{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Stochastic Gradient descent\n", "===========================\n", "\n", "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{ \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$\n", "$\\newcommand{\\eqdef}{\\equiv}$" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This tour details Stochastic Gradient Descent, applied to the binary logistic classification problem.\n", "\n", "We recommend that after doing this Numerical Tours, you apply it to your\n", "own data, for instance using a dataset from [LibSVM](https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/).\n", "\n", "_Disclaimer:_ these machine learning tours are intended to be\n", "overly-simplistic implementations and applications of baseline machine learning methods.\n", "For more advanced uses and implementations, we recommend\n", "to use a state-of-the-art library, the most well known being\n", "[Scikit-Learn](http://scikit-learn.org/)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "options(warn=-1) # turns off warnings, to turn on: \"options(warn=0)\"\n", "library(plot3D)\n", "library(pracma)\n", "\n", "# Importing the libraries\n", "for (f in list.files(path=\"nt_toolbox/toolbox_general/\", pattern=\"*.R\")) {\n", " source(paste(\"nt_toolbox/toolbox_general/\", f, sep=\"\"))\n", "}\n", "for (f in list.files(path=\"nt_toolbox/toolbox_signal/\", pattern=\"*.R\")) {\n", " source(paste(\"nt_toolbox/toolbox_signal/\", f, sep=\"\"))\n", "}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Define a few helper functions:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "fs = 10\n", "\n", "Xm = function(X){as.matrix(X - rep(colMeans(X), rep.int(nrow(X), ncol(X))))}\n", "Cov = function(X){data.matrix(1. / (n - 1) * t(Xm(X)) %*% Xm(X))}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Simple Example\n", "--------------\n", "We first illustrate the concept of stochastic gradient descent on a\n", "simple example\n", "$$ \\umin{x \\in \\RR} f(x) \\eqdef f_1(x) + f_2(x) $$\n", "where $f_1(x) \\eqdef (x-1)^2$ and\n", "$f_2(x) \\eqdef (x+1)^2$.\n", "\n", "\n", "Functions and their derivatives." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "f = function(x,i)\n", "{\n", " if (i==1)\n", " {\n", " return(0.5 * (x - 1)**2)\n", " }\n", " else\n", " {\n", " return(0.5 * (x + 1)**2)\n", " }\n", "}\n", "\n", "df = function(x,i)\n", "{\n", " if (i==1)\n", " {\n", " return(x - 1)\n", " }\n", " else\n", " {\n", " return(x + 1)\n", " }\n", "}\n", "\n", "F = function(x){f(x,1) + f(x,2)}" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtAAAALQCAIAAAA2NdDLAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width=6, repr.plot.height=6)\n", "t = seq(-3,3, length=201)\n", "plot(t, f(t,1), col=\"blue\", type='l', ylab=\"\", xlab=\"\")\n", "lines(t, f(t,2), col=\"orange\", type='l')\n", "lines(t, F(t), col=\"green\", type='l')\n", "legend(\"top\", legend=c(\"f1\", \"f2\", \"F\"), col=c(\"blue\", \"orange\", \"green\"), pch=\"-\")" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Each iteration of SGD reads\n", "$$ x_{\\ell+1} = x_\\ell - \\tau_\\ell \\nabla f_{i(\\ell)}(x_\\ell) $$\n", "where $ i(\\ell) \\in \\{1,2\\} $ is drawn uniformly." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 0__\n", "\n", "Implement the SGD, with a random initial condition $x_0$.\n", "Display several paths (i.e. run several times the algorithm)\n", "to vizualize the evolution of the density of the random variable\n", "$x_\\ell$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtAAAALQCAIAAAA2NdDLAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nJxwAwC7HKAAmTAiAmgAAAABJRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/ml_4_sgd/exo0.R\")" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Dataset Loading\n", "---------------\n", "We load a subset of the \n", "of $n=10000$ features in dimension $78$. The goal in this task is to learn a classification rule that differentiates between two types of particles generated in high energy collider experiments.