{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "brNDGX-kvzds"
   },
   "source": [
    "# Template for Notes for CIS 521 Midterm 2\n",
    "\n",
    "The midterm exam for CIS 521 will be **open notes**. No other matierals are allowed for the exam - you may not use the textbook, the internet, a Python envionement, or communicate with anyone during the exam. \n",
    "\n",
    "This python notebook is where you should save all of your notes.  It provides a structured template that allows you to add summaries for each of the textbook sections that are part of the required reading, plus room for lecture notes and definitions.\n",
    "\n",
    "Your summaries must be written in your own words.  Do not copy and paste from the textbook.  Do not share your notes with classmates, or copy any of your classmates' notes.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aPtM8g7R0Pds"
   },
   "source": [
    "# Instructions\n",
    "\n",
    "1. Make a copy of this Google Colab file. From the colab menu, pick **File > Save a copy in Drive**.  That will save a copy of this notebook in your Google drive.\n",
    "2. Go through each section of the notebook, and fill in all the summaries for each chapter and its corresponding sections.  Be sure to save your work frequently!\n",
    "3. Read the notes below about how you can format your summaries.\n",
    "4. In addition to these notes, you are allowed 1 page (both sides) for figures or handwritten notes.\n",
    "5. Submit your version of this notebook to Gradescope before you start the exam.\n",
    "6. If you are taking the exam in person, then you must print a copy of your notes for yourself.   Here's how to print: \n",
    "* Run the last cell of this notebook\n",
    "* Click the \"Mirror cell in tab\" button (this is located in the upper right corner of the cell, immediately to the right of the trash can).  This will open the cell.  \n",
    "* In Chrome, you can then print your notes using the **File > Print** option from the browser's menu.  \n",
    "* In the print options, change the layout from Landscape to Portrait. \n",
    "* Clicking the Save, will save a PDF that you can then print.\n",
    "\n",
    "## Formatting Notes\n",
    "\n",
    "1. The max length for each section's summary is 500 words / 3000 characters.\n",
    "2. You can also write a 2000 word summary of the lectures for each module.\n",
    "3. You may also write definitions of concepts for each module.  The definitions should be written in your own words (not copy and pasted), and they should be no more than 20 words long for each concept. \n",
    "2. You can use Markdown formatting for your summaries. \n",
    "3. You can use Latex formatting for equations. Put two dollar signs before and after your equation like this: \n",
    "$$ \\epsilon = \\frac{1}{mc^2} $$\n",
    "4. When you write python code or psuedocode algorithms, you should surround it with triple backticks like this:\n",
    "```\n",
    "def function():\n",
    "      print('hello world')\n",
    "```\n",
    "5. Write \\ whenever you want to keep writing on the next line without a newline being inserted."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "cw5IpDLCZa4W"
   },
   "source": [
    "## Example summary\n",
    "\n",
    "This is a sample summary of [Section 2.1.1](https://web.stanford.edu/~jurafsky/slp3/2.pdf ) of Jurfasky and Martin's Speech and Language Processing's book\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "lzaavW96tcxM",
    "outputId": "1a0276ec-792d-46e6-d640-484f8d5b0b28"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The example summary is 116 words long, so you could write an additional 384 words.\n"
     ]
    }
   ],
   "source": [
    "chapter_2_1_example = \"\"\"\n",
    "Regular expressions are an algebraic notation for characterizing \\\n",
    "a set of strings that are useful for searching for a pattern or through a corpus.\\\n",
    "Only the first matching result will be shown. The search string is case sensitive, \\\n",
    "but it can consist of a single character or a sequence of characters. \\\n",
