Guided_Evolutionary_Strategies_Demo_TensorFlow2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Copyright 2020 Google LLC.\n",
    "\n",
    "Licensed under the Apache License, Version 2.0 (the \"License\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "# https://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Guided Evolutionary Strategies Demo (using TensorFlow 2)\n",
    "\n",
    "Date: 06/08/2020\n",
    "\n",
    "This is a self-contained notebook that reproduces the toy example in Fig. 1 of the [Guided ES](https://arxiv.org/abs/1806.10230) paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TensorFlow version: 2.2.0\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import tensorflow as tf\n",
    "\n",
    "print(f'TensorFlow version: {tf.__version__}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem setup\n",
    "\n",
    "We test the algorithms on a toy problem where we explicitly add bias and variance to the gradient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate problem data.\n",
    "rs = np.random.RandomState(seed=0)\n",
    "m = 2000  # Number of data points.\n",
    "n = 1000  # Number of variables.\n",
    "\n",
    "A = rs.randn(m, n)\n",
    "b = rs.randn(m, 1)\n",
    "\n",
    "xstar = np.linalg.lstsq(A, b, rcond=None)[0]\n",
    "f_star = (0.5/float(m)) * np.linalg.norm(np.dot(A, xstar) - b) ** 2\n",
    "\n",
    "A = tf.convert_to_tensor(A, dtype=tf.float32)\n",
    "b = tf.convert_to_tensor(b, dtype=tf.float32)\n",
    "\n",
    "# This is a bias vector that will be added to the gradient\n",
    "grad_bias = 1.0 * tf.nn.l2_normalize(tf.convert_to_tensor(rs.randn(n, 1), dtype=tf.float32))\n",
    "\n",
    "@tf.function\n",
    "def loss_and_grad_fun(x):\n",
    "    residual = tf.matmul(A, x) - b\n",
    "    loss = 0.5 * tf.norm(residual) ** 2 / float(m)\n",
    "    \n",
    "    # The 'gradient' that we observe is a noisy, biased version of the true gradient.\n",
    "    # This is meant to mimic scenarios where we only have access to biased gradients.\n",
    "    err = tf.matmul(tf.transpose(A), residual) / float(m)\n",
    "    grad_noise = 1.5 * tf.nn.l2_normalize(tf.random.normal(shape=(n, 1)))\n",
    "    gradient = err + (grad_bias + grad_noise) * tf.norm(err)\n",
    "    \n",
    "    return loss, gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Algorithm 1: Gradient Descent\n",
    "\n",
    "Our first algorithm is gradient descent, applied directly to the biased gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt = tf.keras.optimizers.SGD(5e-3)\n",
    "\n",
    "@tf.function\n",
    "def step_fun(x):\n",
    "    loss, gradient = loss_and_grad_fun(x)\n",
    "    opt.apply_gradients([(gradient, x)])\n",
    "    return loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 15 s, sys: 989 ms, total: 16 s\n",
      "Wall time: 15.7 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "x = tf.Variable(tf.zeros((n, 1)), dtype=tf.float32)\n",
    "\n",
    "fobj = []\n",
    "for _ in range(10000):\n",
    "    fobj.append(step_fun(x))\n",
    "    \n",
    "# Store training curve for plotting later.\n",
    "f_gd = tf.stack(fobj).numpy().copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Algorithm 2: Vanilla Evolutionary Strategies (Vanilla ES)\n",
    "\n",
    "Our next algorithm is vanilla (standard) evolutionary strategies. This is a zeroth-order optimization algorithm, which means that it only uses the function evaluation (and ignores the biased gradients)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hyperparameters for Vanilla ES\n",
    "sigma = 0.1\n",
    "beta = 1.0\n",
    "learning_rate = 0.2\n",
    "\n",
    "# Defines the distribution for sampling parameter perturbations.\n",
    "scale = sigma / np.sqrt(n)\n",
    "def sample():\n",
    "    return scale * tf.random.normal(shape=(n, 1), dtype=tf.float32)\n",
    "\n",
    "opt = tf.keras.optimizers.SGD(learning_rate)\n",
    "\n",
    "@tf.function\n",
    "def step_fun(x):\n",
    "    epsilon = sample()\n",
