Natural Evolution Strategies.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A bare bones examples of optimizing a black-box function (f) using  \n",
    "Natural Evolution Strategies (NES), where the parameter distribution is a   \n",
    "gaussian of fixed standard deviation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "code from:  https://gist.github.com/karpathy/77fbb6a8dac5395f1b73e7a89300318d  \n",
    "text from:  https://openai.com/blog/evolution-strategies/  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the objective is identical to the one that RL optimizes: the expected reward. However, RL injects noise in the action space and uses backpropagation to compute the parameter updates, while ES injects noise directly in the parameter space. Another way to describe this is that RL is a “guess and check” on actions, while ES is a “guess and check” on parameters. Since we’re injecting noise in the parameters, it is possible to use deterministic policies (and we do, in our experiments). It is also possible to add noise in both actions and parameters to potentially combine the two approaches."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note on supervised learning. It is also important to note that supervised learning problems (e.g. image classification, speech recognition, or most other tasks in the industry), where one can compute the exact gradient of the loss function with backpropagation, are not directly impacted by these findings. For example, in our preliminary experiments we found that using ES to estimate the gradient on the MNIST digit recognition task can be as much as 1,000 times slower than using backpropagation. It is only in RL settings, where one has to estimate the gradient of the expected reward by sampling, where ES becomes competitive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the function we want to optimize\n",
    "def f(w):\n",
    "  # here we would normally:\n",
    "  # ... 1) create a neural network with weights w\n",
    "  # ... 2) run the neural network on the environment for some time\n",
    "  # ... 3) sum up and return the total reward\n",
    "\n",
    "  # but for the purposes of an example, lets try to minimize\n",
    "  # the L2 distance to a specific solution vector. So the highest reward\n",
    "  # we can achieve is 0, when the vector w is exactly equal to solution\n",
    "  reward = -np.sum(np.square(solution - w))\n",
    "  return reward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter 0. w: [ 1.77651471  0.36221492 -0.71565331], solution: [ 0.5  0.1 -0.3], reward: -1.871014\n",
      "iter 20. w: [ 1.58693647  0.32862119 -0.65916721], solution: [ 0.5  0.1 -0.3], reward: -1.362700\n",
      "iter 40. w: [ 1.40984871  0.30371765 -0.59973142], solution: [ 0.5  0.1 -0.3], reward: -0.959164\n",
      "iter 60. w: [ 1.23215604  0.26304805 -0.5451421 ], solution: [ 0.5  0.1 -0.3], reward: -0.622732\n",
      "iter 80. w: [ 1.04559235  0.21477575 -0.48803487], solution: [ 0.5  0.1 -0.3], reward: -0.346202\n",
      "iter 100. w: [ 0.87369119  0.18140093 -0.4303023 ], solution: [ 0.5  0.1 -0.3], reward: -0.163250\n",
      "iter 120. w: [ 0.70832961  0.15398951 -0.36738501], solution: [ 0.5  0.1 -0.3], reward: -0.050857\n",
      "iter 140. w: [ 0.56858087  0.11933484 -0.31472213], solution: [ 0.5  0.1 -0.3], reward: -0.005294\n",
      "iter 160. w: [ 0.51753356  0.10105717 -0.30633002], solution: [ 0.5  0.1 -0.3], reward: -0.000349\n",