    "While square braces specify a disjunction of characters, the dash can more easily look \\\n",
    "for characters over a range. The caret specifies the non-existence of a character. \\\n",
    "Additionally, the (?) is used to for flexibility on a single character, meaning \\\n",
    "\"the preceding character or nothing\". More importantly, the Kleene star means zero or \\\n",
    "more occurrences of the immediately previous character or regular expression in square braces.\\\n",
    "...\n",
    "\"\"\"\n",
    "\n",
    "length = len(chapter_2_1_example.split(\" \"))\n",
    "print(\"The example summary is {len} words long, so you could write an additional \\\n",
    "{remaining} words.\".format(len=length, remaining=(500-length)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "s3Uk9gQTevcj"
   },
   "source": [
    "## Example summary length\n",
    "\n",
    "The maximum summary length for each section is 500 words / 3000 characters.  Hopefully you'll find that to be quite generous. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "8DvZ57A-djo1",
    "outputId": "731702d8-a6f1-4638-f883-1269d848e468"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The length in words is 500\n",
      "The length in characters is 3030\n"
     ]
    }
   ],
   "source": [
    "# This is an example of a 500 word placeholder\n",
    "placeholder = \"\"\"ultrices vitae auctor eu augue ut lectus arcu bibendum at varius \\\n",
    " vel pharetra vel turpis nunc eget lorem dolor sed viverra ipsum nunc aliquet \\\n",
    " bibendum enim facilisis gravida neque convallis a cras semper auctor neque vitae \\\n",
    " tempus quam pellentesque nec nam aliquam sem et tortor consequat id porta nibh \\\n",
    " venenatis cras sed felis eget velit aliquet sagittis id consectetur purus ut \\\n",
    " faucibus pulvinar elementum integer enim neque volutpat ac tincidunt vitae semper \\ \n",
    " quis lectus nulla at volutpat diam ut venenatis tellus in metus vulputate eu \\\n",
    " scelerisque felis imperdiet proin fermentum leo vel orci porta non pulvinar neque \\ \n",
    " laoreet suspendisse interdum consectetur libero id faucibus nisl tincidunt eget \\\n",
    " nullam non nisi est sit amet facilisis magna etiam tempor orci eu lobortis \\\n",
    " elementum nibh tellus molestie nunc non blandit massa enim nec dui nunc mattis \\\n",
    " enim ut tellus elementum sagittis vitae et leo duis ut diam quam nulla porttitor \\\n",
    " massa id neque aliquam vestibulum morbi blandit cursus risus at ultrices mi tempus \\\n",
    " imperdiet nulla malesuada pellentesque elit eget gravida cum sociis natoque \\\n",
    " penatibus et magnis dis parturient montes nascetur ridiculus mus mauris vitae \\\n",
    " ultricies leo integer malesuada nunc vel risus commodo viverra maecenas accumsan \\\n",
    " lacus vel facilisis volutpat est velit egestas dui id ornare arcu odio ut sem nulla \\\n",
    " pharetra diam sit amet nisl suscipit adipiscing bibendum est ultricies integer \\\n",
    " quis auctor elit sed vulputate mi sit amet mauris commodo quis imperdiet massa \\\n",
    " tincidunt nunc pulvinar sapien et ligula ullamcorper malesuada proin libero nunc \\\n",
    " consequat interdum varius sit amet mattis vulputate enim nulla aliquet porttitor \\\n",
    " lacus luctus accumsan tortor posuere ac ut consequat semper viverra nam libero \\\n",
    " justo laoreet sit amet cursus sit amet dictum sit amet justo donec enim diam \\\n",
    " vulputate ut pharetra sit amet aliquam id diam maecenas ultricies mi eget mauris \\\n",
    " pharetra et ultrices neque ornare aenean euismod elementum nisi quis eleifend quam \\\n",
    " adipiscing vitae proin sagittis nisl rhoncus mattis rhoncus urna neque viverra justo \\\n",
    " nec ultrices dui sapien eget mi proin sed libero enim sed faucibus turpis in \\\n",
    " eu mi bibendum neque egestas congue quisque egestas diam in arcu cursus euismod \\\n",
    " quis viverra nibh cras pulvinar mattis nunc sed blandit libero volutpat sed cras \\\n",
    " ornare arcu dui vivamus arcu felis bibendum ut tristique et egestas quis ipsum \\\n",
