ee046211_tutorial_03_optimization_gradient_descent.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# <img src=\"./assets/course-icon.png\" style=\"height:50px;display:inline\"> ECE 046211 - Technion - Deep Learning\n",
    "---\n",
    "\n",
    "#### <a href=\"https://taldatech.guthub.io\"> Tal Daniel</a>\n",
    "\n",
    "## Tutorial 03 - Optimization & Gradient Descent Algorithms\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/bubbles/50/000000/checklist.png\" style=\"height:50px;display:inline\"> Agenda\n",
    "---\n",
    "\n",
    "* [Unimodal vs. Multimodal Optimization](#-Unimodal-vs.-Multimodal-Optimization)\n",
    "* [Convexity](#-Convexity)\n",
    "* [Optimality Conditions](#-Optimality-Conditions)\n",
    "* [(Batch) Gradient Descent](#(Batch)-Gradient-Descent)\n",
    "* [Stochastic Gradient Descent (Mini Batch Gradient Descent)](#Stochastic-Gradient-Descent-(Mini-Batch-Gradient-Descent))\n",
    "* [GD Comparison Summary](#GD-Comparison-Summary)\n",
    "* [The Learning Rate](#-The-Learning-Rate)\n",
    "* [Example - (Multivariate) Linear Least Squares](#-Example---(Multivariate)-Linear-Least-Squares)\n",
    "* [Learning Rate Scheduling (Annealing)](#-Learning-Rate-Scheduling-(Annealing))\n",
    "    * [Learning Rate Scheduling in PyTorch](#-Learning-Rate-Scheduling-in-PyTorch)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* [Momentum & Nesterov Momentum](#-Momentum-&-Nesterov-Momentum)\n",
    "    * [Momentum in PyTorch](#-Momentum-in-PyTorch)\n",
    "* [Adaptive Learning Rate Methods](#-Adaptive-Learning-Rate-Methods)\n",
    "    * [Adagrad](#-Adagrad)\n",
    "        * [Adagrad in PyTorch](#-Adagrad-in-PyTorch)\n",
    "    * [RMSprop](#-RMSprop)\n",
    "        * [RMSprop in PyTorch](#-RMSprop-in-PyTorch)\n",
    "    * [Adam - Adaptive Moment Estimation](#-Adam---Adaptive-Moment-Estimation)\n",
    "        * [Adam in PyTorch](#-Adam-in-PyTorch)\n",
    "* [Comparison Between Methods](#-Comparison-Between-Methods)\n",
    "* [Recent Advances in Optimizers](#-Recent-Advances-in-Optimizers)\n",
    "    * [AdaBelief](#-AdaBelief)\n",
    "    * [MADGRAD](#-MADGRAD)\n",
    "    * [Adan](#-Adan)\n",
    "    * [Schedule-free Optimization](#-Schedule-Free-Optimization)\n",
    "\n",
    "* [Recommended Videos](#-Recommended-Videos)\n",
    "* [Credits](#-Credits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# imports for the tutorial\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from sklearn.model_selection import train_test_split\n",
    "%matplotlib ipympl\n",
    "# %matplotlib inline\n",
    "\n",
    "# pytorch imports\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torchvision.transforms as transforms\n",
    "import torchvision.datasets as dsets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/cute-clipart/64/000000/minimum-value.png\" style=\"height:50px;display:inline\"> Unimodal vs. Multimodal Optimization\n",
    "---\n",
    "* **Unimodal** - only **one** optimum, that is, the *local* optimum is also global.\n",
    "\n",
    "<center><img src=\"./assets/unimodal.jpg\" style=\"height:200px\"></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **Multimodal** - more than one optimum.\n",
    "  \n",
    "<center><img src=\"./assets/multimodal.jpg\" style=\"height:200px\"></center>\n",
    "\n",
    "Most search schemes are based on the assumption of **unimodal** surface. The optimum determined in such cases is called **local optimum design**.\n",
    "\n",
    "The **global optimum** is the best of all *local optimum* designs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/office/80/000000/statistics.png\" style=\"height:50px;display:inline\"> Convexity\n",
    "---\n",
    "* **Definition**: $$\\forall x_1, x_2 \\in X, \\forall t \\in [0,1]: $$ $$ f(tx_1 + (1-t)x_2) \\leq tf(x_1) + (1-t)f(x_2) $$\n",
    "  \n",
    "<center><img src=\"./assets/convex_1.jpg\" style=\"height:200px\"></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<center><img src=\"./assets/convex_concave.gif\" style=\"height:200px\"></center>\n",
    "\n",
    "<a href=\"http://mathworld.wolfram.com/Convex.html\">Image Source</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Convex functions are **unimodal**.\n",
    "    * However, unimodal functions are not always convex, but they are usually still easy to optimize.\n",
    "      \n",
    "<center><img src=\"./assets/convex_2.jpg\" style=\"height:200px\"></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/dusk/64/000000/copyleft.png\" style=\"height:50px;display:inline\"> Optimality Conditions\n",
    "---\n",
    "* If $f: \\mathbb{R}^d \\to \\mathbb{R}$ has *local* optimum at $x_0$ then $\\nabla f(x_0) = 0$. \n",
    "    * $\\nabla f(x_0)$ is also called **the gradient** at $x_0$.\n",
    "* **The Hessian Matrix** : $H(f)(x)_{i,j} = \\frac{\\partial^2}{\\partial x_i \\partial x_j} f(x) \\in \\mathbb{R}^{d \\times d}$\n",
    "$$ H = \\begin{bmatrix} \\frac{\\partial^2 f}{\\partial x_1^2} & \\frac{\\partial^2 f}{\\partial x_1 \\partial x_2} & \\cdots & \\frac{\\partial^2 f}{\\partial x_1 \\partial x_d}  \\\\ \\frac{\\partial^2 f}{\\partial x_2 x_1} & \\frac{\\partial^2 f}{\\partial x_2^2} & \\cdots & \\frac{\\partial^2 f}{\\partial x_2 \\partial x_d}  \\\\ \\vdots  & \\vdots  & \\ddots & \\vdots  \\\\ \\frac{\\partial^2 f}{\\partial x_d x_1} & \\frac{\\partial^2 f}{\\partial x_d \\partial x_2} & \\cdots & \\frac{\\partial^2 f}{\\partial x_d^2}  \\end{bmatrix} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* If the **Hessian** matrix is:\n",
    "    * **Positive Definite** (all eigenvalues *positive*) at $x_0 \\rightarrow$ *local minimum*.\n",
    "    * **Negative Definite** (all eigenvalues *negative*) at $x_0 \\rightarrow$ *local maximum*.\n",
    "    * Both **positive and negative** eigenvalues at $x_0 \\rightarrow$ *saddle* point.\n",
    "      <center><img src=\"./assets/saddle.jpg\" style=\"height:100px\"></center>\n",
    "* Note: the Hessian matrix is symmetric if the second partial derivatives are continuous, but this is not always true (<a href=\"https://en.wikipedia.org/wiki/Symmetry_of_second_derivatives\">Schwarz's theorem</a>)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/dusk/64/000000/treasure-map.png\" style=\"height:50px;display:inline\">(Batch) Gradient Descent\n",
    "---\n",
    "* Generic optimization algorithm capable of finding optimal solutions to a wide range of problems.\n",
    "* The general idea is to tweak parameters **iteratively** to minimize a cost function.\n",
    "* It measures the local gradient of the error function with regards to the parameter vector ($\\theta$ or $w$), and it goes down in the direction of the descending gradient.\n",
    "* **Once the gradient is zero - the minimum is reached (=convergence)**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **Pseudocode**:\n",
    "    * **Require**: Learning rate $\\alpha_k$\n",
    "    * **Require**: Initial parameter vector $w$\n",
    "    * **While** stopping criterion not met **do**\n",
    "        * Compute gradient: $g \\leftarrow \\nabla_w f(x,w)$ \n",
    "        * Apply update: $w \\leftarrow w - \\alpha_k g$\n",
    "        * $k \\leftarrow k + 1$\n",
    "    * **end while**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<center><img src=\"./assets/minimum.jpg\" style=\"height:200px\"></center>\n",
    "\n",
    "* **Convergene**: When the cost function is *convex* and its slope does not change abruptly, (Batch) GD with a (small enough) *fixed* learning rate will eventually converge to the optimal solution (but the time is depndent on the rate)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><img src=\"./assets/gd_animation.gif\" style=\"height:200px\"></center>\n",
    "\n",
    "<a href=\"https://commons.wikimedia.org/wiki/File:Gradient_descent.gif\">Image Source</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/dusk/64/000000/waypoint-map.png\" style=\"height:50px;display:inline\">Stochastic Gradient Descent (Mini-Batch Gradient Descent)\n",
    "---\n",
    "* The main problem with (Batch) GD is that it uses the **whole** training set to compute the gradients. But what if that training set is huge or each sample has a very large number of features? Computing the gradient can take a very long time.\n",
    "* *Stochastic* Gradient Descent on the other hand, samples just one instance randomly at every step and computes the gradients based on that single instance (remember the Perceptron algorithm?). This makes the algorithm much faster but due to its randomness, it is much less stable. Instead of steady decreasing untill reaching the minimum, the cost function will bounce up and down, **decreasing only on average**. With time, it will get *very close* to the minimum, but once it is there it will continue to bounce around!\n",
