alpha * grad_est\n",
    "\n",
    "        # Project x back onto the [0, 1] interval\n",
    "        x = np.clip(x, 0.1, 0.9)\n",
    "        # print(\"x\", x)\n",
    "        \n",
    "        # Store the function value\n",
    "        f_values.append(func(x))\n",
    "    \n",
    "    return x, f_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "6380c632-e6ef-4573-a803-0351a5a5443f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Optimization parameters\n",
    "\n",
    "dim = 1  # Dimension of the input space\n",
    "x0 = [0.3]  # Initial guess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "64632f89-8e4b-4662-9f98-db444806114f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# the modified optimization with the updated LearnModel (optimize on phi space)\n",
    "\n",
    "x_opt, g_values = modified_two_point_feedback_optimization(\n",
    "    func=g,\n",
    "    dim=dim,\n",
    "    x0=x0,\n",
    "    alpha=0.01,  # Adjusted learning rate if necessary\n",
    "    beta=0.1,\n",
    "    num_iterations=500\n",
    ")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1d7ced52-7bb7-4f16-aff3-73e6d66a8cc5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aee5ff82-5132-4d06-a680-23465ef1fe07",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "05a3c1ee-8d93-4382-a1a9-54e673f80dff",
   "metadata": {},
   "outputs": [],
   "source": [
    "# the default two_point_feedback (on \\theta space)\n",
    "x_opt, f_values = two_point_feedback_zeroth_order_optimization(\n",
    "    func=f,\n",
    "    dim=dim,\n",
    "    x0= x0[0]**2,\n",
    "    alpha=0.01,\n",
    "    beta=0.1,\n",
    "    num_iterations=500\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "63fffb61-2229-4082-96d0-78723290a3ba",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "2873b335-27e8-491b-b024-3d111292ecdf",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the function value over iterations with the updated LearnModel\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(g_values, label='PR(phi)')\n",
    "plt.plot(f_values, label='PR(theta)')\n",
    "#plt.yscale('log')\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Function Value')\n",
    "plt.title('Direct Optimization vs Reparametrization')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "87e65b9b-90b3-4139-84c0-93848e62e1fc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "193b2fa6-4525-4165-8948-527c89bbc8f6",
   "metadata": {},
   "source": [
    "## multiple runs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "584aff65-92b9-416d-b3eb-966a4194fc3b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define initial points\n",
    "initial_points_x = np.linspace(0.25, 0.8, 10)  # 10 different initial points\n",
    "#initial_points_x = np.linspace(0.3, 0.75, 10)  # 10 different initial points \n",
    "# # Generate initial points in y by squaring elements in x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "id": "c2cb8d4b-75ad-49cf-a581-cac3e2766974",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.25       0.31111111 0.37222222 0.43333333 0.49444444 0.55555556\n",
      " 0.61666667 0.67777778 0.73888889 0.8       ]\n"
     ]
    }
   ],
   "source": [
    "print(initial_points_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "id": "cef37ad6-e0b9-4350-b081-c0419a376444",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Placeholder for iteration-wise results\n",
    "g_iteration_values = []\n",
    "f_iteration_values = []\n",
    "\n",
    "# Number of iterations for each optimization process\n",
    "num_iterations_g = 100\n",
    "num_iterations_f = 100\n",
    "\n",
    "# Initialize the results storage\n",
    "for _ in range(num_iterations_g):\n",
    "    g_iteration_values.append([])\n",
    "\n",
    "for _ in range(num_iterations_f):\n",
    "    f_iteration_values.append([])\n",
    "\n",