    " suspendisse ultrices gravida dictum fusce ut placerat orci nulla pellentesque \\\n",
    " dignissim enim sit amet venenatis urna cursus eget nunc scelerisque viverra mauris \\\n",
    " in aliquam sem fringilla ut morbi tincidunt augue interdum velit euismod in \\\n",
    " pellentesque massa placerat duis ultricies lacus sed turpis tincidunt id aliquet \\\n",
    " risus feugiat in ante metus dictum at tempor commodo ullamcorper a lacus vestibulum \\\n",
    " sed arcu non odio euismod lacinia at quis risus sed vulputate odio ut enim blandit \\\n",
    " volutpat maecenas volutpat blandit aliquam etiam erat velit scelerisque in \\\n",
    " dictum non consectetur a erat nam at lectus urna\"\"\"\n",
    "\n",
    "print(\"The length in words is\", len(placeholder.split(' ')))\n",
    "print(\"The length in characters is\", len(placeholder))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5yG3-YncJfTB"
   },
   "source": [
    "# Permissions to use your summaries\n",
    "\n",
    "We'd like to use your summaries to help develop better educational resources like [remember.school](https://remember.school) or a question-answering system about the textbook.  \n",
    "\n",
    "1. Please enter your name.  \n",
    "\n",
    "2. If you grant permission for us to use your summaries under a [Creative Commons License](https://creativecommons.org/licenses/by/4.0/), please set ```permission = True```.  If you do not grant permission, please set it to false. Your answer won't affect your grade.\n",
    "\n",
    "3. If you grant us permission, and you'd like to remain anonymous, set ```anonymous = True```.  We'll remove your name before sharing your summaries with anyone. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "2RECnJArJew4"
   },
   "outputs": [],
   "source": [
    "name = \"\"\n",
    "permission = True\n",
    "anonymous = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GZZXyrV-xuAp"
   },
   "source": [
    "# Module 8 - Markov Decision Process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "id": "Y2NfE1CKxzS-"
   },
   "outputs": [],
   "source": [
    "# Russell and Norvig, AIMA Chapter 16, “Making Simple Decisions” (16.1-16.3)\n",
    "\n",
    "sample_equation = r\"\"\"  \n",
    "  \n",
    "$P(\\text{RESULT}(a)=s') = \\sum_s P(s)P(s'|s,a)$  \n",
    "  \n",
    "$EU(a)=\\sum\\limits_{s^{\\prime}}P(result(a)=s^{\\prime})U(s^{\\prime})$\n",
    "\"\"\"\n",
    "\n",
    "chapter16_1 = \"\"\"maximum expected utility (MEU) says that a rational agent should choose the action that maximizes the agent’s expected utility.  \n",
    "  \n",
    "  \"\"\"  + sample_equation\n",
    "chapter16_2 =  \"\"\" six constraints that we require any reasonable preference relation to obey:  \n",
    "1. orderability: the agent cannot avoid deciding. any A and B is comparable.  \n",
    "2. transitivity: if A>B and B>C then A>C.  \n",
    "3. continuity: if A>B>C, then there is a p such that [p, A;1-p, C]=B.  \n",
    "4. substituability: if A=B, then [p, A;1-p, C]=[p, B;1-p, C].  \n",
    "5. monocity: if A>B, then p>q <=> [p, A;1-p, B]>[q, A;1-q, B].  \n",
    "6. decomposability: [p, A; 1-p, [q, B; (1-q), C]]=[p, A; (1-p)q, B; (1-p)(1-q), C].  \n",
    "  \n",
    "These constraints are known as the axioms of utility theory. Violation of these constraints results in irrationality.  \n",
    "\n",
    "As in game-playing, in a deterministic environment an agent needs only a preference ranking on states—the numbers don’t matter. \n",
    "This is called a value function or ordinal utility function.  \n",
    "  \n",
    "It is important to remember that the existence of a utility function that describes an agent’s preference behavior \n",
    "does not necessarily mean that the agent is explicitly maximizing that utility function in its own deliberations. \n",
    "\"\"\"\n",
    "\n",
    "\n",
    "chapter16_3 =  \"\"\"If we want to build a decision-theoretic system that helps a human make decisions or acts\n",
    "on his or her behalf, we must first work out what the human’s utility function is. This\n",