    "    * When we have outliers, SGD may take us to undesirable areas.\n",
    "* The final parameters are good but **not optimal**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* When the cost function is very irregular, this bouncing can actually **help the algorithm escape local minima**, so SGD has better chance to find the *global* minimum.\n",
    "* How to find optimal parameters using SGD?\n",
    "    * **Reduce the learning rate gradually**: this is called *learning rate scheduling*.\n",
    "        * But don't reduce too quickly or you will get stuck at a local minimum or even frozen!\n",
    "* *Mini-Batch* Gradient Descent - same idea as SGD, but instead of one instance each step, $m$ samples.\n",
    "    * Get a little bit closer to the minimum than SGD but a little harder to escape local minima."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **Pseudocode**:\n",
    "    * **Require**: Learning rate $\\alpha_k$\n",
    "    * **Require**: Initial parameter $w$\n",
    "    * **While** stopping criterion not met **do**\n",
    "        * Sample a minibatch of $m$ examples from the training set ($m=1$ for SGD)\n",
    "        * Set $\\{x_1,...,x_m,\\}$ with corresponding targets $\\{y_1,...,y_m\\}$\n",
    "        * Compute gradient: $g \\leftarrow \\frac{1}{m} \\sum_{i=1}^m f'(x_i,w, y_i)$\n",
    "        * Apply update: $w \\leftarrow w - \\alpha_k g$\n",
    "        * $k \\leftarrow k + 1$\n",
    "    * **end while**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<center><img src=\"./assets/sgd.png\" style=\"height:250px\"></center>\n",
    "\n",
    "<a href=\"https://towardsdatascience.com/gradient-descent-algorithm-and-its-variants-10f652806a3\">Image Source</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### GD Comparison Summary\n",
    "---\n",
    "\n",
    "| Method|Accuracy | Update Speed | Memory Usage |Online Learning |\n",
    "|---|---|---|---|---|\n",
    "| **Batch** Gradient Descent | Good | Slow |  High | No |\n",
    "| **Stochastic** Gradient Descent |  Good (with softening) | Fast |  Low |  Yes |\n",
    "| **Mini-Batch** Gradient Descent | Good | Medium | Medium | Yes (depends on the MB size) |\n",
    "\n",
    "\n",
    "* **\"Online\"** - samples arrive while the algorithm runs (that is, when the algorithm starts running, not all samples exist)\n",
    "* Note: all the Gradient Descent algorithms require **scaling** if the features are not within the same range!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Update Speed\n",
    "---\n",
    "* Assume: number of samples $M=100$ and we wish to train for $N=10$ epochs (iterating over all of the samples 10 times).\n",
    "* Denote `batch_size` with $m$.\n",
    "* `batch_size` and `num_epochs` are **hyper-parameters**: parameters that are chosen by the user prior to the training stage, they are not learned.\n",
    "\n",
    "| Method|# Gradients Updates (=iterations) |\n",
    "|-------|----------------------------------|\n",
    "| **Batch** Gradient Descent, $m=100$| $\\frac{M}{m} \\cdot N = 1 * 10$ |\n",
    "| **Stochastic** Gradient Descent, $m=1$ |  $\\frac{M}{m} \\cdot N =100 * 10 = 1000$ |\n",
    "| **Mini-Batch** Gradient Descent, $m=10$ | $\\frac{M}{m} \\cdot N =10 * 10 = 100$ |\n",
    "\n",
    "* The update speed affects how we tune the **learning rate**, which is also a hyper-parameter (usually, larger batches enable using higher learning rates)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Challenges\n",
    "---\n",
    "* Choosing a **learning rate**.\n",
    "    * Defining **learning schedule**.\n",
    "* Working with features of different scales (e.g. heights (cm), weights (kg) and age (scalar)).\n",
    "* Avoiding **local minima** (or *suboptimal* minima)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "###  <img src=\"https://img.icons8.com/fluent/96/000000/sample-rate.png\" style=\"height:50px;display:inline\"> The Learning Rate\n",
    "---\n",
    "* **Learning Rate** hyper-parameter - it is the size of step to be taken in each iteration.\n",
    "    * Too *small* $\\rightarrow$ the algorithm will have to go through many iterations to converge, which will take a long time.\n",
    "    * Too *high* $\\rightarrow$ might make the algorithm diverge as it may miss the minimum.\n",
    "<center><img src=\"./assets/lr.png\" style=\"height:250px\"></center>\n",
    "\n",
    "<a href=\"https://www.jeremyjordan.me/nn-learning-rate/\">Image Source</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><img src=\"./assets/gd_converge_diverge.gif\" style=\"height:300px\"></center>\n",
    "\n",
    "<a href=\"https://towardsai.net/p/machine-learning/analysis-of-learning-rate-in-gradient-descent-algorithm-using-python\">Image Source</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/dusk/64/000000/classroom.png\" style=\"height:50px;display:inline\"> Example - (Multivariate) Linear Least Squares\n",
    "---\n",
    "* **Problem Formulation**\n",
    "    * $y \\in \\mathbb{R}^N$ - vector of values.\n",
    "    * $X \\in \\mathbb{R}^{N \\times L}$ - data matrix with $N$ examples and *$L$ features*.\n",
    "    * $w \\in \\mathbb{R}^L$ - the *parameters* to be learned, a **weight for each feature**.\n",
    "* **Goal**: find $w$ that best fits the measurement y, that is, find a *weighted linear combination* of the feature vector to best fit the measurment $y$.\n",
    "* Mathematiacally, the problem is:\n",
    "$$\\min_w f(w;x,y) = \\min_w \\sum_{i=1}^N||x_i w-y_i||^2 $$\n",
    "* In vector form:\n",
    "$$\\min_w f(w;x,y) = \\min_w ||Xw - Y||^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### <img src=\"https://img.icons8.com/dusk/64/000000/idea.png\" style=\"height:30px;display:inline\">   (Multivariate) LLS - Analytical Solution\n",
    "---\n",
    "* Mathematically:\n",
    "$$\\min_w f(w;x,y) = \\min_w ||Xw - Y||^2 = \\min_w (Xw-Y)^T(Xw-Y)= \\min_w (w^TX^TXw -2w^TX^TY + Y^TY)$$\n",
    "* The derivative: \n",
    "$$\\nabla_w f(w;x,y) = (X^TX + X^TX)w -2X^TY = 0 \\rightarrow w=(X^TX)^{-1}X^TY $$ $$X^TX \\in \\mathbb{R}^{L \\times L} $$\n",
    "\n",
    "* Notice how the gradient is dependent on the features, which is why scaling them is important when applying gradient descent (however, scaling is not necessary if we use the closed-form solution, the least-squares solution)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>diagnosis</th>\n",
       "      <th>radius_mean</th>\n",
       "      <th>texture_mean</th>\n",
       "      <th>perimeter_mean</th>\n",
       "      <th>area_mean</th>\n",
       "      <th>smoothness_mean</th>\n",
       "      <th>compactness_mean</th>\n",
       "      <th>concavity_mean</th>\n",
       "      <th>concave points_mean</th>\n",
       "      <th>...</th>\n",
       "      <th>texture_worst</th>\n",
       "      <th>perimeter_worst</th>\n",
       "      <th>area_worst</th>\n",
       "      <th>smoothness_worst</th>\n",
       "      <th>compactness_worst</th>\n",
       "      <th>concavity_worst</th>\n",
       "      <th>concave points_worst</th>\n",
       "      <th>symmetry_worst</th>\n",
       "      <th>fractal_dimension_worst</th>\n",
       "      <th>Unnamed: 32</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>861648</td>\n",
       "      <td>B</td>\n",
       "      <td>14.620</td>\n",
       "      <td>24.02</td>\n",
       "      <td>94.57</td>\n",
       "      <td>662.7</td>\n",
       "      <td>0.08974</td>\n",
       "      <td>0.08606</td>\n",
       "      <td>0.03102</td>\n",
       "      <td>0.02957</td>\n",
       "      <td>...</td>\n",
       "      <td>29.11</td>\n",
       "      <td>102.90</td>\n",
       "      <td>803.7</td>\n",
       "      <td>0.1115</td>\n",
       "      <td>0.1766</td>\n",
       "      <td>0.09189</td>\n",
       "      <td>0.06946</td>\n",
       "      <td>0.2522</td>\n",
       "      <td>0.07246</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>854253</td>\n",
       "      <td>M</td>\n",
       "      <td>16.740</td>\n",
       "      <td>21.59</td>\n",
       "      <td>110.10</td>\n",
       "      <td>869.5</td>\n",
       "      <td>0.09610</td>\n",
       "      <td>0.13360</td>\n",
       "      <td>0.13480</td>\n",
       "      <td>0.06018</td>\n",
       "      <td>...</td>\n",
       "      <td>29.02</td>\n",
       "      <td>133.50</td>\n",
       "      <td>1229.0</td>\n",
       "      <td>0.1563</td>\n",
       "      <td>0.3835</td>\n",
       "      <td>0.54090</td>\n",
       "      <td>0.18130</td>\n",
       "      <td>0.4863</td>\n",
