GradientDescent.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "292310b6-3bd5-43ac-8758-8422e9d62515",
   "metadata": {},
   "source": [
    "# Welcome to this notebook on Gradient Descent"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8658554-ec89-4453-8a38-f5af9f456b57",
   "metadata": {
    "tags": []
   },
   "source": [
    "## What is gradient descent?\n",
    "Gradient descent is an iterative optimisation algorithm that can be used to find a minimum or maximum of a function $f(\\boldsymbol{\\theta})$. At each iteration, it takes a step in the direction of the gradient $\\nabla f(\\boldsymbol{\\theta})$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fafdaee-d8ca-488d-bb94-1311d6dc7048",
   "metadata": {
    "tags": []
   },
   "source": [
    "## How does gradient descent work?\n",
    "The gradient descent algorithm is as follows:\n",
    "\n",
    "___\n",
    "**Start**: Choose starting value $\\theta_0$, learning rate $\\epsilon$ and take $i = 0$.\n",
    "___\n",
    "**Algorithm**:\n",
    "1) Calculate $\\nabla f(\\theta_i)$.\n",
    "2) Update $\\theta_{i+1} = \\theta_{i} - \\epsilon \\nabla f(\\theta_i)$.\n",
    "3) (a) stop if $i$ large or $|\\theta_{i+1}-\\theta_{i}|$ small enough.  \n",
    "   (b) else: update $i$ to $i+1$ and go back to (1).\n",
    "___\n",
    "\n",
    "In the implementation below, you can perform an one-dimensional gradient descent and/or ascent, in which case $\\nabla f(\\theta_i) = f'(\\theta_i)$.\n",
    "\n",
    "You can also experiment with what happens if stochastic noise is added to the gradient. This is interesting, as in (most) practical situations the true gradient is unkown, and you may only be able to use noisy measurements of the gradient.\n",
    "\n",
    "You can also experiment with the difference between a fixed learning rate $\\epsilon$ and a decreasing learning rate according to $\\epsilon = \\frac{1}{i+1}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "043d8595-13d2-49ed-8910-ddc87df002d9",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Try gradient descent yourself and see what happens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "34503ae8-660d-44fb-a889-078787f9bbae",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "63bfcd10-c44b-4278-b476-c17ed5738f46",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Fill in the objective function you would like to use:\n",
    "def objective_f(theta):\n",
    "    return np.power(theta, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "608e6734-aafa-4cb6-9d56-d97164797a88",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Fill in the gradient of the objective function:\n",
    "def gradient_f(theta, STOCHASTIC, MU, SIGMA):\n",
    "    \n",
    "    function = 2*theta\n",
    "    \n",
    "    if STOCHASTIC:\n",
    "        function = function + add_noise(MU, SIGMA)\n",
    "        \n",
    "    return function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fdf26a33-f9b8-49e1-85f6-fa1c193f2552",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Adds normally distributed noise to the gradient. \n",
    "def add_noise(MU, SIGMA):\n",
    "    return np.random.normal(MU, SIGMA, size=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e6c41904-5385-47df-bc95-8b7a177daec5",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Fill in the number of iterations you would like to run gradient descent.\n",
    "NR_ITERATIONS = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0ce08eee-68bc-44e6-9c31-d11099d91cbf",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Do you want to use decreasing or fixed epsilon?\n",
    "EPSILON_TYPE = 'fixed' #'fixed' or 'decreasing'\n",
    "# Fill in the value for epsilon. The decreasing epsilon uses the form EPSILON_VALUE/(i+1).\n",
    "EPSILON_VALUE = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f63d053e-b4f7-462c-af2d-c095d4d78625",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Fill in the starting value for the optimisation:\n",
    "THETA_0 = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fbaa6f9e-02ab-4be0-bd8d-bd1312651af4",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Do you want to do maximization or minimization?\n",
    "OPTIMIZATION_TYPE = 'minimization' #or 'maximization' b##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "99d862e9-30aa-43c4-a092-25f10bb30d1f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Do you want to add stochasticity?\n",
    "STOCHASTIC = False #False or True\n",
    "MU = 0 # mu parameter of the normal distribution for the noise.\n",
    "SIGMA = 1 # sigma parameter of the normal distribution for the noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3c5eb818-357e-4ff4-a56a-d7c123c14b6c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# The gradient descent algorithm\n",
    "def gradient_descent(THETA_0, EPSILON_TYPE, EPSILON_VALUE, NR_ITERATIONS, STOCHATIC, MU, SIGMA):\n",
    "    thetas = np.zeros(NR_ITERATIONS+1)\n",
    "    thetas[0] = THETA_0\n",
    "    \n",
    "    for i in range(NR_ITERATIONS):\n",
    "        if EPSILON_TYPE == 'fixed':\n",
    "            if OPTIMIZATION_TYPE == 'minimization':\n",
    "                thetas[i+1] = thetas[i] - EPSILON_VALUE * gradient_f(thetas[i], STOCHASTIC, MU, SIGMA)\n",
    "            if OPTIMIZATION_TYPE == 'maximization':\n",
    "                thetas[i+1] = thetas[i] + EPSILON_VALUE * gradient_f(thetas[i], STOCHASTIC, MU, SIGMA)\n",
    "        if EPSILON_TYPE == 'decreasing':\n",
    "            if OPTIMIZATION_TYPE == 'minimization':\n",
    "                thetas[i+1] = thetas[i] - EPSILON_VALUE/(i+1) * gradient_f(thetas[i], MU, STOCHASTIC, SIGMA)\n",
    "            if OPTIMIZATION_TYPE == 'maximization':\n",
    "                thetas[i+1] = thetas[i] + EPSILON_VALUE/(i+1) * gradient_f(thetas[i], MU, STOCHASTIC, SIGMA)\n",
    "        \n",
    "    return thetas    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ead5a4ba-046d-40fe-9c5e-1947af97c14c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Plot the iterates and objective values during the optimisation\n",
    "def plot_iterate_and_objective(thetas):\n",
    "    #Calculate the objective value at each iterate\n",
    "    objective_values = objective_f(thetas)\n",
    "    \n",
    "    fig, axs = plt.subplots(1,2, figsize=(10,5))\n",
    "\n",
    "    # Plot the iterate\n",
    "    axs[0].plot(thetas, color=\"darkblue\")\n",
    "    axs[0].set_xlabel(\"Iteration\")\n",
    "    axs[0].set_ylabel(r\"$\\theta_n$\")\n",
    "    axs[0].set_title(r\"$\\theta_n$\")\n",
    "        \n",
    "    # Plot the objective values\n",
    "    axs[1].plot(objective_values, color=\"darkblue\")\n",
    "    axs[1].set_xlabel(\"Iteration\")\n",
    "    axs[1].set_ylabel(r\"f($\\theta_n$)\")\n",
    "    axs[1].set_title(r\"f($\\theta_n$)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c3bc1ded-9220-4fc3-9b72-160853ee68c9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run gradient descent and plot the optimisation.\n",
    "thetas = gradient_descent(THETA_0, EPSILON_TYPE, EPSILON_VALUE, NR_ITERATIONS, STOCHASTIC, MU, SIGMA)\n",
    "plot_iterate_and_objective(thetas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "067f9a17-2022-4185-b5dc-7ba8a7a69b62",
   "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": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}