tutorial/01.BasicTutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 01. Basic Tutorial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial, you can learn how to:\n",
    "\n",
    "* Define Search Space\n",
    "* Optimize Objective Function\n",
    "\n",
    "This tutorial describes how to optimize Hyperparameters using HyperOpt without having a mathematical understanding of any algorithm implemented in HyperOpt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import HyperOpt Library\n",
    "from hyperopt import tpe, hp, fmin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Declares a purpose function to optimize. In this tutorial, we will optimize a simple function called `objective`, which is a simple quadratic function.\n",
    "\n",
    "$$ y = (x-3)^2 + 2 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "objective = lambda x: (x-3)**2 + 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's visualize this objective function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x = np.linspace(-10, 10, 100)\n",
    "y = objective(x)\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are trying to optimize the objective function by changing the HyperParameter $x$. That's why we will declare a search space for $x$. The functions related to the search space are implemented in `hyperopt.hp`. The list is as follows.\n",
    "\n",
    "* `hp.randint(label, upper)` or `hp.randint(label, low, high)`\n",
    "* `hp.uniform(label, low, high)`\n",
    "* `hp.loguniform(label, low, high)`    \n",
    "* `hp.normal(label, mu, sigma)`\n",
    "* `hp.lognormal(label, mu, sigma)`\n",
    "* `hp.quniform(label, low, high, q)`\n",
    "* `hp.qloguniform(label, low, high, q)`\n",
    "* `hp.qnormal(label, mu, sigma, q)`\n",
    "* `hp.qlognormal(label, mu, sigma, q)`\n",
    "* `hp.choice(label, list)`\n",
    "* `hp.pchoice(label, p_list)` with `p_list` as a list of `(probability, option)` pairs\n",
    "* `hp.uniformint(label, low, high, q)` or `hp.uniformint(label, low, high)` since `q = 1.0`\n",
    "\n",
    "We will use the most basic `hp.uniform` in this tutorial.\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the search space of x between -10 and 10.\n",
    "space = hp.uniform('x', -10, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, there's only one last step left. So far, we have defined a function of purpose, and we have defined a search space for $x$. Now we can search through the search space $x$ and find the value of $x$ that can optimize the objective function. HyperOpt performs it using `fmin`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:05<00:00, 168.66trial/s, best loss: 2.0000156172178776]\n",
      "{'x': 3.0039518625833104}\n"
     ]
    }
   ],
   "source": [
    "best = fmin(\n",
    "    fn=objective, # Objective Function to optimize\n",
    "    space=space, # Hyperparameter's Search Space\n",
    "    algo=tpe.suggest, # Optimization algorithm\n",
    "    max_evals=1000 # Number of optimization attempts\n",
    ")\n",
    "print(best)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimal $x$ value found by HyperOpt is approximately 3.0. This is very close to a solution of $y=(x-3)^2+2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(x, y)\n",
    "plt.scatter(best['x'], objective(best['x']), color='red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using `space=\"annotated\"`\n",
    "\n",
    "Starting on release 0.2.6, it is allowed to declare the space within the function using type annotations. This saves one step and makes prototyping and space tuning faster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def objective(\n",
    "    x: hp.uniform('x', -10, 10)  # Declare space as typed\n",
    "):\n",
    "    return (x-3)**2 + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:05<00:00, 169.21trial/s, best loss: 2.0000028071024434]\n",
      "{'x': 3.001675440969827}\n"
     ]
    }
   ],
   "source": [
    "best = fmin(\n",
    "    fn=objective, # Objective Function to optimize\n",
    "    space=\"annotated\", # Hyperparameter's Search Space now is declared on objective\n",
    "    algo=tpe.suggest, # Optimization algorithm\n",
    "    max_evals=1000 # Number of optimization attempts\n",
    ")\n",
    "print(best)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(x, y)\n",
    "plt.scatter(best['x'], objective(best['x']), color='red')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}