       "      <td>0.08633</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>862722</td>\n",
       "      <td>B</td>\n",
       "      <td>6.981</td>\n",
       "      <td>13.43</td>\n",
       "      <td>43.79</td>\n",
       "      <td>143.5</td>\n",
       "      <td>0.11700</td>\n",
       "      <td>0.07568</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>...</td>\n",
       "      <td>19.54</td>\n",
       "      <td>50.41</td>\n",
       "      <td>185.2</td>\n",
       "      <td>0.1584</td>\n",
       "      <td>0.1202</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.2932</td>\n",
       "      <td>0.09382</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>118</th>\n",
       "      <td>864877</td>\n",
       "      <td>M</td>\n",
       "      <td>15.780</td>\n",
       "      <td>22.91</td>\n",
       "      <td>105.70</td>\n",
       "      <td>782.6</td>\n",
       "      <td>0.11550</td>\n",
       "      <td>0.17520</td>\n",
       "      <td>0.21330</td>\n",
       "      <td>0.09479</td>\n",
       "      <td>...</td>\n",
       "      <td>30.50</td>\n",
       "      <td>130.30</td>\n",
       "      <td>1272.0</td>\n",
       "      <td>0.1855</td>\n",
       "      <td>0.4925</td>\n",
       "      <td>0.73560</td>\n",
       "      <td>0.20340</td>\n",
       "      <td>0.3274</td>\n",
       "      <td>0.12520</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433</th>\n",
       "      <td>908445</td>\n",
       "      <td>M</td>\n",
       "      <td>18.820</td>\n",
       "      <td>21.97</td>\n",
       "      <td>123.70</td>\n",
       "      <td>1110.0</td>\n",
       "      <td>0.10180</td>\n",
       "      <td>0.13890</td>\n",
       "      <td>0.15940</td>\n",
       "      <td>0.08744</td>\n",
       "      <td>...</td>\n",
       "      <td>30.93</td>\n",
       "      <td>145.30</td>\n",
       "      <td>1603.0</td>\n",
       "      <td>0.1390</td>\n",
       "      <td>0.3463</td>\n",
       "      <td>0.39120</td>\n",
       "      <td>0.17080</td>\n",
       "      <td>0.3007</td>\n",
       "      <td>0.08314</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>530</th>\n",
       "      <td>91858</td>\n",
       "      <td>B</td>\n",
       "      <td>11.750</td>\n",
       "      <td>17.56</td>\n",
       "      <td>75.89</td>\n",
       "      <td>422.9</td>\n",
       "      <td>0.10730</td>\n",
       "      <td>0.09713</td>\n",
       "      <td>0.05282</td>\n",
       "      <td>0.04440</td>\n",
       "      <td>...</td>\n",
       "      <td>27.98</td>\n",
       "      <td>88.52</td>\n",
       "      <td>552.3</td>\n",
       "      <td>0.1349</td>\n",
       "      <td>0.1854</td>\n",
       "      <td>0.13660</td>\n",
       "      <td>0.10100</td>\n",
       "      <td>0.2478</td>\n",
       "      <td>0.07757</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>525</th>\n",
       "      <td>91805</td>\n",
       "      <td>B</td>\n",
       "      <td>8.571</td>\n",
       "      <td>13.10</td>\n",
       "      <td>54.53</td>\n",
       "      <td>221.3</td>\n",
       "      <td>0.10360</td>\n",
       "      <td>0.07632</td>\n",
       "      <td>0.02565</td>\n",
       "      <td>0.01510</td>\n",
       "      <td>...</td>\n",
       "      <td>18.45</td>\n",
       "      <td>63.30</td>\n",
       "      <td>275.6</td>\n",
       "      <td>0.1641</td>\n",
       "      <td>0.2235</td>\n",
       "      <td>0.17540</td>\n",
       "      <td>0.08512</td>\n",
       "      <td>0.2983</td>\n",
       "      <td>0.10490</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>855625</td>\n",
       "      <td>M</td>\n",
       "      <td>19.070</td>\n",
       "      <td>24.81</td>\n",
       "      <td>128.30</td>\n",
       "      <td>1104.0</td>\n",
       "      <td>0.09081</td>\n",
       "      <td>0.21900</td>\n",
       "      <td>0.21070</td>\n",
       "      <td>0.09961</td>\n",
       "      <td>...</td>\n",
       "      <td>33.17</td>\n",
       "      <td>177.40</td>\n",
       "      <td>1651.0</td>\n",
       "      <td>0.1247</td>\n",
       "      <td>0.7444</td>\n",
       "      <td>0.72420</td>\n",
       "      <td>0.24930</td>\n",
       "      <td>0.4670</td>\n",
       "      <td>0.10380</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>914580</td>\n",
       "      <td>B</td>\n",
       "      <td>12.470</td>\n",
       "      <td>17.31</td>\n",
       "      <td>80.45</td>\n",
       "      <td>480.1</td>\n",
       "      <td>0.08928</td>\n",
       "      <td>0.07630</td>\n",
       "      <td>0.03609</td>\n",
       "      <td>0.02369</td>\n",
       "      <td>...</td>\n",
       "      <td>24.34</td>\n",
       "      <td>92.82</td>\n",
       "      <td>607.3</td>\n",
       "      <td>0.1276</td>\n",
       "      <td>0.2506</td>\n",
       "      <td>0.20280</td>\n",
       "      <td>0.10530</td>\n",
       "      <td>0.3035</td>\n",
       "      <td>0.07661</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>337</th>\n",
       "      <td>897630</td>\n",
       "      <td>M</td>\n",
       "      <td>18.770</td>\n",
       "      <td>21.43</td>\n",
       "      <td>122.90</td>\n",
       "      <td>1092.0</td>\n",
       "      <td>0.09116</td>\n",
       "      <td>0.14020</td>\n",
       "      <td>0.10600</td>\n",
       "      <td>0.06090</td>\n",
       "      <td>...</td>\n",
       "      <td>34.37</td>\n",
       "      <td>161.10</td>\n",
       "      <td>1873.0</td>\n",
       "      <td>0.1498</td>\n",
       "      <td>0.4827</td>\n",
       "      <td>0.46340</td>\n",
       "      <td>0.20480</td>\n",
       "      <td>0.3679</td>\n",
       "      <td>0.09870</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10 rows × 33 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         id diagnosis  radius_mean  texture_mean  perimeter_mean  area_mean  \\\n",
       "90   861648         B       14.620         24.02           94.57      662.7   \n",
       "35   854253         M       16.740         21.59          110.10      869.5   \n",
       "101  862722         B        6.981         13.43           43.79      143.5   \n",
       "118  864877         M       15.780         22.91          105.70      782.6   \n",
       "433  908445         M       18.820         21.97          123.70     1110.0   \n",
       "530   91858         B       11.750         17.56           75.89      422.9   \n",
       "525   91805         B        8.571         13.10           54.53      221.3   \n",
       "42   855625         M       19.070         24.81          128.30     1104.0   \n",
       "497  914580         B       12.470         17.31           80.45      480.1   \n",
       "337  897630         M       18.770         21.43          122.90     1092.0   \n",
       "\n",
       "     smoothness_mean  compactness_mean  concavity_mean  concave points_mean  \\\n",
       "90           0.08974           0.08606         0.03102              0.02957   \n",
       "35           0.09610           0.13360         0.13480              0.06018   \n",
       "101          0.11700           0.07568         0.00000              0.00000   \n",
       "118          0.11550           0.17520         0.21330              0.09479   \n",
       "433          0.10180           0.13890         0.15940              0.08744   \n",
       "530          0.10730           0.09713         0.05282              0.04440   \n",
       "525          0.10360           0.07632         0.02565              0.01510   \n",
       "42           0.09081           0.21900         0.21070              0.09961   \n",
       "497          0.08928           0.07630         0.03609              0.02369   \n",
       "337          0.09116           0.14020         0.10600              0.06090   \n",
       "\n",
       "     ...  texture_worst  perimeter_worst  area_worst  smoothness_worst  \\\n",
       "90   ...          29.11           102.90       803.7            0.1115   \n",
       "35   ...          29.02           133.50      1229.0            0.1563   \n",
       "101  ...          19.54            50.41       185.2            0.1584   \n",
       "118  ...          30.50           130.30      1272.0            0.1855   \n",
       "433  ...          30.93           145.30      1603.0            0.1390   \n",
       "530  ...          27.98            88.52       552.3            0.1349   \n",
       "525  ...          18.45            63.30       275.6            0.1641   \n",
       "42   ...          33.17           177.40      1651.0            0.1247   \n",
       "497  ...          24.34            92.82       607.3            0.1276   \n",
       "337  ...          34.37           161.10      1873.0            0.1498   \n",