\n", "\n", "\n", "\n", "Load the dataset.\n", "Randomly permute it.\n", "Separate the features $X$ from the data $y$ to predict information." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "file_name = 'nt_toolbox/data/quantum.csv'\n", "A = read.table(file_name, sep=\",\", head=FALSE)\n", "#A = A[sample(dim(A)[1]),]\n", "X = A[,1:(dim(A)[2] - 1)]\n", "y = A[,dim(A)[2]]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Set the classes indexes to be $\\{-1,+1\\}$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "y = (2 * y - 1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Remove empty features, normalize $X$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "X[,1] = as.numeric(X[,1])\n", "I = colMeans(abs(as.matrix(X))) > 1e-1 \n", "X = X[,I]\n", "X = scale(X)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "$n$ is the number of samples, $p$ is the dimensionality of the features," ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "n = dim(X)[1]\n", "p = dim(X)[2]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute PCA main axes for display." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAIAAADytinCAAAABmJLR0QA/wD/AP+gvaeTAAAg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", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "svd_decomp = svd(Xm(X))\n", "U = svd_decomp$u\n", "s = svd_decomp$d\n", "V = svd_decomp$v\n", "Xr = X %*% t(V)\n", "\n", "options(repr.plot.width=4, repr.plot.height=4)\n", "plot(s, type=\"o\", col=4, ylab=\"\", xlab=\"\", pch=16)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Plot the classes." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAJYCAIAAAAxBA+LAAAABmJLR0QA/wD/AP+gvaeTAAAg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\n6jTl500xoQAAAABJRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width=5, repr.plot.height=5)\n", "I = sample(n)\n", "I = I[1:200]\n", "plot_multiclasses(X[I,],y[I], 2)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAJYCAIAAAAxBA+LAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nHxlQ+q7XgR0zAAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_multiclasses(X[I,],y[I], 3)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Batch Gradient Descent (BGD)\n", "----------------------------\n", "We first test the usual (batch) gradient descent (BGD) on the problem of\n", "supervised logistic classification.\n", "\n", "\n", "We refer to the dedicated numerical tour on logistic classification for\n", "background and more details about the derivations of the energy and its\n", "gradient.\n", "\n", "\n", "Logistic classification aims at solving the following convex program\n", " $$ \\umin{w} E(w) \\eqdef \\frac{1}{n} \\sum_{i=1}^n L(\\dotp{x_i}{w},y_i) $$\n", "where the logistic loss reads\n", " $$ L( s,y ) \\eqdef \\log( 1+\\exp(-sy) ) $$\n", "\n", "\n", "Define energy $E$ and its gradient $\\nabla E$." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "L = function(s,y){1/n * sum( log(1 + exp(-s * y)))}\n", "E = function(w,X,y){L(X %*% w, y)}\n", "theta = function(v){1 / (1 + exp(-v))}\n", "nablaL = function(s, r){ - 1/n * y * theta(-s * y)}\n", "nablaE = function(w,X,y){t(X) %*% nablaL(X %*% w,y)}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 1__\n", "\n", "Implement a gradient descent\n", "$$ w_{\\ell+1} = w_\\ell - \\tau_\\ell \\nabla E(w_\\ell). $$\n", "Monitor the energy decay.\n", "Test different step size, and compare with the theory (in particular\n", "plot in log domain to illustrate the linear rate)." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAHgCAIAAAD2dYQOAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nAACtEUIAgNb+Hyt7JOhmMzSSAAAAAElFTkSuQmCC", "text/plain": [ "Plot with title \"E(w_i)\"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAHgCAIAAAD2dYQOAAAABmJLR0QA/wD/AP+gvaeTAAAg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", "text/plain": [ "Plot with title \"log(E(w_l) - min E)\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/ml_4_sgd/exo1.R\")" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Stochastic Gradient Descent (SGD)\n", "---------------------------------\n", "As any empirical risk minimization procedure, the\n", "logistic classification minimization problem can be written as\n", "$$ \\umin{w} E(w) = \\frac{1}{n} \\sum_i E_i(w) \\qwhereq E_i(w) = L(\\dotp{x_i}{w},y_i). $$\n", "\n", "\n", "For very large $n$ (which could in theory even be infinite, in which case the sum needs to be replaced\n", "by an expectation or equivalenty an integral), computing $\\nabla E$ is prohebitive.