      "iter 180. w: [ 0.50212379  0.11118285 -0.31304034], solution: [ 0.5  0.1 -0.3], reward: -0.000300\n",
      "iter 200. w: [ 0.50506783  0.0945389  -0.29733818], solution: [ 0.5  0.1 -0.3], reward: -0.000063\n",
      "iter 220. w: [ 0.498403    0.09013075 -0.29365163], solution: [ 0.5  0.1 -0.3], reward: -0.000140\n",
      "iter 240. w: [ 0.50168288  0.09965659 -0.30263651], solution: [ 0.5  0.1 -0.3], reward: -0.000010\n",
      "iter 260. w: [ 0.50015901  0.10163543 -0.29814195], solution: [ 0.5  0.1 -0.3], reward: -0.000006\n",
      "iter 280. w: [ 0.50070813  0.10133502 -0.30571899], solution: [ 0.5  0.1 -0.3], reward: -0.000035\n"
     ]
    }
   ],
   "source": [
    "# hyperparameters\n",
    "npop = 50 # population size\n",
    "sigma = 0.1 # noise standard deviation\n",
    "alpha = 0.001 # learning rate\n",
    "eps = 1e-9\n",
    "\n",
    "# start the optimization\n",
    "solution = np.array([0.5, 0.1, -0.3])\n",
    "w = np.random.randn(3) # our initial guess is random\n",
    "for i in range(300):\n",
    "\n",
    "  # print current fitness of the most likely parameter setting\n",
    "  if i % 20 == 0:\n",
    "    print('iter %d. w: %s, solution: %s, reward: %f' % \n",
    "          (i, str(w), str(solution), f(w)))\n",
    "\n",
    "  # initialize memory for a population of w's, and their rewards\n",
    "  N = np.random.randn(npop, 3) # samples from a normal distribution N(0,1)\n",
    "  R = np.zeros(npop)\n",
    "  for j in range(npop):\n",
    "    w_try = w + sigma*N[j] # jitter w using gaussian of sigma 0.1\n",
    "    R[j] = f(w_try) # evaluate the jittered version\n",
    "\n",
    "  # standardize the rewards to have a gaussian distribution\n",
    "  A = (R - np.mean(R)) / (np.std(R) + eps)   # add in eps here to prevent division by zero error\n",
    "  # perform the parameter update. The matrix multiply below\n",
    "  # is just an efficient way to sum up all the rows of the noise matrix N,\n",
    "  # where each row N[j] is weighted by A[j]\n",
    "  w = w + alpha/(npop*sigma) * np.dot(N.T, A)\n",
    "\n",
    "# when run, prints:\n",
    "# iter 0. w: [ 1.76405235  0.40015721  0.97873798], solution: [ 0.5  0.1 -0.3], reward: -3.323094\n",
    "# iter 20. w: [ 1.63796944  0.36987244  0.84497941], solution: [ 0.5  0.1 -0.3], reward: -2.678783\n",
    "# iter 40. w: [ 1.50042904  0.33577052  0.70329169], solution: [ 0.5  0.1 -0.3], reward: -2.063040\n",
    "# iter 60. w: [ 1.36438269  0.29247833  0.56990397], solution: [ 0.5  0.1 -0.3], reward: -1.540938\n",
    "# iter 80. w: [ 1.2257328   0.25622233  0.43607161], solution: [ 0.5  0.1 -0.3], reward: -1.092895\n",
    "# iter 100. w: [ 1.08819889  0.22827364  0.30415088], solution: [ 0.5  0.1 -0.3], reward: -0.727430\n",
    "# iter 120. w: [ 0.95675286  0.19282042  0.16682465], solution: [ 0.5  0.1 -0.3], reward: -0.435164\n",
    "# iter 140. w: [ 0.82214521  0.16161165  0.03600742], solution: [ 0.5  0.1 -0.3], reward: -0.220475\n",
    "# iter 160. w: [ 0.70282088  0.12935569 -0.09779598], solution: [ 0.5  0.1 -0.3], reward: -0.082885\n",
    "# iter 180. w: [ 0.58380424  0.11579811 -0.21083135], solution: [ 0.5  0.1 -0.3], reward: -0.015224\n",
    "# iter 200. w: [ 0.52089064  0.09897718 -0.2761225 ], solution: [ 0.5  0.1 -0.3], reward: -0.001008\n",
    "# iter 220. w: [ 0.50861791  0.10220363 -0.29023563], solution: [ 0.5  0.1 -0.3], reward: -0.000174\n",
