{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# %load /Users/facai/Study/book_notes/preconfig.py\n", "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "sns.set(color_codes=True)\n", "#sns.set(font='SimHei')\n", "plt.rcParams['axes.grid'] = False\n", "\n", "#from IPython.display import SVG\n", "def show_image(filename, figsize=None, res_dir=True):\n", " if figsize:\n", " plt.figure(figsize=figsize)\n", "\n", " if res_dir:\n", " filename = './res/{}'.format(filename)\n", "\n", " plt.imshow(plt.imread(filename))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Chapter 8 Optimization for Training Deep Models\n", "=========\n", "\n", "optimization: finding the parameters $\\theta$ of a neural network that significantly reduce a cost function $J(\\theta)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.1 How Learning Differs from Pure Optimization\n", "\n", "expectation is taken across **the data generating distribution** $p_{data}$ rather than just over the finite training set:\n", "\n", "\\begin{equation}\n", " J^*(\\theta) = \\mathcal{E}_{(x, y) \\sim p_{data}} L(f(x; \\theta), y)\n", "\\end{equation}\n", "\n", "\n", "#### 8.1.1 Empirical Risk Minimization\n", "\n", "Rather than optimizing the risk direcly, we optimize the empirical risk, and hope that the risk decreases significantly as well.\n", "\n", "\n", "#### 8.1.2 Surrogate Loss Functions and Early Stopping\n", "\n", "\n", "#### 8.1.3 Batch and Minibatch Algorithms\n", "\n", "Small batches can offer a regularing effect.\n", "\n", "gradient can handle smaller batch size like 100, while second-order methods typically require much large batch sizes like 10,000.\n", "\n", "minibatches must be selected randomly. For very large datasets, it is usually sufficient to shuffle the order of the dataset once and then store it in shuffled fashion.\n", "\n", "On the second pass, the estimator becomes biased because it is formed by re-sampling values used before." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.2 Challenges in Neural Network Optimization\n", "\n", "\n", "#### 8.2.1 Ill-Conditioning\n", "\n", "To determin whether ill-conditioning, one can monitor the squared gradient norm $g^T g$ and the $g^T H g$ term. In many cases, the gradient norm does not shrink significantly throughout learning, but the $g^T H g$ term grows by more than order of magnitude.\n", "\n", "\n", "#### 8.2.2 Local Minima\n", "\n", "model identifiability problem: models with latent variables are often not identifiable <= weight space symmetry.\n", "\n", "\n", "#### 8.2.3 Plateaus, Saddle Points and Other Flat Regions\n", "\n", "+ saddle point: local minimum along one cross-section, and local maximum along another another cross-section.\n", " - in higher dimensional spaces, local minima are rare and saddle points are more common.\n", " - difficult for newton's method, while easy for gradient descent.\n", "\n", "+ maxima\n", "+ wide, flat regions of constant value \n", "\n", "\n", "#### 8.2.4 Cliffs and Exploding Gradients" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CqmeGigo1O3h4WPXOnpw0OPmii/IyFbt15goX94jeLMWZ0E78OBRS6p7PS+rq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\nWlrw3nvv4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_image(\"fig8_3.png\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "can be avoided using the *gradient clipping* heuristic\n", "\n", "\n", "#### 8.2.5 Long-Term Dependencies\n", "\n", "when graph becomes extremely deep => vanishing and exploding gradient problem\n", "\n", "Vanishing gradients make it difficult to know which direction the parameters should move to improve to the cost function, while exploding gradients can make learning unstable.\n", "\n", "\n", "#### 8.2.6 Inexact Gradients\n", "\n", "\n", "#### 8.2.7 Poor Correspondence between Local and Global Structure\n", "\n", "Many existing research directions are aimed at finding good initial points, rather than developing algorithms that use non-local moves.\n", "\n", "\n", "#### 8.2.8 Theoretical Limits of Optimization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.3 Basic Algorithms\n", "\n", "\n", "#### 8.3.1 Stochastic Gradient Descent\n", "\n", "In practice, it is necessary to gradually decrease the learning rate over time.\n", "\n", "In practice, it is common to decay the learning rate linearly until iteration $\\tau$:\n", "\n", "\\begin{equation}\n", " \\epsilon_k = (1 - \\alpha) \\epsilon_0 + \\alpha \\epsilon_{\\tau}\n", "\\end{equation}\n", "\n", "+ $\\tau$: a few hundred passes through the training set\n", "+ $\\epsilon_\\tau \\approx 1\\% \\, \\epsilon_0$\n", "+ $\\epsilon_0$: monitor the first several iterations and use a learning rate that is higher than the best-performing learning rate at this time, but not so high that it causes severe instability.\n", "\n", "To study the convergence rate of an optimization algorithm, it is common to measure the *excess error* $J(\\theta) - \\min_\\theta J(\\theta)$.\n", "+ SGD is applied to a convex problem: $O(\\frac{1}{\\sqrt{k}}$\n", "+ in the stronly convex case it is $O(\\frac{1}{k})$.\n", "\n", "\n", "#### 8.3.2 Momentum\n", "\n", "The momentum algorithm accumulates an exponentially decaying moving average of past gradients and continues to move in their direction.\n", "\n", "\\begin{align}\n", " v &\\gets \\alpha v - \\epsilon \\Delta_\\theta \\left ( \\frac1{m} \\displaystyle \\sum^m_{i = 1} L \\left ( f(x^{(i)}; \\theta), y^{(i)} \\right ) \\right ) \\\\\n", " \\theta &\\gets \\theta + v\n", "\\end{align}\n", "\n", "The larger $\\alpha$ is relative to $\\epsilon$, the more previous gradients affect the current direction." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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TU9VNwPeA0WjExcVF+dzlt2Qp4GAQn+kSOqcwlv2vLQB0e8TjbtRhs7Zx5fR+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\nIFircHU08+nc1zlc40BvNNB0q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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_image(\"fig8_5.png\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "the size of each step is $\\frac{\\epsilon \\| g \\|}{1 - \\alpha} \\implies$ it is thus helpful to think of the momentum hyperparameter in terms of $\\frac1{1 - \\alpha}$.\n", "\n", "+ Common values of $\\alpha$ used in practice include 0.5, 0.9 and 0.99.\n", "+ Typically it begins with a small value and is later raised. \n", "+ It is less important to adapt $\\alpha$ over time than to shrink $\\epsilon$ over time.\n", "\n", "\n", "#### 8.3.3 Nesterov Momentum\n", "\n", "Nesterov momentum: the gradient is evaluated after the current velocity is applied.\n", "\n", "\\begin{align}\n", " v &\\gets \\alpha v - \\epsilon \\Delta_\\theta \\left ( \\frac1{m} \\displaystyle \\sum^m_{i = 1} L \\left ( f(x^{(i)}; \\theta + \\color{blue}{\\alpha v}), y^{(i)} \\right ) \\right ) \\\\\n", " \\theta &\\gets \\theta + v\n", "\\end{align}\n", "\n", "考虑了提前量" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.4 Parameter Initialization Strategies\n", "\n", "Designing improved initialization strategies is a difficult task because neural network optimization is not yet well understood.\n", "\n", "A further difficulty is that some initial points may be benefical from the viewpoint of optimization but detrimental from the viewpoint of generalization.\n", "\n", "complete certainty: break symmetry between different units\n", "\n", "+ initialize each unit to compute a different function from all of the other units.\n", "+ random initialization of the parameters.\n", " - Typically, set biases for each unit to heuristically chosen constants, and initilize only the weights randomly.\n", "\n", "##### weight\n", "\n", "We can think of initializing the parameters $\\theta$ to $\\theta_0$ as being similar to imposing a Gaussian prior $p(\\theta)$ with mean $\\theta_0$. \n", "$\\implies$ choose $\\theta_0$ to be near 0 = more likely that units do not interact with each other than that they do interact.\n", "\n", "1. normalized initialization: $W_{i, j} \\sim U \\left ( - \\frac{6}{\\sqrt{m + n}}, \\frac{6}{\\sqrt{m + n}} \\right )$\n", "2. initializing to random orthogonal matrices\n", "3. perserve norms\n", "4. sparse initialization\n", "\n", "A good rule of thumb for choosing the initial scales is to look at the range or standard deviation of activations or gradients on a single minibatch of data.\n", "\n", "##### biase\n", "\n", "1. Setting the biases to zero is compatible with most weight initialization schemes.\n", "2. a few situations where we may set some biases to non-zero values:\n", " + for an output unit, often feneficial to initialize the bias to obtain the right marginal statistics of the output.\n", " + choose the bias to avoid causing too much saturation at initialization. \n", " eg: set the bias of ReLU hidden unit to 0.1 rather than 0\n", " + Sometimes a unit controls whether other units are able to participate in a function => all units have a chance to learn.\n", " \n", "##### initialize model parameters using machine learning\n", "\n", "eg: to initialize a supervised model with the parameters learned by an unsupervised model trained on the same inputs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.5 Algorithms with Adaptive Learning Rates\n", "\n", "the cost is often highly sensitive to some directions in parameter space and insensitive to others. => adapt the learning rates of model parameters.\n", "\n", "\n", "#### 8.5.1 AdaGrad\n", "\n", "gradient accumulation\n", "\n", "$\\text{rate} = \\frac1{\\sum \\text{squared gradients}}$\n", "\n", "\n", "#### 8.5.2 RMSProp\n", "\n", "changing the gradient accumulation into an exponentially weighted moving average.\n", "\n", "\n", "#### 8.5.3 Adam\n", "\n", "adaptive moments: combination of RMSProp and momentum\n", "\n", "Currently, the most popular optimization algorithms actively in use include \n", "+ SGD, \n", "+ SGD with momentum, \n", "+ RMSProp, \n", "+ RMSProp with momentum, \n", "+ AdaDelta and Adam.\n", "\n", "The choice of which algorithm to use, at this point, seems to depend largely on the user’s familiarity with the algorithm (for ease of hyperparameter tuning)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.6 Approximate Second-Order Methods\n", "\n", "#### 8.6.1 Newton's Method\n", "\n", "a two-step iterative procedure:\n", "\n", "+ update or compute the inverse Hessian\n", "+ update the parameters: $\\theta^* = \\theta_0 - \\mathbf{H}^{-1} \\Delta_\\theta J(\\theta_0)$\n", "\n", "\n", "#### 8.6.2 Conjugate Gradients\n", "\n", "\n", "#### 8.6.3 BFGS\n", "\n", "L-BFGS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.7 Optimization Strategies and Meta-Algorithms\n", "\n", "#### 8.7.1 Batch Normalization\n", "\n", "adaptive reparametrization => training very deep models\n", "\n", "\n", "#### 8.7.2 Coordinate Descent\n", "\n", "bad: variables are dependent.\n", "\n", "\n", "#### 8.7.3 Polyak Averaging\n", "\n", "averaging points.\n", "\n", "\n", "#### 8.7.4 Supervised Pretraining\n", "\n", "training sample models on simple tasks => then make the model more complex.\n", "\n", "\n", "#### 8.7.5 Designing Models to Aid Optimization\n", "\n", "In practice, it is more important to choose a model family that is easy to optimize than to use a powerful optimization algorithm.\n", "\n", "\n", "#### 8.7.6 Continuous Methods and Curriculumn Learning" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }