{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 2. Linesearch\n", "For this training course we'll be using the optimization routines in SciPy." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.optimize as opt\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also need to define a callback function so that we can plot the optimization steps." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def callback(x):\n", " global xprev\n", " plt.plot([xprev[0],x[0]],[xprev[1],x[1]],'b.-')\n", " xprev = x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.1 Naive Linesearch Methods\n", "Consider the quadratic optimization problem\n", "\n", "$\n", "\\begin{align}\n", "\\min_{x} f(x) = \\frac{1}{2}(a x_1^2 + x_2^2)\n", "\\end{align}\n", "$\n", "\n", "for some $a >0$.\n", "\n", "The gradient for this problem is\n", "\n", "$\n", "\\begin{align}\n", "\\nabla f(x) = \n", "\\begin{pmatrix}\n", "a x_1 \\\\\n", "x_2\n", "\\end{pmatrix}\n", "\\end{align}\n", "$\n", "\n", "and thus $x^* = 0$ is the stationary point.\n", "\n", "The Hessian for this problem is\n", "\n", "$\n", "\\begin{align}\n", "\\nabla^2 f(x) = \n", "\\begin{pmatrix}\n", "a & 0 \\\\\n", "0 & 1\n", "\\end{pmatrix} \n", "\\succ 0\n", "\\end{align}\n", "$\n", "\n", "and hence (as $a >0$) the problem is convex, so $x^* = 0$ is the unique global minimizer." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1.1 Steepest Descent\n", "Recall that steepest descent proceeds as a step of the form\n", "\n", "$\n", "\\begin{align}\n", "x^{k+1} = x^k + \\alpha^k p^k\n", "\\end{align}\n", "$\n", "\n", "along the steepest descent direction \n", "\n", "$\n", "\\begin{align}\n", "p^k = -\\nabla f(x^k)\n", "\\end{align}\n", "$ \n", "\n", "with step-size $\\alpha^k$ obtained by linesearch. For convex quadratics, we have an explicit formula for exact linesearch:\n", "\n", "$\n", "\\begin{align}\n", "\\alpha^k = -\\frac{(p^k)^T \\nabla f(x^k)}{(p^k)^T\\nabla^2f(x^k)p^k} = \\frac{\\nabla f(x^k)^T\\nabla f(x^k)}{\\nabla f(x^k)^T \\nabla^2 f(x^k) \\nabla f(x^k)} = \\frac{a^2 (x_1^k)^2 + (x_2^k)^2}{a^3 (x_1^k)^2 + (x_2^k)^2}\n", "\\end{align}\n", "$\n", "\n", "for our specific quadratic objective function $f(x) = 0.5(a x_1^2 + x_2^2)$ defined above." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Textbook steepest descent method with exact linesearch for 0.5(ax_1^2+x_2^2)\n", "# fun - objective function \n", "# x0 - starting point\n", "# jac - objective function gradient\n", "# tol - tolerance for termination\n", "# callback - callback function (for plotting)\n", "def steepest_descent(fun, x0, args=(), jac=None, tol=1e-1, callback=None, **options):\n", " \n", " x = x0\n", " it = 0\n", " while np.linalg.norm(jac(x)) > tol: # first-order optimality (zero gradient)\n", " alpha = ((a**2)*x[0]**2 + x[1]**2)/((a**3)*x[0]**2 + x[1]**2) # exact linesearch for 0.5(ax_1^2+x_2^2)\n", " x = x + alpha*(-jac(x)) # steepest descent iteration\n", "\n", " if callback is not None: # callback function (for plotting)\n", " callback(x)\n", " \n", " it += 1 # number of iterations\n", " \n", " return opt.OptimizeResult(x=x, fun=fun(x), jac=jac(x), nit=it, success=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Coding Task:\n", "Now apply the steepest descent method starting from $x^0 = (1,a)$ to solve the above problem for various values of $a$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 0.002414648411261648\n", " jac: array([-0.06625911, 0.06625911])\n", " nit: 25\n", " success: True\n", " x: array([-0.00662591, 0.06625911])\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Scaling parameter\n", "a = 10\n", "\n", "# Initial guess\n", "x0 = np.array([1,a])\n", "\n", "# Objective function and gradient\n", "fun = lambda x: 0.5*(a*x[0]**2+x[1]**2)\n", "jac = lambda x: np.array([a*x[0],x[1]])\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-1,1.5)\n", "Y = np.linspace(-a,a+1)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "\n", "# Call steepest descent via scipy\n", "xprev = x0 # for plotting\n", "res = opt.minimize(fun, x0, method=steepest_descent, jac=jac, tol=1e-1, callback=callback)\n", "\n", "# Print results and show plot\n", "print(res)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is going on here? Steepest descent is sensitive to problem scaling: one can show that each iterate is\n", "\n", "$\n", "\\begin{align}\n", "x^k = \n", "\\left(\n", "\\frac{a-1}{a+1}\n", "\\right)^k\n", "\\begin{pmatrix}\n", "(-1)^k \\\\\n", "a\n", "\\end{pmatrix}\n", "\\end{align}\n", "$\n", "\n", "and thus the iterates jump around. Moreover since \n", "\n", "$\n", "\\begin{align}\n", "\\frac{\\lVert x^{k+1} - x^* \\rVert}{\\lVert x^k - x^* \\rVert} = \\frac{\\lVert x^{k+1} - 0 \\rVert}{\\lVert x^k - 0 \\rVert} = \\left| \\frac{a-1}{a+1} \\right| < 1\n", "\\end{align}\n", "$\n", "\n", "the convergence is linear with rate $|(a-1)/(a+1)|$ and the closer to $1$ this is (the larger $a$ is) the more iterations will be needed to converge. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1.2 (Damped) Newton's Method\n", "Recall that (damped) Newton's method proceeds as a step of the form\n", "\n", "$\n", "\\begin{align}\n", "x^{k+1} = x^k + \\alpha^k p^k\n", "\\end{align}\n", "$\n", "\n", "along the Newton direction $p^k$ which solves\n", "\n", "$\n", "\\begin{align}\n", "\\nabla^2 f(x^k) \\, p^k = -\\nabla f(x^k)\n", "\\end{align}\n", "$ \n", "\n", "with step-size $\\alpha^k$ obtained by linesearch. For convex quadratics, we have an explicit formula for exact linesearch:\n", "\n", "$\n", "\\begin{align}\n", "\\alpha^k = -\\frac{(p^k)^T \\nabla f(x^k)}{(p^k)^T\\nabla^2f(x^k)p^k} = \\frac{\\left(\\nabla^2 f(x^k)^{-1}\\nabla f(x^k)\\right)^T\\nabla f(x^k)}{\\left(\\nabla^2 f(x^k)^{-1}\\nabla f(x^k)\\right)^T \\nabla^2 f(x^k) \\nabla^2 f(x^k)^{-1}\\nabla f(x^k)} = \\, 1\n", "\\end{align}\n", "$\n", "\n", "for any convex quadratic." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Textbook (damped) Newton method with exact linesearch for for convex quadratics\n", "# fun - objective function \n", "# x0 - starting point\n", "# jac - objective function gradient\n", "# hess - objective function Hessian\n", "# tol - tolerance for termination\n", "# callback - callback function (for plotting)\n", "def newton(fun, x0, args=(), jac=None, hess=None, tol=1e-1, callback=None, **options):\n", " \n", " x = x0\n", " it = 0\n", " while np.linalg.norm(jac(x)) > tol: # first-order optimality (zero gradient)\n", " alpha = 1 # exact linesearch for convex quadratics\n", " x = x + alpha*np.linalg.solve(hess(x),-jac(x)) # Newton iteration\n", "\n", " if callback is not None: # callback function (for plotting)\n", " callback(x)\n", " \n", " it += 1 # number of iterations\n", " \n", " return opt.OptimizeResult(x=x, fun=fun(x), jac=jac(x), hess=hess(x), nit=it, success=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Coding Task: \n", "Now apply Newton's method starting from $x^0 = (1,a)$ to solve the above problem for various values of $a$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 0.0\n", " hess: array([[10, 0],\n", " [ 0, 1]])\n", " jac: array([0., 0.])\n", " nit: 1\n", " success: True\n", " x: array([0., 0.])\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Scaling parameter\n", "a = 10\n", "\n", "# Initial guess\n", "x0 = np.array([1,a])\n", "\n", "# Objective function, gradient and Hessian\n", "fun = lambda x: 0.5*(a*x[0]**2+x[1]**2)\n", "jac = lambda x: np.array([a*x[0],x[1]])\n", "hess = lambda x: np.array([[a,0],[0,1]])\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-1,1.5)\n", "Y = np.linspace(-a,a+1)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "\n", "# Call Newton's method via scipy\n", "xprev = x0 # for plotting\n", "res = opt.minimize(fun, x0, method=newton, jac=jac, hess=hess, tol=1e-1, callback=callback)\n", "\n", "# Print results and show plot\n", "print(res)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is going on here? Newton's method is not sensitive to problem scaling: the first iterate is\n", "\n", "$\n", "\\begin{align}\n", "x^1 = x^0 - \\nabla^2 f(x^0)^{-1}\\nabla f(x^0) = x^0 - \n", "\\begin{pmatrix}\n", "1/a & 0 \\\\\n", "0 & 1\n", "\\end{pmatrix}\n", "\\begin{pmatrix}\n", "a x_1^0 \\\\\n", "x_2^0\n", "\\end{pmatrix}\n", "= x^0 - x^0 = 0 = x^*\n", "\\end{align}\n", "$\n", "\n", "and thus we converge in one step. Moreover, consider the general convex quadratic\n", "\n", "$\n", "\\begin{align}\n", "f(x) = \\frac{1}{2}x^TAx + b^Tx\n", "\\end{align}\n", "$\n", "\n", "with $A \\succ 0$, then (solving $\\nabla f(x) = 0$) we get that $x^* = -A^{-1}b$ and \n", "\n", "$\n", "\\begin{align}\n", "x^1 = x^0 - \\nabla^2 f(x^0)^{-1}\\nabla f(x^0) = x^0 - A^{-1}(Ax^0 + b) = -A^{-1}b = x^*\n", "\\end{align}\n", "$\n", "\n", "therefore Newton's method converges in one step for any convex quadratic! " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1.3 Conjugate Gradient Method\n", "Recall that for a general convex quadratic ($A \\succ 0$)\n", "\n", "$\n", "\\begin{align}\n", "f(x) = \\frac{1}{2}x^TAx + b^Tx\n", "\\end{align}\n", "$\n", "\n", "the conjugate gradient method proceeds as steps of the form\n", "\n", "$\n", "\\begin{align}\n", "x^{k+1} = x^k + \\alpha^k p^k\n", "\\end{align}\n", "$\n", "\n", "along the conjugate directions \n", "\n", "$\n", "\\begin{align}\n", "p^k = -\\nabla f(x^k) + \\beta^k p^{k-1}\n", "\\end{align}\n", "$ \n", "\n", "where $\\beta^k$ is chosen to ensure $A$-conjugacy of the directions\n", "\n", "$\n", "\\begin{align}\n", "\\beta_k = \\frac{\\nabla f(x^k)^T\\nabla f(x^k)}{\\nabla f(x^{k-1})^T\\nabla f(x^{k-1})}\n", "\\end{align}\n", "$\n", "\n", "and the step-size $\\alpha^k$ is given by exact linesearch (from our explicit formula)\n", "\n", "$\n", "\\begin{align}\n", "\\alpha^k = \\frac{\\nabla f(x^k)^T \\nabla f(x^k)}{(p^k)^TAp^k}. \n", "\\end{align}\n", "$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# Textbook conjugate gradient method for convex quadratics\n", "# fun - objective function \n", "# x0 - starting point\n", "# jac - objective function gradient\n", "# hess - objective function Hessian\n", "# tol - tolerance for termination\n", "# callback - callback function (for plotting)\n", "def conjugate_gradient(fun, x0, args=(), jac=None, hess=None, tol=1e-1, callback=None, **options):\n", " \n", " x = x0\n", " g = jac(x)\n", " A = hess(x)\n", " p = -g\n", " it = 0\n", " while np.linalg.norm(g) > tol: # first-order optimality (zero gradient)\n", " alpha = g.T.dot(g)/p.T.dot(A.dot(p)) # exact linesearch\n", " x = x + alpha*p # take step\n", " gnew = g + alpha*A.dot(p) # new gradient\n", " beta = gnew.dot(gnew)/g.dot(g)\n", " p = -gnew + beta*p # new conjugate direction\n", " g = gnew\n", " \n", " if callback is not None: # callback function (for plotting)\n", " callback(x)\n", " \n", " it += 1 # number of iterations\n", " \n", " return opt.OptimizeResult(x=x, fun=fun(x), jac=jac(x), hess=hess(x), nit=it, success=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Coding