\n", "It is possible instead to use a stochastic gradient descent (SGD) scheme\n", " $$ w_{\\ell+1} = w_\\ell - \\tau_\\ell \\nabla E_{i(\\ell)}(w_\\ell) $$\n", "where, for each iteration index $\\ell$, $i(\\ell)$\n", "is drawn uniformly at random in $ \\{1,\\ldots,n\\} $.\n", "\n", "\n", "Note that here\n", "$$ \\nabla E_{i}(w) = x_i \\nabla L( \\dotp{x_i}{w}, y_i )\n", " \\qwhereq \\nabla L(u,v) = v \\odot \\th(-u) $$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "nablaEi = function(w,i){as.numeric(-y[i] * t(X[i,]) * c(theta(-y[i] * (X[i,] %*% w))))}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Note that each step of a batch gradient descent has complexity $O(np)$,\n", "while a step of SGD only has complexity $O(p)$. SGD is thus\n", "advantageous when $n$ is very large, and one cannot afford to do\n", "several passes through the data. In some situation, SGD can provide\n", "accurate results even with $\\ell \\ll n$, exploiting redundancy between\n", "the samples.\n", "\n", "\n", "A crucial question is the choice of step size schedule $\\tau_\\ell$. It\n", "must tends to 0 in order to cancel the noise induced on the gradient by\n", "the stochastic sampling. But it should not go too fast to zero in order\n", "for the method to keep converging.\n", "\n", "\n", "A typical schedule that ensures both properties is to have asymptically $\\tau_\\ell \\sim \\ell^{-1}$ for\n", "$\\ell\\rightarrow +\\infty$. We thus propose to use\n", "$$ \\tau_\\ell \\eqdef \\frac{\\tau_0}{1 + \\ell/\\ell_0} $$\n", "where $\\ell_0$ indicates roughly the number of iterations serving as a\n", "\"warmup\" phase.\n", "\n", "\n", "One can prove the following convergence result\n", " $$ \\EE( E(w_\\ell) ) - E(w^\\star) = O\\pa{ \\frac{1}{\\sqrt{\\ell}} }, $$\n", "where $\\EE$ indicates an expectation with respect to the i.i.d.\n", "sampling performed at each iteration.\n", "\n", "\n", "Select default values for $ (\\ell_0,\\tau_0) $." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "l0 = 100\n", "tau0 = 0.05" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 2__\n", "\n", "Perform the Stochastic gradient descent.\n", "Display the evolution of the energy $E(w_\\ell)$.\n", "One can overlay on top (black dashed curve) the convergence of the batch gradient descent, with a carefull scaling of the\n", "number of iteration to account for the fact that the complexity of a batch iteration is $n$ times larger.\n", "Perform several runs to illustrate the probabilistic nature of the method.\n", "Explore different values for $ (\\ell_0,\\tau_0) $." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAHgCAIAAAD2dYQOAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nIGn/BbvNhHBw/QItAAAAAElFTkSuQmCC", "text/plain": [ "Plot with title \"E(wi)\"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAHgCAIAAAD2dYQOAAAABmJLR0QA/wD/AP+gvaeTAAAg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", "text/plain": [ "Plot with title \"log(E(w_l) - min E)\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/ml_4_sgd/exo2.R\")" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Stochastic Gradient Descent with Averaging (SGA)\n", "------------------------------------------------\n", "Stochastic gradient descent is slow because of the fast decay of\n", "$\\tau_\\ell$ toward zero.