       "\n",
       "     compactness_worst  concavity_worst  concave points_worst  symmetry_worst  \\\n",
       "90              0.1766          0.09189               0.06946          0.2522   \n",
       "35              0.3835          0.54090               0.18130          0.4863   \n",
       "101             0.1202          0.00000               0.00000          0.2932   \n",
       "118             0.4925          0.73560               0.20340          0.3274   \n",
       "433             0.3463          0.39120               0.17080          0.3007   \n",
       "530             0.1854          0.13660               0.10100          0.2478   \n",
       "525             0.2235          0.17540               0.08512          0.2983   \n",
       "42              0.7444          0.72420               0.24930          0.4670   \n",
       "497             0.2506          0.20280               0.10530          0.3035   \n",
       "337             0.4827          0.46340               0.20480          0.3679   \n",
       "\n",
       "     fractal_dimension_worst  Unnamed: 32  \n",
       "90                   0.07246          NaN  \n",
       "35                   0.08633          NaN  \n",
       "101                  0.09382          NaN  \n",
       "118                  0.12520          NaN  \n",
       "433                  0.08314          NaN  \n",
       "530                  0.07757          NaN  \n",
       "525                  0.10490          NaN  \n",
       "42                   0.10380          NaN  \n",
       "497                  0.07661          NaN  \n",
       "337                  0.09870          NaN  \n",
       "\n",
       "[10 rows x 33 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's load the cancer dataset\n",
    "dataset = pd.read_csv('./datasets/cancer_dataset.csv')\n",
    "# print the number of rows in the data set\n",
    "number_of_rows = len(dataset)\n",
    "# reminder, the data looks like this\n",
    "dataset.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_3d_lls(x, y, z, lls_sol, title=\"\"):\n",
    "    # plot\n",
    "    fig = plt.figure(figsize=(5, 5))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    ax.scatter(x, y, z, label='Y')\n",
    "    ax.scatter(x, y, lls_sol, label='Xw')\n",
    "    ax.legend()\n",
    "    ax.set_xlabel('Radius Mean')\n",
    "    ax.set_ylabel('Area Mean')\n",
    "    ax.set_zlabel('Perimeter Mean')\n",
    "    ax.set_title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def batch_generator(x, y, batch_size, shuffle=True):\n",
    "    \"\"\"\n",
    "    This function generates batches for a given dataset x.\n",
    "    \"\"\"\n",
    "    N, L = x.shape\n",
    "    num_batches = N // batch_size\n",
    "    batch_x = []\n",
    "    batch_y = []\n",
    "    if shuffle:\n",
    "        # shuffle\n",
    "        rand_gen = np.random.RandomState(0)\n",
    "        shuffled_indices = rand_gen.permutation(np.arange(N))\n",
    "        x = x[shuffled_indices, :]\n",
    "        y = y[shuffled_indices, :]\n",
    "    for i in range(N):\n",
    "        batch_x.append(x[i, :])\n",
    "        batch_y.append(y[i, :])\n",
    "        if len(batch_x) == batch_size:\n",
    "            yield np.array(batch_x).reshape(batch_size, L), np.array(batch_y).reshape(batch_size, 1)\n",
    "            batch_x = []\n",
    "            batch_y = []\n",
    "    if batch_x:\n",
    "        yield np.array(batch_x).reshape(-1, L), np.array(batch_y).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **Pseudocode** for Linear Regression:\n",
    "    * **Require**: Learning rate $\\alpha_k$\n",
    "    * **Require**: Initial parameter $w$\n",
    "    * **While** stopping criterion not met **do**\n",
    "        * Sample a minibatch of $m$ examples from the training set ($m=1$ for SGD)\n",
    "        * Set $\\tilde{X} = [x_1,...,x_m] $ with corresponding targets $\\tilde{Y} = [y_1,...,y_m]$\n",
    "        * Compute gradient: $g \\leftarrow 2\\tilde{X}^T\\tilde{X}w - 2\\tilde{X}^T \\tilde{Y}$\n",
    "        * Apply update: $w \\leftarrow w - \\alpha_k g$\n",
    "        * $k \\leftarrow k + 1$\n",
    "    * **end while**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total batches: 56\n"
     ]
    }
   ],
   "source": [
    "# multivaraite mini-batch gradient descent\n",
    "X = dataset[['radius_mean', 'area_mean']].values\n",
    "Y = dataset[['perimeter_mean']].values\n",
    "# Scaling\n",
    "X = (X - X.mean(axis=0, keepdims=True)) / X.std(axis=0, keepdims=True)\n",
    "Y = (Y - Y.mean(axis=0, keepdims=True)) / Y.std(axis=0, keepdims=True)\n",
    "N = X.shape[0]\n",
    "batch_size = 10\n",
    "num_batches = N // batch_size\n",
    "print(\"total batches:\", num_batches)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter: 0 batch: 0  w = \n",
      "[[0.]\n",
      " [0.]]\n",
      "iter: 0 batch: 50  w = \n",
      "[[0.4391737 ]\n",
      " [0.41735388]]\n",
      "iter: 1 batch: 0  w = \n",
      "[[0.45621431]\n",
      " [0.43296123]]\n",
      "iter: 1 batch: 50  w = \n",
      "[[0.50458588]\n",
      " [0.46953377]]\n",
      "iter: 2 batch: 0  w = \n",
      "[[0.50659246]\n",
      " [0.46976394]]\n",
      "iter: 2 batch: 50  w = \n",
      "[[0.51664408]\n",
      " [0.46913792]]\n",
      "iter: 3 batch: 0  w = \n",
      "[[0.51715596]\n",
      " [0.46786206]]\n",
      "iter: 3 batch: 50  w = \n",
      "[[0.52339741]\n",
      " [0.46367398]]\n",
      "iter: 4 batch: 0  w = \n",
      "[[0.52374047]\n",
      " [0.4622501 ]]\n",
      "iter: 4 batch: 50  w = \n",
      "[[0.5295512 ]\n",
      " [0.45779193]]\n",
      "iter: 5 batch: 0  w = \n",
      "[[0.52985556]\n",
      " [0.456353  ]]\n",
      "iter: 5 batch: 50  w = \n",
      "[[0.53556725]\n",
      " [0.45194588]]\n",
      "iter: 6 batch: 0  w = \n",
      "[[0.53584598]\n",
      " [0.45050492]]\n",
      "iter: 6 batch: 50  w = \n",
      "[[0.54149192]\n",
      " [0.44617918]]\n",
      "iter: 7 batch: 0  w = \n",
      "[[0.54174661]\n",
      " [0.44473749]]\n",
      "iter: 7 batch: 50  w = \n",
      "[[0.54733087]\n",
      " [0.44049501]]\n",
      "iter: 8 batch: 0  w = \n",
      "[[0.54756198]\n",
      " [0.43905271]]\n",
      "iter: 8 batch: 50  w = \n",
      "[[0.55308576]\n",
      " [0.43489257]]\n",
      "iter: 9 batch: 0  w = \n",
      "[[0.55329364]\n",
      " [0.43344969]]\n",
      "iter: 9 batch: 50  w = \n",
      "[[0.55875783]\n",
      " [0.42937075]]\n"
     ]
    }
   ],
   "source": [
    "num_epochs = 10\n",
    "alpha_k = 0.001\n",
    "batch_gen = batch_generator(X, Y, batch_size, shuffle=True)\n",
    "L = X.shape[-1]\n",
    "# initialize w\n",
    "w = np.zeros((L, 1))\n",
    "for i in range(num_epochs):\n",
    "    for batch_i, batch in enumerate(batch_gen):\n",
    "        batch_x, batch_y = batch\n",
    "        if batch_i % 50 == 0:\n",
    "            print(\"iter:\", i, \"batch:\", batch_i, \" w = \")\n",
    "            print(w)\n",
    "        gradient = 2 * batch_x.T @ batch_x @ w - 2 * batch_x.T @ batch_y\n",
    "        w = w - alpha_k * gradient\n",
    "    batch_gen = batch_generator(X, Y, batch_size, shuffle=True)\n",
    "\n",
    "lls_sol = X @ w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w:\n",
      "[[0.55894282]\n",
      " [0.42792729]]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3560d0ab9b21404995cfd251a0d31441",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": "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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,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' width=500.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "plot_3d_lls(X[:,0], X[:, 1], Y, lls_sol, \"Breast Cancer - Radius Mean vs. Area Mean vs. Perimeter Mean - LLS Mini-Batch GD\")\n",
    "print(\"w:\")\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/clouds/100/000000/stopwatch.png\" style=\"height:50px;display:inline\"> Learning Rate Scheduling (Annealing)\n",
    "---\n",
    "* When training deep networks, it is usually helpful to anneal (gradually change the rate) the learning rate over time. \n",
    "    * **Physics intuition**: with a high learning rate, the system contains too much *kinetic energy* and the parameter vector bounces around chaotically, unable to settle down into deeper, but narrower parts of the loss function. \n",
    "* Knowing when to decay the learning rate can be tricky: decay it **slowly** and you’ll be wasting computation bouncing around chaotically with little improvement for a long time. But decay it **too aggressively** and the system will cool too quickly, unable to reach the best position it can. \n",