    "# iter 240. w: [ 0.50428202  0.10834192 -0.29828744], solution: [ 0.5  0.1 -0.3], reward: -0.000091\n",
    "# iter 260. w: [ 0.50147991  0.1044559  -0.30255291], solution: [ 0.5  0.1 -0.3], reward: -0.000029\n",
    "# iter 280. w: [ 0.50208135  0.0986722  -0.29841024], solution: [ 0.5  0.1 -0.3], reward: -0.000009"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Another example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://github.com/karpathy/randomfun/blob/master/es.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.gridspec as gridspec\n",
    "from IPython import display\n",
    "plt.rcParams['image.cmap'] = 'gray'\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "import json\n",
    "import time\n",
    "import numpy as np\n",
    "from random import shuffle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate a toy 2D regression dataset\n",
    "sz = 100\n",
    "X,Y = np.meshgrid(np.linspace(-1,1,sz),np.linspace(-1,1,sz))\n",
    "mux,muy,sigma=0.3,-0.3,4\n",
    "G1 = np.exp(-((X-mux)**2+(Y-muy)**2)/2.0*sigma**2)\n",
    "mux,muy,sigma=-0.3,0.3,2\n",
    "G2 = np.exp(-((X-mux)**2+(Y-muy)**2)/2.0*sigma**2)\n",
    "mux,muy,sigma=0.6,0.6,2\n",
    "G3 = np.exp(-((X-mux)**2+(Y-muy)**2)/2.0*sigma**2)\n",
    "mux,muy,sigma=-0.4,-0.2,3\n",
    "G4 = np.exp(-((X-mux)**2+(Y-muy)**2)/2.0*sigma**2)\n",
    "G = G1 + G2 - G3 - G4\n",
    "fig,ax = plt.subplots()\n",
    "im = ax.imshow(G, vmin=-1, vmax=1, cmap='jet')\n",
    "#plt.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(3)\n",
    "nn = 4 # number of steps to take (and plot horizontally)\n",
    "alpha = 0.03 # learning rate\n",
    "sigma = 3 # standard deviation of the samples around current parameter vector\n",
    "\n",
    "w = np.array([70.0, 60.0]) # start point\n",
    "plt.figure(figsize=(20,5))\n",
    "\n",
    "prevx, prevy = [], []\n",
    "for q in range(nn):\n",
    "    \n",
    "    # draw the optimization landscape\n",
    "    ax1 = plt.subplot(1,nn,q+1)\n",
    "    plt.imshow(G, vmin=-1, vmax=1, cmap='jet')\n",
    "\n",
    "    # draw a population of samples in black\n",
    "    noise = np.random.randn(200, 2)\n",
    "    wp = np.expand_dims(w, 0) + sigma*noise\n",
    "    x,y = zip(*wp)\n",
    "    plt.scatter(x,y,4,'k', edgecolors='face')\n",
    "\n",
    "    # draw the current parameter vector in white\n",
    "    plt.scatter([w[0]],[w[1]],40,'w', edgecolors='face')\n",
    "\n",
    "    # draw estimated gradient as white arrow\n",
    "    R = np.array([G[int(wi[1]), int(wi[0])] for wi in wp])\n",
    "    R -= R.mean()\n",
    "    R /= R.std() # standardize the rewards to be N(0,1) gaussian\n",
    "    g = np.dot(R, noise)\n",
    "    u = alpha * g\n",
    "    plt.arrow(w[0], w[1], u[0], u[1], head_width=3, head_length=5, fc='w', ec='w')\n",
    "    plt.axis('off')\n",
    "    plt.title('iteration %d, reward %.2f' % (q+1, G[int(w[0]), int(w[1])]))\n",
    "    \n",
    "    # draw the history of optimization as a white line\n",
    "    prevx.append(w[0])\n",
    "    prevy.append(w[1])\n",
    "    if len(prevx) > 0:\n",
    "        plt.plot(prevx, prevy, 'wo-')\n",
    "    \n",
    "    w += u\n",
    "    plt.axis('tight')\n",
    "    \n",
    "#plt.savefig('evo.png',bbox_inches='tight',pad_inches=0,dpi=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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