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Last active December 18, 2015 08:09
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OptimisationPlayground
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{
"metadata": {
"name": "OptimisationPlayground"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Objective\n",
"\n",
"Finding stationary points of a continuous and derivable function $f$. [Iterative algorithms](http://en.wikipedia.org/wiki/Optimization_algorithm#Iterative_methods) for problems without analytical known solutions, choosing from a starting point $a$ a direction $b$ towards a local minimum Local minima $x$ of $f$ with $\\nabla f(x) = 0$ and $H f(x) > 0$.\n",
"\n",
"A quick read through wikipedia pages:\n",
"\n",
"- The simple [gradient descent](http://en.wikipedia.org/wiki/Gradient_descent) chooses at each step the steepest descent direction, i.e. a step proportionnal proportionnal to the negative of the gradient $ b = - \\gamma \\nabla f$;\n",
"\n",
"- [Newton's_method](http://en.wikipedia.org/wiki/Newton%27s_method_in_optimization) is a family of algorithm based on local quadratic approximation of $f$ through Taylor's expansion (i.e. calculation of the Gradient $\\nabla f$ and the [Hessian](http://en.wikipedia.org/wiki/Hessian_matrix) $H f$);\n",
"\n",
"- [Quasi-Newton's method](http://en.wikipedia.org/wiki/Quasi-Newton_method) do not directly inverse $H f$ but use less-costly approximation. These methods can be seen as generalisation of the [secant method](http://en.wikipedia.org/wiki/Secant_method). The most popular methods include the [BFGS_method](http://en.wikipedia.org/wiki/BFGS_method), the DFP method, ...;\n",
"\n",
"- The [Levenberg\u2013Marquardt algorithm (LMA)](http://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm) optimize over a space of parameters of a function for least squares curve fitting. It uses a trust region approach which interpolates between the Gauss\u2013Newton algorithm and the method of gradient descent. The trust region has a form analogous to a $L_2$ penalty.\n",
"\n",
"- The [Nelder\u2013Mead_method](http://en.wikipedia.org/wiki/Nelder\u2013Mead_method) is heuristical method for $f$ which derivatives may not be known. It relies on the concept of a simplex, and replaces worst test positions by better estimation...\n",
"\n",
"- [Conjugate_gradient_method](http://en.wikipedia.org/wiki/Conjugate_gradient_method)\n",
"\n",
"### For global maxima :\n",
" - [Stochastic gradient descent](http://en.wikipedia.org/wiki/Stochastic_gradient_descent)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2D parabolic curve\n",
"\n",
"$$ X = (x,y) \\in \\mathbb{R}^2$$\n",
"\n",
"\n",
"$$f(X) = f(x,y) = A X^T X + B X + c$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Could use polyval with sum_ij c_ij * x^i * x^j\n",
"from numpy.polynomial import polynomial\n",
"\n",
"polynomial.polyval2d(.5, -.5, [[1, 1], [0, 1]])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 1,
"text": [
"0.25"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"x_lims = [-1, 1]\n",
"y_lims = [-1, 1]\n",
"\n",
"x_grid = np.linspace(*x_lims, num=1000)\n",
"y_grid = np.linspace(*y_lims, num=1000)\n",
"x_mesh, y_mesh = np.meshgrid(x_grid, y_grid)\n",
"\n",
"a_x, a_y, a_xy = [.005, .005, - .005]\n",
"b_x, b_y = [-.005, .002]\n",
"def goal_function(x, y):\n",
" return a_x * x * x + a_y * y * y + a_xy * x * y + b_x * x + b_y * y\n",
"\n",
"f_mesh = goal_function(x_mesh, y_mesh)\n",
"\n",
"import matplotlib.pyplot as plt\n",
"fig = plt.figure(figsize=(6,6))\n",
"plt.contour(x_grid, y_grid, f_mesh, 25);\n",
"\n",
"x_start, y_start = -0.95, 0\n",
"plt.plot(x_start, y_start, ls='-', marker='x', color='k', ms=7, mew=3);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
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wgSqqCsNegoGP6Vflln+t2Sy7dbpAygs147W9Bh2slh3waz0oNfDA9x2C9Mbg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\n8p//PEy1auM5diyCGjUstsn7GxnwycMWgHaouRLkOfO4V4u0ViNM2V2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chG5MjJOPPjrE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\nH8eP59h6K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2dkiT5AsmDCE/CXUNFzSyM9vw+QWgyhMp/nAg14K3g25OIMOguVv9cOg1u3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\nR0enjKEbfh0dHZ0yxv8BO3UteJITlLAAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ \\nabla f(x,y) \\approx \\Big( \\frac{f(x + \\Delta x, y)}{\\Delta x}, \\frac{f(x , y + \\Delta y)}{\\Delta y} \\Big)^T $$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"h = .01\n",
"\n",
"descent_xys = np.repeat(np.nan, 2 * 100).reshape((2, 100))\n",
"\n",
"i = 0\n",
"descent_xys[:,i] = x_start, y_start"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"f_x_y = goal_function(*descent_xys[:,i])\n",
"f_xh_y = goal_function(descent_xys[0,i]+h, descent_xys[1,i])\n",
"f_x_yh = goal_function(descent_xys[0,i], descent_xys[1,i]+h)\n",
"\n",
"print 'i={} -> i+1'.format(i)\n",
"i += 1\n",
"\n",
"grad_i = np.array([(f_xh_y-f_x_y)/h, (f_x_yh-f_x_y)/h])\n",
"gamma = 5 * i \n",
"descent_xys[:,i] = descent_xys[:,i-1] - gamma * grad_i\n",
"\n",
"print grad_i, np.linalg.norm(grad_i), gamma\n",
"\n",
"fig = plt.figure(figsize=(6,6))\n",
"plt.plot(*descent_xys, ls='-', marker='x', color='k', ms=7, mew=3)\n",
"plt.contour(x_grid, y_grid, f_mesh, 25);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"i=14 -> i+1\n",
"[-0.00018738 -0.00018738] 0.000265000050516 75\n"
]
},
{
"output_type": "display_data",
"png": 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wgSqqCsNegoGP6Vflln+t2Sy7dbpAygs147W9Bh2slh3waz0oNfDA9x2C9Mbg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\nkoWRXHOKuFylX4+KpiyeZaU/v8oG7AAuTvBiZ9l70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}
],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Back-log\n",
"\n",
"- Combine the descent with $\\gamma$ optimised through a [linear search](http://en.wikipedia.org/wiki/Linear_search) method like the [secant's method](http://en.wikipedia.org/wiki/Secant_method), which is a first-order finite approximation of Newton's method.\n",
"\n",
"- Show improvements with [Netwon's method](http://en.wikipedia.org/wiki/Newton's_method_in_optimization) based on second-order Taylor approximation. Using forward Difference approximation of $H \\in \\mathcal{M}_{2,2}$ based on gradient calls as documented [here](http://www.okstate.edu/sas/v8/sashtml/ormp/chap5/sect28.htm).\n",
"\n",
"- Enter here LMA methods which summarizes all\n"
]
}
],
"metadata": {}
}
]
}
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