    "* There are three common types of implementing the learning rate decay: step deacy, exponential decay and $1/t$ decay.\n",
    "    * Recently, *cyclic* learning schedulers, such as <a href=\"https://www.kaggle.com/residentmario/one-cycle-learning-rate-schedulers\">One-cycle learning rate scheduler</a> or *cosine* scheduling, have been gaining popularity as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **(Multi) Step decay**: Reduce the learning rate by some factor every few epochs. \n",
    "    * Typical values might be reducing the learning rate by a half every 5 epochs, or by 0.1 every 20 epochs. These numbers depend heavily on the type of problem and the model. \n",
    "    * One heuristic you may see in practice is to watch the *validation error* while training with a fixed learning rate, and reduce the learning rate by a constant (e.g. 0.5) whenever the validation error stops improving."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **Exponential decay**: has the mathematical form: $$\\alpha = \\alpha_0 \\exp(-kt),$$ where $\\alpha_0, k$ are hyperparameters and $t$ is the iteration number (but you can also use units of epochs).\n",
    "    * $\\alpha_0$ is the initial learning rate.\n",
    "    * $k$ is also referred to as the `gamma` ($\\gamma$) hyperparameter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **1/t decay**: has the mathematical form: $$\\alpha = \\frac{\\alpha_0}{1+kt},$$ where $\\alpha_0,k$ are hyperparameters and $t$ is the iteration number."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **Cosine annealing**: has the mathematical form: $$ \\alpha = \\alpha_{min} +\\frac{1}{2}(\\alpha_0 - \\alpha_{min})\\left(1 +\\cos\\left(\\frac{t}{t_{max}}\\pi\\right) \\right), $$ where $\\alpha_{min}$ is the minimum learning rate (deafult is 0) and $t_{max}$ is number of iterations to perform a cycle."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* In practice, we usually find that the **step decay** is slightly preferable because the hyperparameters it involves (the fraction of decay and the step timings in units of epochs) are more interpretable than the hyperparameter $k$. \n",
    "* Lastly, if you can afford the computational budget, you can try a slower decay and train for a longer time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/cotton/64/000000/olympic-torch.png\" style=\"height:50px;display:inline\"> Learning Rate Scheduling in PyTorch\n",
    "---\n",
    "* We will use learning rate scheduling to train the neural network models later in the course.\n",
    "* PyTorch offers several schedulers which can be found <a href=\"https://pytorch.org/docs/stable/optim.html#how-to-adjust-learning-rate\">here</a>.\n",
    "* A typical workflow with schedulers (learning rate scheduling should be applied **after** optimizer’s update):\n",
    "<code>\n",
    "scheduler = ...\n",
    "for epoch in range(100):\n",
    "    train(...)\n",
    "    validate(...)\n",
    "    scheduler.step()\n",
    "</code>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* <a href=\"https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.StepLR.html#torch.optim.lr_scheduler.StepLR\">`torch.optim.lr_scheduler.StepLR`</a>\n",
    "* <a href=\"https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.MultiStepLR.html#torch.optim.lr_scheduler.MultiStepLR\">`torch.optim.lr_scheduler.MultiStepLR`</a>\n",
    "* <a href=\"https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.ExponentialLR.html#torch.optim.lr_scheduler.ExponentialLR\">`torch.optim.lr_scheduler.ExponentialLR`</a>\n",
    "* <a href=\"https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.CosineAnnealingLR.html#torch.optim.lr_scheduler.CosineAnnealingLR\">`torch.optim.lr_scheduler.CosineAnnealingLR`</a>\n",
    "* <a href=\"https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.OneCycleLR.html#torch.optim.lr_scheduler.OneCycleLR\">`torch.optim.lr_scheduler.OneCycleLR`</a>\n",
    "* <a href=\"https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.CyclicLR.html#torch.optim.lr_scheduler.CyclicLR\">`torch.optim.lr_scheduler.CyclicLR`</a>\n",
    "* And more..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Reducing LR on Plateau\n",
    "---\n",
    "* Reduce learning rate when a metric has stopped improving. Usually the validation accuracy.\n",
    "* Models often benefit from reducing the learning rate by a factor of 2-10 once learning does not improve. \n",
    "* This scheduler reads a metrics quantity and if no improvement is seen for a `patience` number of epochs, the learning rate is reduced.\n",
    "* In PyTorch: <a href=\"https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.ReduceLROnPlateau.html#torch.optim.lr_scheduler.ReduceLROnPlateau\">`torch.optim.lr_scheduler.ReduceLROnPlateau`</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<center><img src=\"./assets/tut_opt_reduce_lr.png\" style=\"height:300px\"></center>\n",
    "\n",
    "* <a href=\"https://www.researchgate.net/publication/339252130_Exponential_Step_Sizes_for_Non-Convex_Optimization\">Exponential Step Sizes for Non-Convex Optimization, Li et al. 2020</a>.\n",
    "* Plots of the train loss and test accuracy for training a 20-layer Residual Network to do image classification on CIFAR-10.\n",
    "* The number of milestones in the legend denotes how many times we can choose to decrease the step size during training."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/clouds/100/000000/hill-descent-control.png\" style=\"height:50px;display:inline\"> Momentum & Nesterov Momentum\n",
    "---\n",
    "* Gradient descent is simple and has many virtues, but **speed** is not one of them.\n",
    "* For a step-size small enough, gradient descent makes a monotonic improvement at every iteration. It should always converge (sometimes to a local minimum).\n",
    "* **Momentum update** is another optimization approach that *almost always* enjoys better convergence rates in deep networks. \n",
    "    * It can be seen as a **\"global\" (equally for all parameters) adaptive learning rate**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* This update can be motivated from a physical perspective of the optimization problem. In particular, the loss can be interpreted as the height of a *hilly terrain*.\n",
    "    *  Initializing the parameters with random numbers is equivalent to setting a particle with zero initial velocity at some location. The optimization process can then be seen as equivalent to the process of simulating the parameter vector (i.e. a particle) as rolling on the landscape.\n",
    "    * Since the force on the particle is related to the gradient of potential energy (i.e. $F=−\\nabla U$ ), the force felt by the particle is precisely the (negative) gradient of the loss function. \n",
    "    * Moreover, $F=ma$ so the (negative) gradient is in this view proportional to the acceleration of the particle.\n",
    "    * The physics view suggests an update in which the gradient only directly influences the velocity (and maintains information about the acceleration), which in turn has an effect on the position."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Momentum proposes the following tweak to gradient descent, giving gradient descent **a short-term memory**: $$ z^{k+1} = \\beta z^k -\\alpha\\nabla f(w^k) $$ $$ w^{k+1} = w^k + z^{k+1} $$\n",
    "    * $\\alpha$ is the learning rate.\n",
    "\n",
    "* When $\\beta = 0$ , we recover gradient descent. But for $\\beta = 0.99$ (sometimes 0.999, if things are really bad), this appears to be the boost we need. Our iterations regain that speed and boldness it lost, speeding to the optimum with a renewed energy.\n",
    "* $\\beta$ is a variable that is sometimes called *momentum*.\n",
    "* Effectively, this variable **damps the velocity and reduces the kinetic energy of the system**, or otherwise the particle would never come to a stop at the bottom of a hill.\n",
    "* With Momentum update, the parameter vector will build up velocity in any direction that has consistent gradient.\n",
    "* <a href=\"https://distill.pub/2017/momentum/\">Momentum Demo</a>\n",
    "* Note: Momentum usually works in **larger batches** and may break in smaller batches."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<center><img src=\"./assets/sgd-mom.png\" style=\"height:250px\"></center>\n",
    "\n",
    "* <a href=\"https://dominikschmidt.xyz/nesterov-momentum\">Image Source</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Nesterov Momentum\n",
    "---\n",
    "* Nesterov Momentum is a slightly different version of the momentum update that has gained popularity. \n",