    "# Perform optimizations for each initial point\n",
    "\n",
    "for x0 in initial_points_x:\n",
    "    x0_list = [x0]\n",
    "    y0_list = [x0**2]\n",
    "    \n",
    "    # Modified optimization (phi space)\n",
    "    _, g_values = modified_two_point_feedback_optimization(\n",
    "        func = g,\n",
    "        dim = 1,\n",
    "        x0=x0_list,\n",
    "        alpha=0.01,\n",
    "        beta=0.1,\n",
    "        num_iterations=num_iterations_g\n",
    "    )\n",
    "    for i, val in enumerate(g_values):\n",
    "        g_iteration_values[i].append(val)\n",
    "    \n",
    "    # Default two-point feedback optimization (theta space)\n",
    "    _, f_values = two_point_feedback_zeroth_order_optimization(\n",
    "        func=f,\n",
    "        dim=1,\n",
    "        x0=y0_list,\n",
    "        alpha=0.01,\n",
    "        beta=0.1,\n",
    "        num_iterations=num_iterations_f\n",
    "    )\n",
    "    for i, val in enumerate(f_values):\n",
    "        f_iteration_values[i].append(val)\n",
    "\n",
    "# Calculate averages and standard deviations for plotting\n",
    "g_avg = [np.mean(vals) for vals in g_iteration_values]\n",
    "g_std = [np.std(vals) for vals in g_iteration_values]\n",
    "f_avg = [np.mean(vals) for vals in f_iteration_values]\n",
    "f_std = [np.std(vals) for vals in f_iteration_values]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1d6ff960-83e8-442e-b9c7-06a6160f1f0b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "id": "509098a2-e607-4de1-a883-9ee83e1546d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert to NumPy arrays if not already (assuming these variables are defined as lists)\n",
    "g_avg = np.array(g_avg)\n",
    "g_std = np.array(g_std)\n",
    "f_avg = np.array(f_avg)\n",
    "f_std = np.array(f_std)\n",
    "\n",
    "# Assuming num_iterations_g, num_iterations_f, g_avg, g_std, f_avg, f_std are defined\n",
    "\n",
    "# Set the size of the plot\n",
    "plt.figure(figsize=(10, 6), facecolor='white')\n",
    "\n",
    "# Define the iteration range for g and f values\n",
    "iterations_g = range(num_iterations_g)\n",
    "iterations_f = range(num_iterations_f)\n",
    "\n",
    "# Plotting for g_values and f_values across iterations with fill_between\n",
    "plt.plot(iterations_g, g_avg, label=r'$PR(\\phi)$')\n",
    "plt.fill_between(iterations_g, g_avg - g_std, g_avg + g_std, alpha=0.2)\n",
    "\n",
    "plt.plot(iterations_f, f_avg, label=r'$PR(\\theta)$')\n",
    "plt.fill_between(iterations_f, f_avg - f_std, f_avg + f_std, alpha=0.2)\n",
    "\n",
    "# Customize the plot\n",
    "plt.xlabel('Iterations', fontsize=15)\n",
    "plt.ylabel('PR Value', fontsize=15)\n",
    "plt.title(r'PR($\\phi$) vs PR($\\theta$)', fontsize=15, fontweight='bold')\n",
    "\n",
    "# Customizing the x-axis and y-axis tick labels\n",
    "plt.xticks(fontsize=14, fontweight='bold')\n",
    "plt.yticks(fontsize=14, fontweight='bold')\n",
    "\n",
    "# Adding a grid\n",
    "plt.grid(True, which='both', linestyle='--', linewidth=0.5, alpha=0.7)\n",
    "\n",
    "# Adding and customizing the legend\n",
    "legend = plt.legend(frameon=True, fontsize=12)\n",
    "legend.get_frame().set_alpha(0.7)\n",
    "legend.get_frame().set_edgecolor(\"black\")\n",
    "\n",
    "# Save the plot if needed\n",
    "plt.savefig('pr_comparison_test3.png')\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a80fc983-2a13-41ec-b9a2-4187aeb8be60",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c468924b-31d1-4538-b304-f7a58f913758",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d4b00c6f-b404-487c-9b45-1eb05392c580",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fb983c08-db03-4db6-945c-9167639d6559",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "56c9951a-eaf1-414b-933c-8f0a7f2e607a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}