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October 15, 2017 21:43
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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import os\n", | |
"import sys\n", | |
"import json\n", | |
"import time\n", | |
"import numpy as np\n", | |
"from random import shuffle\n", | |
"import matplotlib.pyplot as plt\n", | |
"import matplotlib.gridspec as gridspec\n", | |
"from IPython import display\n", | |
"from IPython.display import HTML\n", | |
"from matplotlib import animation, rc\n", | |
"\n", | |
"plt.rcParams['image.cmap'] = 'gray'\n", | |
"plt.rcParams['image.interpolation'] = 'nearest'\n", | |
"rc('animation', html='html5')\n", | |
"\n", | |
"%matplotlib inline" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"scrolled": true | |
}, | |
"outputs": [], | |
"source": [ | |
"size = 400\n", | |
"dim_x, dim_y = np.meshgrid(np.linspace(-1.0, 1.0, size),\n", | |
" np.linspace(-1.0, 1.0, size))\n", | |
"\n", | |
"def g(dim_x, dim_y, mu_x, mu_y, sigma):\n", | |
" a = (dim_x - mu_x)**2\n", | |
" b = (dim_y - mu_y)**2\n", | |
" return np.exp(-(a + b) / 2.0 * sigma**2)\n", | |
"\n", | |
"g1 = g(dim_x, dim_y, 0.3, -0.4, 2.0)\n", | |
"g2 = g(dim_x, dim_y, -0.3, 0.6, 3.0)\n", | |
"g3 = g(dim_x, dim_y, 0.6, 0.6, 2.0)\n", | |
"g4 = g(dim_x, dim_y, -0.3, -0.2, 2.0)\n", | |
"\n", | |
"gs = g1 + g2 - g3 - g4\n", | |
"fig, ax = plt.subplots()\n", | |
"\n", | |
"im = ax.imshow(gs, vmin=-1, vmax=1, cmap='jet')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def init():\n", | |
" global position, start_position\n", | |
" position = start_position\n", | |
" del prev_x[:]\n", | |
" del prev_y[:]\n", | |
" \n", | |
"\n", | |
"def run(it):\n", | |
" global position, size\n", | |
" plt.cla()\n", | |
" plt.imshow(gs, vmin=-1, vmax=1, cmap='jet')\n", | |
" \n", | |
" noise = np.random.randn(population_size, 2)\n", | |
" noise_positions = np.expand_dims(position, 0) + sigma * noise\n", | |
" noise_positions = np.clip(noise_positions, 0, size - 1)\n", | |
" x, y = zip(*noise_positions)\n", | |
" \n", | |
" plt.scatter(x, y, 1, 'k', edgecolors='face')\n", | |
" plt.scatter(position[0], position[1], 20, 'w', edgecolors='face')\n", | |
" \n", | |
" rewards = np.array([gs[int(pos[0]), int(pos[1])] for pos in noise_positions])\n", | |
" rewards -= rewards.mean()\n", | |
" rewards /= rewards.std()\n", | |
" \n", | |
" gradient = np.dot(rewards, noise)\n", | |
" update = learning_rate * gradient\n", | |
" \n", | |
" plt.arrow(position[0], position[1], update[0], update[1], head_width=3, head_length=5, fc='w', ec='w')\n", | |
" \n", | |
" plt.axis('off')\n", | |
" plt.title('iteration %d, reward %.2f' % ((it + 1), gs[int(position[0]), int(position[1])]))\n", | |
" \n", | |
" prev_x.append(position[0])\n", | |
" prev_y.append(position[1])\n", | |
" if len(prev_x) > 0:\n", | |
" plt.plot(prev_x, prev_y, 'wo-')\n", | |
" \n", | |
" position += update \n", | |
" position = np.clip(position, 0, size - 1)\n", | |
" plt.axis('tight')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Sigma: standard deviation of the samples around current parameter vector\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"scrolled": false | |
}, | |
"outputs": [], | |
"source": [ | |
"iterations = 100\n", | |
"learning_rate = 0.01\n", | |
"sigma = 20\n", | |
"seed = 8\n", | |
"population_size = 300\n", | |
"start_position = np.array([size / 2, size / 2])\n", | |
"\n", | |
"np.random.seed(seed)\n", | |
"fig = plt.figure(figsize=(10, 10))\n", | |
"\n", | |
"prev_x, prev_y = [], [] \n", | |
"position = None\n", | |
" \n", | |
"anim = animation.FuncAnimation(fig, run, frames=iterations, init_func=init)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 54, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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"\">\n", | |
" Your browser does not support the video tag.\n", | |
"</video>" | |
], | |
"text/plain": [ | |
"<IPython.core.display.HTML object>" | |
] | |
}, | |
"execution_count": 54, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"HTML(anim.to_html5_video())" | |
] | |
} | |
], | |
"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": "3.5.2" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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