    "* It enjoys stronger theoretical convergence guarantees for **convex functions** and in practice it also consistenly works slightly better than standard momentum.\n",
    "* The core idea behind Nesterov momentum is that when the current parameter vector is at some position $x$, then looking at the momentum update above, we know that the momentum term alone (i.e. ignoring the second term with the gradient) is about to nudge the parameter vector by $\\beta * z_k$. \n",
    "* Therefore, if we are about to compute the gradient, we can treat the future approximate position $x + \\beta * z_k$ as a **“lookahead”** - this is a point in the vicinity of where we are soon going to end up. \n",
    "* Hence, it makes sense to compute the **gradient** at $x + \\beta * z_k$ instead of at the “old/stale” position $x$, since while the gradient term always points in the right direction, the momentum term may not. \n",
    "* If the momentum term points in the wrong direction or overshoots, the gradient can still \"go back\" and correct it in the same update step."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **Nesterov Momentum**: $$ z^{k+1} = \\beta z^k -\\alpha \\nabla f(w^k +\\beta z^k) $$ $$ w^{k+1} = w^k + z^{k+1} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<center><img src=\"./assets/sgd-nag.png\" style=\"height:250px\"></center>\n",
    "\n",
    "* <a href=\"https://dominikschmidt.xyz/nesterov-momentum\">Image Source</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/cotton/64/000000/olympic-torch.png\" style=\"height:50px;display:inline\"> Momentum in PyTorch\n",
    "---\n",
    "* `torch.optim.SGD(model.parameters(), lr=learning_rate, momentum=0.9, nesterov=True)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# simple optimizer and lr scheduling example\n",
    "# courtesy of: deeplearningwizard.com/deep_learning/boosting_models_pytorch/lr_scheduling/\n",
    "\n",
    "from torch.optim.lr_scheduler import ReduceLROnPlateau\n",
    "\n",
    "'''\n",
    "STEP 1: LOADING DATASET\n",
    "'''\n",
    "\n",
    "train_dataset = dsets.MNIST(root='./data', \n",
    "                            train=True, \n",
    "                            transform=transforms.ToTensor(),\n",
    "                            download=True)\n",
    "\n",
    "test_dataset = dsets.MNIST(root='./data', \n",
    "                           train=False, \n",
    "                           transform=transforms.ToTensor())\n",
    "\n",
    "'''\n",
    "STEP 2: MAKING DATASET ITERABLE\n",
    "'''\n",
    "\n",
    "batch_size = 100\n",
    "n_iters = 6000\n",
    "num_epochs = n_iters / (len(train_dataset) / batch_size)\n",
    "num_epochs = int(num_epochs)\n",
    "\n",
    "train_loader = torch.utils.data.DataLoader(dataset=train_dataset, \n",
    "                                           batch_size=batch_size, \n",
    "                                           shuffle=True)\n",
    "\n",
    "test_loader = torch.utils.data.DataLoader(dataset=test_dataset, \n",
    "                                          batch_size=batch_size, \n",
    "                                          shuffle=False)\n",
    "\n",
    "'''\n",
    "STEP 3: CREATE MODEL CLASS\n",
    "'''\n",
    "class SimpleModel(nn.Module):\n",
    "    def __init__(self, input_dim, hidden_dim, output_dim):\n",
    "        super(SimpleModel, self).__init__()\n",
    "        # Linear function\n",
    "        self.fc1 = nn.Linear(input_dim, hidden_dim) \n",
    "        # Non-linearity\n",
    "        self.relu = nn.ReLU()\n",
    "        # Linear function (readout)\n",
    "        self.fc2 = nn.Linear(hidden_dim, output_dim)  \n",
    "\n",
    "    def forward(self, x):\n",
    "        # Linear function\n",
    "        out = self.fc1(x)\n",
    "        # Non-linearity\n",
    "        out = self.relu(out)\n",
    "        # Linear function (readout)\n",
    "        out = self.fc2(out)\n",
    "        return out\n",
    "'''\n",
    "STEP 4: INSTANTIATE MODEL CLASS AND DEVICE\n",
    "'''\n",
    "input_dim = 28 * 28\n",
    "hidden_dim = 100\n",
    "output_dim = 10\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "model = SimpleModel(input_dim, hidden_dim, output_dim).to(device)\n",
    "\n",
    "'''\n",
    "STEP 5: INSTANTIATE LOSS CLASS\n",
    "'''\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "\n",
    "\n",
    "'''\n",
    "STEP 6: INSTANTIATE OPTIMIZER CLASS\n",
    "'''\n",
    "learning_rate = 0.1\n",
    "\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate, momentum=0.9, nesterov=True)\n",
    "\n",
    "'''\n",
    "STEP 7: INSTANTIATE STEP LEARNING SCHEDULER CLASS\n",
    "'''\n",
    "# lr = lr * factor \n",
    "# mode='max': look for the maximum validation accuracy to track\n",
    "# patience: number of epochs - 1 where loss plateaus before decreasing LR\n",
    "        # patience = 0, after 1 bad epoch, reduce LR\n",
    "# factor = decaying factor\n",
    "scheduler = ReduceLROnPlateau(optimizer, mode='max', factor=0.1, patience=0, verbose=True)\n",
    "# multi-step\n",
    "# scheduler = MultiStepLR(optimizer, milestones=[50, 80, 100], gamma=0.1)  # reduce lr by x0.1 at epoch 50, 80 and 100\n",
    "\n",
    "'''\n",
    "STEP 7: TRAIN THE MODEL\n",
    "'''\n",
    "iteration = 0\n",
    "for epoch in range(num_epochs):\n",
    "    for i, (images, labels) in enumerate(train_loader):\n",
    "        # Send images and labels to device\n",
    "        images = images.view(-1, 28 * 28).to(device)\n",
    "        labeles = labels.to(device)\n",
    "\n",
    "        # Forward pass to get output/logits\n",
    "        outputs = model(images)\n",
    "\n",
    "        # Calculate Loss: softmax --> cross entropy loss\n",
    "        loss = criterion(outputs, labels)\n",
    "        \n",
    "        # Clear gradients w.r.t. parameters\n",
    "        optimizer.zero_grad()\n",
    "\n",
    "        # Getting gradients w.r.t. parameters\n",
    "        loss.backward()\n",
    "\n",
    "        # Updating parameters\n",
    "        optimizer.step()\n",
    "\n",
    "        iteration += 1\n",
    "\n",
    "        if iteration % 500 == 0:\n",
    "            # Calculate Accuracy         \n",
    "            correct = 0\n",
    "            total = 0\n",
    "            # Iterate through test dataset\n",
    "            for images, labels in test_loader:\n",
    "                # Send images and labels to device\n",
    "                images = images.view(-1, 28 * 28).to(device)\n",
    "                labeles = labels.to(device)\n",
    "\n",
    "                # Forward pass only to get logits/output\n",
    "                outputs = model(images)\n",
    "\n",
    "                # Get predictions from the maximum value\n",
    "                _, predicted = torch.max(outputs.data, 1)\n",
    "\n",
    "                # Total number of labels\n",
    "                total += labels.size(0)\n",
    "\n",
    "                # Total correct predictions\n",
    "                # Without .item(), it is a uint8 tensor which will not work when you pass this number to the scheduler\n",
    "                correct += (predicted == labels).sum().item()\n",
    "\n",
    "            accuracy = 100 * correct / total\n",
    "\n",
    "            # Print Loss\n",
    "            # print('Iteration: {}. Loss: {}. Accuracy: {}'.format(iter, loss.data[0], accuracy))\n",
    "\n",
    "    # Decay Learning Rate, pass validation accuracy for tracking at every epoch\n",
    "    print('Epoch {} completed'.format(epoch))\n",
    "    print('Loss: {}. Accuracy: {}'.format(loss.item(), accuracy))\n",
    "    print('-' * 20)\n",
    "    scheduler.step(accuracy)  # accuracy is used to track down a plateau\n",
    "    # scheduler.step()  # for multi-step, no need to pass anything to the scheduler when advancing it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/dusk/64/000000/wired-network.png\" style=\"height:50px;display:inline\"> Adaptive Learning Rate Methods\n",
    "---\n",
    "**Adapative learning methods compute individual learning rates for different parameters.**\n",
    "Previously, we performed an update for all parameters $w$ (or $\\theta$) at once as every parameter $w_i$ used the same learning rate $\\alpha$.\n",
    "\n",
    "\n",
    "Popular algorithms include: AdaGrad, Rprop, RMSprop, Adam and more..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/cotton/64/000000/olympic-torch.png\" style=\"height:50px;display:inline\"> Optimizers in PyTorch\n",
    "---\n",
    "All optimizers mentioned in this tutorial and more can be imported from the `torch.optim` library. Check out the full list of available optimizers in <a href=\"https://pytorch.org/docs/stable/optim.html#algorithms\">this link</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/plasticine/100/000000/horizontal-settings-mixer.png\" style=\"height:50px;display:inline\"> Adagrad\n",
    "---\n",
    "* **Adagrad**: one of the first adaptive learning rate algorithm, with the basic idea of adapting the learning rate to the parameters by performing smaller updates (i.e. low learning rates) for parameters associated with *frequently* occurring features, and larger updates (i.e. high learning rates) for parameters associated with *infrequent* features.\n",
    "    * For this reason, it works well with *sparse* data.\n",
    "* Adagrad uses a different learning rate for every parameter $w_i$ at every time step $k$.\n",
    "* We denote:\n",
    "    * $\\alpha$ - the learning rate.\n",
    "    * $g_k = \\nabla f(w^k)$, the gradient at time step $k$, and $g_{i, k}$ the *partial* derivative w.r.t. the parameter $w_i$ at time step $k$.\n",
    "    * $G_k \\in \\mathbb{R}^{d \\times d}$ - a *diagonal* matrix, where each element $G_{i,i}^k$ is the **sum of squares of the gradients w.r.t $w_i$ up to time step $k$**, $G_{i, i}^k = \\sum_{j=1}^k g_{i, j}^2$.\n",
    "    * $\\epsilon$, a \"smoothing\" term that prevents division by zero, deafult is $10^{-8}$, but can range from $10^{-4}$ to $10^{-8}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* The Adagrad update rule: $$ w_i^{k+1} = w_i^k -\\frac{\\alpha}{\\sqrt{G_{i,i}^k + \\epsilon}} \\cdot g_{i, k} $$\n",
    "* Interestingly, without the square root operation, the algorithm performs much worse.\n",
    "* In vectorized form, we use the matrix-vector product $\\odot$ between $G_k$ and $g_k$: $$ w^{k+1} = w^k -\\frac{\\alpha}{\\sqrt{G^k + \\epsilon}} \\odot g_{k} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Adagrad eliminates, or alleviates, the need to manually tune the learning rate, which is nice. \n",
    "* Most implementations use a default value of 0.01 for the learning rate.\n",
    "* However, its main **weakness** is the accumulation of the squared gradients (a positive quantity) in the denominator which keeps growing during training and causes the learning rate to **shrink** and eventually become very small, at which point the algorithm doesn't acquire additional knowledge."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/cotton/64/000000/olympic-torch.png\" style=\"height:50px;display:inline\"> Adagrad in PyTorch\n",
    "---\n",
    "* `torch.optim.Adagrad(model.parameters(), lr=learning_rate, initial_accumulator_value=0, eps=1e-10)`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/cute-clipart/64/000000/square-root.png\" style=\"height:50px;display:inline\"> RMSprop\n",
    "---\n",
    "* **RMSprop**: an unpublished (no official paper) optimization algorithm designed for neural networks, first proposed by Geoffrey Hinton in <a href=\"https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf\">lecture 6 (slide 29)</a> of the online course “Neural Networks for Machine Learning”.\n",
    "* The RMSProp update adjusts the **Adagrad** method in a very simple way in an attempt to reduce its aggressive, monotonically decreasing learning rate.\n",
    "* In particular, it uses **a moving average of squared gradients** instead.\n",
    "* We denote:\n",
    "    * $\\alpha$ - the learning rate.\n",
    "    * $g_k = \\nabla f(w^k)$\n",
    "    * $\\mathbb{E}[g^2]$ - moving average of squared gradients (stored in a cache with squared gradients from previous iterations).\n",
    "    * $\\beta$ - moving average parameter (good default value — 0.9)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* The RMSprop update rule: $$ \\mathbb{E}[g^2]_{k+1} = \\beta\\mathbb{E}[g^2]_k + (1-\\beta)g_k^2 $$ $$ w^{k+1} = w^k -\\frac{\\alpha}{\\sqrt{\\mathbb{E}[g^2]_{k+1}}}\\nabla f(w^k) $$\n",
    "* The learning rate is adapted by dividing by the root of squared gradient, but since we only have the estimate of the gradient on the current mini-batch, we need instead to use the moving average of it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/cotton/64/000000/olympic-torch.png\" style=\"height:50px;display:inline\"> RMSprop in PyTorch\n",
    "---\n",
    "* `torch.optim.RMSprop(model.parameters(), lr=learning_rate, alpha=0.99)`\n",
    "    * `alpha` is $\\beta$ from the equations above, the moving average parameter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/clouds/100/000000/heat-map.png\" style=\"height:50px;display:inline\"> Adam - Adaptive Moment Estimation\n",
    "---\n",
    "* **Adam**: another optimization method that computes adaptive learning rates for each parameter. \n",
    "* Adam combines the advantages of Adagrad, RMSprop and Momentum: It uses the **squared gradients to scale the learning rate** like RMSprop and it takes advantage of momentum by using **moving average of the gradient instead of the gradient itself** like SGD with momentum.\n",
    "* In addition to storing an exponentially decaying average of past **squared gradients** like Adadelta and RMSprop, Adam also keeps an exponentially decaying average of past **gradients** similar to momentum.\n",
    "    * Whereas momentum can be seen as a ball running down a slope, Adam behaves like a heavy ball with friction, and thus prefers flat minima in the error surface."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "* We denote:\n",
    "    * $\\alpha$ - the learning rate.\n",
    "    * $m$ - moving average of gradients. Estimates the first moment (mean) of the gardients.\n",
    "    * $v$ - moving average of squared gradients. Estimates the second momemnt (variance) of the gradients.\n",
    "    * $\\beta_1$ - moving average parameter for $m$ (default: 0.9).\n",
    "    * $\\beta_2$ - moving average parameter for $v$ (default: 0.999)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* The Adam update rule: $$ \\mathbb{E}[g]_{k+1} = m_{k+1} = \\beta_1 m_k + (1-\\beta_1)\\nabla f(w^k) = \\beta_1 m_k + (1-\\beta_1)g_k $$  $$ \\mathbb{E}[g^2]_{k+1} = v_{k+1} = \\beta_2 v_k + (1-\\beta_2)(\\nabla f(w^k))^2 = \\beta_2 v_k + (1-\\beta_2)g^2_k $$ Then, we use an **unbiased** estimation: $$ \\hat{m}_{k+1} = \\frac{m_{k+1}}{1 -\\beta_1^{k+1}} $$ $$ \\hat{v}_{k+1} = \\frac{v_{k+1}}{1 -\\beta_2^{k+1}} $$ (the $\\beta$'s are taken with the power of the current iteration) $$ w^{k+1} = w^k -\\frac{\\alpha}{\\sqrt{\\hat{v}_{k+1}} +\\epsilon}\\hat{m}_{k+1} $$\n",
    "\n",
    "* $\\epsilon$, a \"smoothing\" term that prevents diviosn by zero, deafult's is $10^{-8}$, but can range from $10^{-4}$ to $10^{-8}$. Note that the default $\\epsilon = 1e-8$ might be sub-optimal for various tasks, and thus it is recommended to test other values $\\in [1e-3, 1e-12]$ as well.\n",
    "    *  <a href=\"https://arxiv.org/abs/2011.02150\">EAdam Optimizer: How ε Impact Adam</a> - Wei Yuan, Kai-Xin Gao.\n",
    "    *  <a href=\"http://zna.do/epsilon\">ε, a A Nuisance No More</a> - Zack Nado."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/cotton/64/000000/olympic-torch.png\" style=\"height:50px;display:inline\"> Adam in PyTorch\n",
    "---\n",
    "* `torch.optim.Adam(model.parameters(), lr=learning_rate, betas=(0.9, 0.999))`\n",
    "    \n",
    "If you want to use weight decay (i.e., $L_2$ regularization on the weights), use `AdamW`, which adds a fix to the update rule to account for the weight regularization.\n",
    "\n",
    "* <a href=\"https://pytorch.org/docs/stable/generated/torch.optim.AdamW.html#torch.optim.AdamW\">`torch.optim.AdamW(model.parameters(), lr=learning_rate, betas=(0.9, 0.999), weight_decay=0.01)`</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/doodle/96/000000/scales--v1.png\" style=\"height:50px;display:inline\"> Comparison Between Methods\n",
    "---\n",
    "<center><img src=\"./assets/loss_conturs_all_grad_w_adam.gif\" style=\"height:300px\"></center>\n",
    "\n",
    "* Contours of a loss surface and time evolution of different optimization algorithms. \n",
    "* Notice the \"overshooting\" behavior of **momentum-based methods**, which makes the optimization look like a ball rolling down the hill.\n",
    "\n",
    "* <a href=\"https://github.com/ilguyi/optimizers.numpy\">Image Source</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<center><img src=\"./assets/saddle_point_all_grad.gif\" style=\"height:250px\"></center>\n",
    "\n",
    "* A visualization of a **saddle point** in the optimization landscape, where the curvature along different dimension has different signs (one dimension curves up and another down). \n",
    "* Notice that SGD has a very hard time breaking symmetry and gets *stuck* on the top. \n",