    "    \n",
    "    # We utilize antithetic (positive and negative) samples.\n",
    "    f_pos, _ = loss_and_grad_fun(x + epsilon)\n",
    "    f_neg, _ = loss_and_grad_fun(x - epsilon)\n",
    "    \n",
    "    # This update is a stochastic finite difference estimate of the true gradient.\n",
    "    update = (beta / (2 * sigma ** 2)) * (f_pos - f_neg) * epsilon\n",
    "    opt.apply_gradients([(update, x)])\n",
    "    \n",
    "    return loss_and_grad_fun(x)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 19.9 s, sys: 1.11 s, total: 21 s\n",
      "Wall time: 19.6 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "x = tf.Variable(tf.zeros((n, 1)), dtype=tf.float32)\n",
    "\n",
    "# Run the optmizer.\n",
    "fobj = []\n",
    "for _ in range(10000):\n",
    "    fobj.append(step_fun(x))\n",
    "\n",
    "# Store training curve for plotting later.\n",
    "f_ves = tf.stack(fobj).numpy().copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Algorithm 3: Guided Evolutionary Strategies (Guided ES)\n",
    "\n",
    "Guided ES is our proposed method. It uses a diagonal plus low-rank covariance matrix for drawing perturbations, where the low-rank subspace is spanned by the available gradient information.\n",
    "\n",
    "This allows it to incorporate the biased gradient information, while still minimizing the true loss function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hyperparameters for Guided ES\n",
    "sigma = 0.1\n",
    "alpha = 0.5\n",
    "beta = 1.0\n",
    "k = 1        # Defines the dimensionality of the low-rank subspace.\n",
    "\n",
    "# Defines parameters of the distribution for sampling perturbations.\n",
    "a = sigma * np.sqrt(alpha / float(n))\n",
    "c = sigma * np.sqrt((1. - alpha) / float(k))\n",
    "\n",
    "def sample(gradient_subspace):\n",
    "    epsilon_full = tf.random.normal(shape=(n, 1), dtype=tf.float32)\n",
    "    epsilon_subspace = tf.random.normal(shape=(k, 1), dtype=tf.float32)\n",
    "    \n",
    "    Q, _ = tf.linalg.qr(gradient_subspace)\n",
    "    epsilon = a * epsilon_full + c * tf.matmul(Q, epsilon_subspace)\n",
    "    \n",
    "    return epsilon\n",
    "\n",
    "opt = tf.keras.optimizers.SGD(0.2)\n",
    "\n",
    "@tf.function\n",
    "def step_fun(x):\n",
    "    \n",
    "    # We pass the gradient to our sampling function.\n",
    "    loss, gradient = loss_and_grad_fun(x)\n",
    "    epsilon = sample(gradient)\n",
    "    \n",
    "    # We utilize antithetic (positive and negative) samples.\n",
    "    f_pos, _ = loss_and_grad_fun(x + epsilon)\n",
    "    f_neg, _ = loss_and_grad_fun(x - epsilon)\n",
    "    \n",
    "    # This update is a stochastic finite difference estimate of the true gradient.\n",
    "    update = (beta / (2 * sigma ** 2)) * (f_pos - f_neg) * epsilon\n",
    "    opt.apply_gradients([(update, x)])\n",
    "\n",
    "    return loss_and_grad_fun(x)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 32.1 s, sys: 1.58 s, total: 33.7 s\n",
      "Wall time: 28.4 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "x = tf.Variable(tf.zeros((n, 1)), dtype=tf.float32)\n",
    "\n",
    "# Run the optmizer.\n",
    "fobj = []\n",
    "for _ in range(10000):\n",
    "    fobj.append(step_fun(x))\n",
    "\n",
    "# Store training curve for plotting later.\n",
    "f_ges = tf.stack(fobj).numpy().copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "COLORS = {'ges': '#7570b3', 'ves': '#1b9e77', 'sgdm': '#d95f02'}\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(f_ves - f_star, color=COLORS['ves'], label='Vanilla ES')\n",
    "plt.plot(f_gd - f_star, color=COLORS['sgdm'], label='Grad. Descent')\n",
    "plt.plot(f_ges - f_star, color=COLORS['ges'], label='Guided ES')\n",
    "plt.legend(fontsize=16, loc=0)\n",
    "plt.xlabel('Iteration', fontsize=16)\n",
    "plt.ylabel('Loss', fontsize=16)\n",
    "plt.title('Demo of Guided Evolutionary Strategies', fontsize=16);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}