Task: \n", "Now apply conjugate gradient starting from $x^0 = (1,a)$ to solve the above problem for various values of $a$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 2.1323896344255475e-30\n", " hess: array([[10, 0],\n", " [ 0, 1]])\n", " jac: array([-3.33066907e-15, -1.77635684e-15])\n", " nit: 2\n", " success: True\n", " x: array([-3.33066907e-16, -1.77635684e-15])\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Scaling parameter\n", "a = 10\n", "\n", "# Initial guess\n", "x0 = np.array([1,a])\n", "\n", "# Objective function, gradient and Hessian\n", "fun = lambda x: 0.5*(a*x[0]**2+x[1]**2)\n", "jac = lambda x: np.array([a*x[0],x[1]])\n", "hess = lambda x: np.array([[a,0],[0,1]])\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-1,1.5)\n", "Y = np.linspace(-a,a+1)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "\n", "# Call Newton's method via scipy\n", "xprev = x0 # for plotting\n", "res = opt.minimize(fun, x0, method=conjugate_gradient, jac=jac, hess=hess, tol=1e-1, callback=callback)\n", "\n", "# Print results and show plot\n", "print(res)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is going on here? Conjugate gradient is guaranteed to converge in at most as many iterations as there are dimensions of the problem, in this case since we are in 2D that means just two iterations! \n", "\n", "In practice, convergence speed depends on the spectrum of the Hessian (and can be much faster for large problems):\n", "\n", "$\n", "\\begin{align}\n", "\\frac{\\lVert x^k - x^* \\rVert_A}{\\lVert x^0 - x^* \\rVert_A}\n", "\\le 2 \\left( \\frac{\\sqrt{\\kappa(A)}-1}{\\sqrt{\\kappa(A)}+1} \\right)^k\n", "\\end{align}\n", "$\n", "\n", "where $\\kappa(A)$ is the Hessian condition number." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2 More Sophisticated Linesearch Methods\n", "Consider the Rosenbrock function defined as\n", "\n", "$\n", "f(x) = (a - x_1)^2 + b(x_2 - x_1^2)^2\n", "$\n", "\n", "where usually $a=1$ and $b=100$.\n", "\n", "#### Exercises: \n", "1. Find the stationary point $x^*$ of this function.\n", "2. Compute numerically the eigenvalue of the Hessian at $x^*$ to verify that $x^*$ is a minimum.\n", "\n", "#### Answers:\n", "The gradient for this function is\n", "\n", "$\n", "\\begin{align}\n", "\\nabla f(x) = \n", "\\begin{pmatrix}\n", "-2(a - x_1) -2x_1 2b(x_2 - x_1^2) \\\\\n", "2b(x_2 - x_1^2)\n", "\\end{pmatrix}\n", "\\end{align}\n", "$\n", "\n", "and thus $x^* = (a,a^2)$ is the stationary point.\n", "\n", "The Hessian for this function is\n", "\n", "$\n", "\\begin{align}\n", "\\nabla^2 f(x) = \n", "\\begin{pmatrix}\n", "2 -4bx_2 +12bx_1^2 & -4bx_1 \\\\\n", "-4bx_1 & 2b\n", "\\end{pmatrix}\n", "\\end{align}\n", "$\n", "\n", "and since \n", "\n", "$\n", "\\begin{align}\n", "\\nabla^2 f(x^*) = \n", "\\begin{pmatrix}\n", "2 +8ba^2 & -4ba \\\\\n", "-4ba & 2b\n", "\\end{pmatrix}\n", "\\succ 0\n", "\\end{align}\n", "$\n", "\n", "$x^* = (a,a^2)$ is the minimizer, which is global since $f(x^*) = 0$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2.1 Nonlinear Conjugate Gradient\n", "Recall that nonlinear conjugate gradient proceeds as a step of the form\n", "\n", "$\n", "\\begin{align}\n", "x^{k+1} = x^k + \\alpha^k p^k\n", "\\end{align}\n", "$\n", "\n", "along the conjugate direction\n", "\n", "$\n", "\\begin{align}\n", "p^k = -\\nabla f(x^k) + \\beta^k p^{k-1}\n", "\\end{align}\n", "$ \n", "\n", "where $\\beta^k$ is chosen to ensure conjugacy of the directions, several choices are possible here, e.g. Fletcher-Reeves:\n", "\n", "$\n", "\\begin{align}\n", "\\beta_k = \\frac{\\nabla f(x^k)^T\\nabla f(x^k)}{\\nabla f(x^{k-1})^T\\nabla f(x^{k-1})}\n", "\\end{align}\n", "$\n", "\n", "and the step-size $\\alpha^k$ is obtained by suitable linesearch." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Coding Task: \n", "Now apply Scipy's CG starting from $x^0 = (2a,2a)$ to solve the above problem for $a=1$ and $b=100$. Then try again from $x^0 = (10a,10a)$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 0.0002630476487862676\n", " jac: array([0.00612101, 0.0129357 ])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 21\n", " nit: 9\n", " njev: 21\n", " status: 0\n", " success: True\n", " x: array([1.01620584, 1.03273899])\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Parameters\n", "a = 1\n", "b = 100\n", "\n", "# Initial guess\n", "x0 = np.array([2*a,2*a])\n", "\n", "# Objective function and gradient\n", "fun = lambda x: (a-x[0])**2 + b*(x[1]-x[0]**2)**2\n", "jac = lambda x: np.array([-2*(a-x[0])-2*x[0]*2*b*(x[1]-x[0]**2),2*b*(x[1]-x[0]**2)])\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-2,2.5)\n", "Y = np.linspace(-2,2.5)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "\n", "# Call Scipy's CG\n", "xprev = x0 # for plotting\n", "res = opt.minimize(fun, x0, method='CG', jac=jac, tol=1e-1, callback=callback)\n", "\n", "# Print results and show plot\n", "print(res)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2.2 Truncated Newton\n", "Recall that Truncated Newton methods proceed as a step of the form\n", "\n", "$\n", "\\begin{align}\n", "x^{k+1} = x^k + \\alpha^k p^k\n", "\\end{align}\n", "$\n", "\n", "along the approximate Newton direction $p^k$ which approximately solves\n", "\n", "$\n", "\\begin{align}\n", "\\nabla^2 f(x^k) \\, p^k \\approx -\\nabla f(x^k)\n", "\\end{align}\n", "$ \n", "\n", "for example, using a limited number of conjugate-gradient iterations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Coding Task: \n", "Now apply Scipy's Newton-CG starting from $x^0 = (2a,2a)$ to solve the above problem for $a=1$ and $b=100$. Then try again from $x^0 = (10a,10a)$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 2.8378641430679393e-16\n", " jac: array([ 5.56370924e-06, -2.79313233e-06])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 37\n", " nhev: 24\n", " nit: 24\n", " njev: 37\n", " status: 0\n", " success: True\n", " x: array([0.99999998, 0.99999997])\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Parameters\n", "a = 1\n", "b = 100\n", "\n", "# Initial guess\n", "x0 = np.array([2*a,2*a])\n", "\n", "# Objective function, gradient and Hessian\n", "fun = lambda x: (a-x[0])**2 + b*(x[1]-x[0]**2)**2\n", "jac = lambda x: np.array([-2*(a-x[0])-2*x[0]*2*b*(x[1]-x[0]**2),2*b*(x[1]-x[0]**2)])\n", "hess = lambda x: np.array([[2-4*b*x[1]+12*b*x[0]**2,-4*b*x[0]],[-4*b*x[0],2*b]])\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-2,2.5)\n", "Y = np.linspace(-2,2.5)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "\n", "# Call Scipy's Newton-CG\n", "xprev = x0 # for plotting\n", "res = opt.minimize(fun, x0, method='Newton-CG', jac=jac, hess=hess, callback=callback)\n", "\n", "# Print results and show plot\n", "print(res)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2.3 Quasi-Newton\n", "Recall that Quasi-Newton proceed as a step of the form\n", "\n", "$\n", "\\begin{align}\n", "x^{k+1} = x^k + \\alpha^k p^k\n", "\\end{align}\n", "$\n", "\n", "along the Quasi-Newton direction $p^k$ which solves\n", "\n", "$\n", "\\begin{align}\n", "B^k \\, p^k = -\\nabla f(x^k)\n", "\\end{align}\n", "$ \n", "\n", "where $B^k$ is a suitable approximation to $\\nabla^2 f(x^k)$, chosen to statisfy the secant