    "* Conversely, algorithms such as RMSprop will see very low gradients in the saddle direction. Due to the denominator term in the RMSprop update, this will increase the effective learning rate along this direction, helping RMSProp proceed.\n",
    "\n",
    "* Image credit: <a href=\"https://twitter.com/alecrad\">Alec Radford</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <img src=\"https://img.icons8.com/bubbles/50/new.png\" style=\"height:50px;display:inline\"> Recent Advances in Optimizers\n",
    "---\n",
    "* Adam, \"the king of optimizers\", has been the go-to optimizer for some time now, and while there were several attempts to dethrone it, there was not a major breakthrough in the optimizers literature to replace it, and Adam is still widely used in all major deep learning domains.\n",
    "* However, several notable recent works have proposed alternatives that show great promise as candidates to replace Adam, which we cover below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <img src=\"https://img.icons8.com/cute-clipart/64/pray.png\" style=\"height:50px;display:inline\"> AdaBelief\n",
    "---\n",
    "* Introduced in <a href=\"https://arxiv.org/abs/2010.07468\">AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients</a> - Zhuang et al., NeurIPS 2020.\n",
    "* **Motivation**: achieve three goals -- fast convergence as in adaptive methods, good generalization as in SGD, and training stability.\n",
    "* **Main idea**: adapt the step-size according to the \"belief\" in the current gradient direction -- the moving average (EMA) of the noisy gradient serves as the prediction of the gradient at the next time step; take a small step if the prediction and current gradient have a large difference and otherwise take a large step.\n",
    "  \n",
    "<center><img src=\"./assets/adabelief_algo.png\" style=\"height:250px\"></center>\n",
    "\n",
    "<center><img src=\"./assets/adabelief2.gif\" style=\"height:300px\"></center>\n",
    "\n",
    "\n",
    "* <a href=\"https://juntang-zhuang.github.io/adabelief/\">Website</a>, <a href=\"https://github.com/juntang-zhuang/Adabelief-Optimizer\">PyTorch Code</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <img src=\"https://img.icons8.com/external-bzzricon-smooth-bzzricon-studio/64/external-mad-puppy-bzzricon-smooth-bzzricon-smooth-bzzricon-studio.png\" style=\"height:50px;display:inline\"> MADGRAD\n",
    "---\n",
    "* Introduced in <a href=\"https://arxiv.org/abs/2101.11075\">Adaptivity without Compromise: A Momentumized, Adaptive, Dual Averaged Gradient Method for Stochastic Optimization</a> - Aaron Defazio and Samy Jelassi (META AI Research), JMLR 2022.\n",
    "* **Motivation**: combine adaptivity with strong generalization performance.\n",
    "* **Main idea**: based the dual averaging formulation of AdaGrad, combined with momentum and adaptivity to achieve the generalization performance of SGD and the fast convergence of Adam. \n",
    "  \n",
    "<center><img src=\"./assets/madgrad_algo.PNG\" style=\"height:250px\"></center>\n",
    "\n",
    "* <a href=\"https://madgrad.readthedocs.io/en/latest/\">Website</a>, <a href=\"https://github.com/facebookresearch/madgrad\">PyTorch Code</a>.\n",
    "    * Notes: GPU-only. Typically, the same learning rate schedule that is used for SGD or Adam may be used. MADGRAD requires less weight decay than other methods, often as little as zero. Momentum values used for SGD or Adam’s $\\beta_1$ should work here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <img src=\"https://img.icons8.com/external-goofy-color-kerismaker/96/external-Seesaw-momentum-science-goofy-color-kerismaker.png\" style=\"height:50px;display:inline\"> Adan\n",
    "---\n",
    "* Introduced in <a href=\"https://arxiv.org/abs/2208.06677\">Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models</a> - Xie et al., 2022.\n",
    "* **Motivation**: improve the deep learning model training speed by utilizing an accurate and stable estimation of the gradient moments.\n",
    "* **Main idea**: a new Nesterov momentum estimation (NME) method, which avoids the extra overhead of computing gradient at the extrapolation point and used to estimate the gradient's first-order and second-order moments in adaptive gradient algorithms for convergence acceleration.\n",
    "  \n",
    "<center><img src=\"./assets/adan_algo.PNG\" style=\"height:300px\"></center>\n",
    "\n",
    "<center><img src=\"./assets/adan_table.PNG\" style=\"height:300px\"></center>\n",
    "\n",
    "* <a href=\"https://github.com/sail-sg/Adan\">PyTorch Code</a>.\n",
    "    * Notes: Adan has a slightly higher GPU memory cost than Adam/AdamW on a single node."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <img src=\"https://img.icons8.com/clouds/100/overtime.png\" style=\"height:50px;display:inline\"> Schedule-Free Optimization\n",
    "---\n",
    "* Introduced in <a href=\"https://arxiv.org/abs/2405.15682\">The Road Less Scheduled</a> - Defazio et al., 2024.\n",
    "* Presents two new optimizers: **Schedule-free SGD** and **Schedule-free Adam**, that do not require learning rate scheduling (but can optionally be combined with one).\n",
    "* **Motivation**: learning rate schedules that depend on a stopping-step $T$ greatly outperform schedulers that do not require specification of $T$.\n",
    "* **Main idea**: eliminating the need for $T$ by unifiying scheduling and iterate averaging with no additional hyper-parameters.\n",
    "  \n",
    "<center><img src=\"./assets/schedule_free_adam_algo.PNG\" style=\"height:300px\"></center>\n",
    "\n",
    "<center><img src=\"./assets/schedule_free_graphs.PNG\" style=\"height:300px\"></center>\n",
    "\n",
    "* <a href=\"https://github.com/facebookresearch/schedule_free\">PyTorch Code</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/bubbles/50/000000/video-playlist.png\" style=\"height:50px;display:inline\"> Recommended Videos\n",
    "---\n",
    "#### <img src=\"https://img.icons8.com/cute-clipart/64/000000/warning-shield.png\" style=\"height:30px;display:inline\"> Warning!\n",
    "* These videos do not replace the lectures and tutorials.\n",
    "* Please use these to get a better understanding of the material, and not as an alternative to the written material.\n",
    "\n",
    "#### Video By Subject\n",
    "\n",
    "* Gradient Descent - <a href=\"https://www.youtube.com/watch?v=sDv4f4s2SB8\">Gradient Descent, Step-by-Step</a>\n",
    "    * <a href=\"https://www.youtube.com/watch?v=jc2IthslyzM\">Mathematics of Gradient Descent - Intelligence and Learning</a>\n",
    "* Stochastic Gradient Descent - <a href=\"https://www.youtube.com/watch?v=vMh0zPT0tLI\">Stochastic Gradient Descent, Clearly Explained</a>\n",
    "* Momentum - <a href=\"https://www.youtube.com/watch?v=k8fTYJPd3_I\">Gradient Descent With Momentum (C2W2L06)</a>\n",
    "* RMSProp - <a href=\"https://www.youtube.com/watch?v=_e-LFe_igno\">RMSProp (C2W2L07)</a>\n",
    "* Adam - <a href=\"https://www.youtube.com/watch?v=JXQT_vxqwIs\">Adam Optimization Algorithm (C2W2L08)</a>\n",
    "* Learning Rate Decay - <a href=\"https://www.youtube.com/watch?v=QzulmoOg2JE\">Learning Rate Decay (C2W2L09)</a>\n",
    "* Momentum, Adagrad, RMSProp, Adam - <a href=\"https://www.youtube.com/watch?v=gmwxUy7NYpA\">UC Berkeley, STAT 157 - Momentum, Adagrad, RMSProp, Adam</a>\n",
    "* AdaBelief - <a href=\"https://www.youtube.com/watch?v=oGH7dmwvuaY\">AdaBelief Optimizer: Theory and Practical Guidelines</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/dusk/64/000000/prize.png\" style=\"height:50px;display:inline\"> Credits\n",
    "---\n",
    "* Icons made by <a href=\"https://www.flaticon.com/authors/becris\" title=\"Becris\">Becris</a> from <a href=\"https://www.flaticon.com/\" title=\"Flaticon\">www.flaticon.com</a>\n",
    "* Icons from <a href=\"https://icons8.com/\">Icons8.com</a> - https://icons8.com\n",
    "* Datasets from <a href=\"https://www.kaggle.com/\">Kaggle</a> - https://www.kaggle.com/\n",
    "* Examples and code snippets were taken from <a href=\"http://shop.oreilly.com/product/0636920052289.do\">\"Hands-On Machine Learning with Scikit-Learn and TensorFlow\"</a>\n",
    "* <a href=\"https://cs231n.github.io/neural-networks-3/\">CS231n: Convolutional Neural Networks for Visual Recognition</a>\n",
    "* <a href=\"https://www.deeplearningwizard.com/deep_learning/boosting_models_pytorch/lr_scheduling/\">Deep Learning Wizard -Learning Rate Scheduling</a>\n",
    "* <a href=\"https://dominikschmidt.xyz/nesterov-momentum\">Understanding Nesterov Momentum (NAG)</a>\n",
    "* <a href=\"https://ruder.io/optimizing-gradient-descent/\">Sebastian Ruder - An overview of gradient descent optimization algorithms</a>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}