{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "In this blog post, I want to share something that I recently discovered while using Scipy’s optimizing library and its general optimizers. I’ll try to recreate a context in which the same problem occurs.\n", "\n", "Let’s say we want to find the miminum of a function of two parameters." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from turtle import color\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "def f(x):\n", " return np.exp(-1/(.01*x[0]**2 + x[1]**2))\n", "\n", "X, Y = np.meshgrid(np.linspace(-1, 1, 100), np.linspace(-2, 2, 200))\n", "\n", "\n", "plt.pcolormesh(X, Y, f([X, Y]), shading=\"auto\")\n", "plt.colorbar()\n", "plt.contour(X, Y, f([X, Y]), 20, colors=\"w\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What makes this founction special? It is very insensitive to its first parameter, $x$, while being quite sensitive to its second parameter $y$.\n", "\n", "Where does its minimum lie? At (0, 0). However, judging by its graph, it’s not so easy to be sure of it. Let’s plot the same thing in log scale to see if it’s easier to spot.\n" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\FL232714\\AppData\\Local\\Temp\\ipykernel_12820\\3585886120.py:1: RuntimeWarning: divide by zero encountered in log10\n", " plt.pcolormesh(X, Y, np.log10(f([X, Y])), shading=\"auto\")\n", "C:\\Users\\FL232714\\AppData\\Local\\Temp\\ipykernel_12820\\3585886120.py:3: RuntimeWarning: divide by zero encountered in log10\n", " plt.contour(X, Y, np.log10(f([X, Y])), 3, colors=\"w\")\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.pcolormesh(X, Y, np.log10(f([X, Y])), shading=\"auto\")\n", "plt.colorbar(label=\"log-scale\")\n", "plt.contour(X, Y, np.log10(f([X, Y])), 3, colors=\"w\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the log-scale, it appears that the minimum is indeed quite flat along the x-direction.\n", "\n", "Now imagine that we need to find the minimum of this function, using gradient information. How does the standard BFGS opitimizer do?" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " fun: 2.435735557933475e-13\n", " hess_inv: array([[ 29232.03943579, 795452.12702773],\n", " [ 795452.12702773, 21646309.1232013 ]])\n", " jac: array([4.06228669e-12, 6.46097188e-11])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 78\n", " nit: 24\n", " njev: 26\n", " status: 0\n", " success: True\n", " x: array([0.98850958, 0.15703429])" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy import optimize\n", "\n", "\n", "result = optimize.minimize(f, [1, 1], method=\"BFGS\", tol=1e-10, options={'eps': 1e-5})\n", "\n", "result" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Interestingly, the optimizer does not work as we would expect. The reason is clear: the gradient becomes very small and below the tolerance set by the options so the procedure stops.\n", "\n", "However, we are still quite far from the true optimum, and more so in the first dimension. So in this case, we cannot find the true solution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One way of getting out of this situation is to rescale the variables. Let’s define a second function with rescaled values." ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " fun: 2.2402323795942752e-14\n", " hess_inv: array([[1.66295961e+01, 4.57339817e+03],\n", " [4.57339817e+03, 1.33744703e+06]])\n", " jac: array([8.79065825e-12, 7.97821424e-11])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 66\n", " nit: 10\n", " njev: 22\n", " status: 0\n", " success: True\n", " x: array([0.00197755, 0.0177274 ])" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def g(x):\n", " return f([100*x[0], 10*x[1]])\n", "\n", "result = optimize.minimize(g, [.01, .1], method=\"BFGS\", tol=1e-10, options={'eps': 1e-5})\n", "\n", "result\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What did just happen? The rescaled version of the same function leads to a much better solution! Is this surprising? Let’s see a plot of the function `g`." ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.pcolormesh(X, Y, g([X, Y]), shading=\"auto\")\n", "plt.colorbar()\n", "plt.contour(X, Y, g([X, Y]), 40, colors=\"w\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.13 ('py39')", "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": "3.9.13" }, "orig_nbformat": 4, "vscode": { "interpreter": { "hash": "c48da811019b21ada6a9dfb9a0ff4368148dfb5c21a76710ac3a89a05db6501f" } } }, "nbformat": 4, "nbformat_minor": 2 }