equation\n", "\n", "$\n", "\\begin{align}\n", "B^{k+1} (x^{k+1} - x^k) = \\nabla f(x^{k+1}) - \\nabla f(x^k)\n", "\\end{align}\n", "$\n", "\n", "For example, one of the most popular approximations is BFGS (a rank two update)\n", "\n", "$\n", "\\begin{align}\n", "B^{k+1} = B^k + \\frac{y^k(y^k)^T}{(y^k)^Ts^k} - \\frac{B^ks^k(B^ks^k)^T}{(s^k)^TB^ks^k}\n", "\\end{align}\n", "$\n", "\n", "where $s^k = x^{k+1} - x^k$ and $y^k = \\nabla f(x^{k+1}) - \\nabla f(x^k)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Coding Task: \n", "Now apply Scipy's BFGS starting from $x^0 = (2a,2a)$ to solve the above problem for $a=1$ and $b=100$. Then try again from $x^0 = (10a,10a)$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 1.2472338472171815e-06\n", " hess_inv: array([[0.4298175 , 0.85281652],\n", " [0.85281652, 1.69711661]])\n", " jac: array([ 0.01516525, -0.00862175])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 32\n", " nit: 27\n", " njev: 32\n", " status: 0\n", " success: True\n", " x: array([0.99896976, 0.99789747])\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Parameters\n", "a = 1\n", "b = 100\n", "\n", "# Initial guess\n", "x0 = np.array([2*a,2*a])\n", "\n", "# Objective function and gradient\n", "fun = lambda x: (a-x[0])**2 + b*(x[1]-x[0]**2)**2\n", "jac = lambda x: np.array([-2*(a-x[0])-2*x[0]*2*b*(x[1]-x[0]**2),2*b*(x[1]-x[0]**2)])\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-2,2.5)\n", "Y = np.linspace(-2,2.5)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "\n", "# Call SciPy's BFGS\n", "xprev = x0 # for plotting\n", "res = opt.minimize(fun, x0, method='BFGS', jac=jac, tol=1e-1, callback=callback)\n", "\n", "# Print results and show plot\n", "print(res)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2.4 Limited-Memory Quasi-Newton\n", "Recall that limited-memory Quasi-Newton is a variant of Quasi-Newton which stores only the last $m$ values of $s^k$ and $y^k$ for some small $m$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Coding Task: \n", "Now apply Scipy's L-BFGS-B starting from $x^0 = (2a,2a)$ to solve the above problem for $a=1$ and $b=100$. Then try again from $x^0 = (10a,10a)$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 6.758747192886498e-10\n", " hess_inv: <2x2 LbfgsInvHessProduct with dtype=float64>\n", " jac: array([-0.00059594, 0.00031851])\n", " message: 'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n", " nfev: 28\n", " nit: 25\n", " njev: 28\n", " status: 0\n", " success: True\n", " x: array([1.00002055, 1.00004269])\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Parameters\n", "a = 1\n", "b = 100\n", "m = 10\n", "\n", "# Initial guess\n", "x0 = np.array([2*a,2*a])\n", "\n", "# Objective function and gradient\n", "fun = lambda x: (a-x[0])**2 + b*(x[1]-x[0]**2)**2\n", "jac = lambda x: np.array([-2*(a-x[0])-2*x[0]*2*b*(x[1]-x[0]**2),2*b*(x[1]-x[0]**2)])\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-2,2.5)\n", "Y = np.linspace(-2,2.5)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "\n", "# Call SciPy's L-BFGS-B\n", "xprev = x0 # for plotting\n", "res = opt.minimize(fun, x0, method='L-BFGS-B', jac=jac, callback=callback, options=dict(ftol=1e-5,maxcor=m))\n", "\n", "# Print results and show plot\n", "print(res)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercises: \n", "\n", "1. Compare the number of objective function, gradient and Hessian evaluations across the different linesearch methods above (these are reported as nfev, njev and nhev in the outputs above). What do you observe?" ] }, { "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": "3.8.7" } }, "nbformat": 4, "nbformat_minor": 4 }