\n", "\n", "\n", "To improve somehow the convergence speed, it is possible to average the past\n", "iterate, i.e. run a \"classical\" SGD on auxiliary variables $ (\\tilde w_\\ell)_\\ell$\n", " $$ \\tilde w_{\\ell+1} = \\tilde w_\\ell - \\tau_\\ell \\nabla E_{i(\\ell)}(\\tilde w_\\ell) $$\n", "and output as estimated weight vector the average\n", "$$ w_\\ell \\eqdef \\frac{1}{\\ell} \\sum_{k=1}^\\ell \\tilde w_\\ell. $$\n", "This defines the Stochastic Gradient Descent with Averaging (SGA)\n", "algorithm.\n", "\n", "\n", "Note that it is possible to avoid explicitely storing all the iterates by simply\n", "updating a running average as follow\n", "$$ w_{\\ell+1} = \\frac{1}{\\ell} \\tilde w_\\ell + \\frac{\\ell-1}{\\ell} w_\\ell. $$\n", "\n", "\n", "In this case, a typical choice of decay is rather of the form\n", "$$ \\tau_\\ell \\eqdef \\frac{\\tau_0}{1 + \\sqrt{\\ell/\\ell_0}}. $$\n", "Notice that the step size now goes much slower to 0, at rate $\\ell^{-1/2}$.\n", "\n", "\n", "Typically, because the averaging stabilizes the iterates, the choice of\n", "$(\\ell_0,\\tau_0)$ is less important than for SGD.\n", "\n", "\n", "[Bach proves that](https://arxiv.org/pdf/1303.6149.pdf) for logistic classification,\n", "it leads to a faster convergence (the constant involved are\n", "smaller) than SGD, since\n", "on contrast to SGD, SGA is adaptive to the local strong convexity of $E$." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 3__\n", "\n", "Implement the Stochastic gradient descent with averaging.\n", "Display the evolution of the energy $E(w_\\ell)$." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAJYCAIAAADXJFGjAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nSUVORK5CYII=", "text/plain": [ "Plot with title \"log(E(w_l) - min E)\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/ml_4_sgd/exo3.R\")" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Stochastic Averaged Gradient Descent (SAG)\n", "------------------------------------------\n", "For problem size $n$ where the dataset (of size $n \\times p$) can\n", "fully fit into memory, it is possible to further improve the SGA method\n", "by bookeeping the previous gradient. This gives rise to the\n", "[Stochastic Averaged Gradient Descent (SAG)](https://arxiv.org/pdf/1309.2388) algorithm.\n", "\n", "\n", "We stored all the previously computed gradient in $ (G^i)_{i=1}^n $,\n", "which necessitate $n \\times p$ memory.\n", "The iterates are defined by using a proxy $g$ for the batch gradient,\n", "which is progressively enhanced during the iterates.\n", "\n", "\n", "The algorithm reads\n", "$$ h \\leftarrow \\nabla E_{i(\\ell)}(\\tilde w_\\ell), $$\n", "$$ g \\leftarrow g - G^{i(\\ell)} + h, $$\n", "$$ G^{i(\\ell)} \\leftarrow h, $$\n", "$$ w_{\\ell+1} = w_\\ell - \\tau g. $$\n", "Note that in contrast to SGD and SGA, this method uses a fixed step\n", "size $\\tau$. Similarely to the BGD, in order to ensure convergence,\n", "the step size $\\tau$ should be of the order of $1/L$\n", "where $L$ is the Lipschitz constant of $E$.\n", "\n", "\n", "This algorithm improves over SGA and BGD\n", "since it has a convergence rate of $O(1/\\ell)$.\n", "Furthermore, in the presence of strong convexity (for instance when $X$ is\n", "injective for logistic classification), it has a linear convergence rate,\n", "i.e.\n", " $$ \\EE( E(w_\\ell) ) - E(w^\\star) = O\\pa{ \\rho^\\ell }, $$\n", "for some $0 < \\rho < 1$.\n", "\n", "\n", "Note that this improvement over SGD and SGA is made possible only because\n", "SAG explictely use the fact that $n$ is finite (while SGD and SGA can\n", "be extended to infinite $n$ and more general minimization of\n", "expectations)." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 4__\n", "\n", "Implement SAG.\n", "Display the evolution of the energy $E(w_\\ell)$." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAJYCAIAAADXJFGjAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nEv8DSuRPMqlBwfYAAAAASUVORK5CYII=", "text/plain": [ "Plot with title \"log(E(w_l) - min E)\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/ml_4_sgd/exo4.R\")" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "" ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.4.2" } }, "nbformat": 4, "nbformat_minor": 0 }