    "process, often called preference elicitation, involves presenting choices to the human and\n",
    "using the observed preferences to pin down the underlying utility function.  \n",
    "  \n",
    "there is no absolute scale for utilities, but it is helpful, nonetheless, \n",
    "to establish some scale on which utilities can be recorded and compared for any particular problem. \n",
    "Usually we use normalized utilities where the best utility we can get is 1 and the worse is 0.  \n",
    "  \n",
    "standard lottery: [p, best; (1-p), worse].  \n",
    "  \n",
    "This tendency for the estimated expected utility of the best choice to be too high as k(number of events) grows is called\n",
    "the optimizer’s curse.  \n",
    "  \n",
    "Decision theory is a normative theory: it describes how a rational agent should act. \n",
    "A descriptive theory, on the other hand, describes how actual agents—for example, humans— really do act.  \n",
    "  \n",
    "Certain effect: people are strongly attracted by gains that are certain.  \n",
    "  \n",
    "ambiguity aversion: Most people elect the known probability rather than the unknown unknowns.  \n",
    "  \n",
    "framing effect: Experiments show that people like a\n",
    "medical procedure that is described as having a “90% survival rate” about twice as much as\n",
    "one described as having a “10% death rate,”  \n",
    "\n",
    "anchoring effect: People feel more comfortable making relative utility judgments rather than absolute ones.\n",
    "\"\"\"\n",
    "\n",
    "\n",
    "# Russell and Norvig, AIMA Chapter 17, “Making Complex Decision” (17.1-17.2)\n",
    "chapter17_1 = \"\"\"Markovian: the probability of reaching s' from s depends only on s and not on the history of earlier states.  \n",
    "  \n",
    "a sequential decision problem for a fully observable, stochastic environment \n",
    "with a Markovian transition model and additive rewards is called a Markov decision process, or MDP.  \n",
    "   \n",
    "dynamic programming: simplifying a problem by recursively breaking it into smaller pieces and remembering the optimal solutions to the pieces.  \n",
    "  \n",
    "A solution to MDP must specify what the agent should do for any state that the agent might reach. A solution of this kind is called a policy.  \n",
    "  \n",
    "An optimal policy is a policy that yields the highest expected utility.  \n",
    "  \n",
    "A policy that depends on the time is called nonstationary.  \n",
    "\n",
    "An optimal action depends only on the current state, and the optimal policy is stationary.  \n",
    "\n",
    "A policy that is guaranteed to reach a terminal state is called a proper policy.  \n",
    "  \n",
    "Bellman equation: $U(s)=\\max\\limits_{a\\in A(s)}\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U(s^{\\prime})]$, $O(|S|^2|A|)$.  \n",
    "  \n",
    "action-utility function, or Q-function: $Q(s, a)=\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U(s^{\\prime})]$,  \n",
    "then we have $U(s)=\\max\\limits_{a\\in A(s)}Q(s, a)$ and $\\pi^{*}=argmax Q(s, a)$\n",
    "\"\"\"\n",
    "chapter17_2 =  \"\"\"\n",
    "Value Iteration:  each step is called a Bellman update: $U_{i+1}(s)=\\max\\limits_{a\\in A(s)}\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U_i(s^{\\prime})]$.  \n",
    "\n",
    "Policy Iteration: each step contains two parts:  \n",
    "1. policy evaluation: given a policy $\\pi_{i}$, we calculate $U_i=U^{\\pi_i}$, the utility of each state under this policy.  \n",
    "2. policy improvement: Calculate a new MEU policy $\\pi_{i+1}$, using one-step look-ahead based on $U_i$.  \n",
    "  \n",
    "Linear Programming: we seek to minimize $U(s)$ for all subject to the inequalities $U(s)\\geq\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U(s^{\\prime})]$.  \n",
    "  \n",
    "Value iteration and policy iteration are offline algorithms: like the A* algorithm, \n",
    "they generate an optimal solution for the problem, which can then be executed by a simple agent. \n",
    "For sufficiently large MDPs, such as the Tetris MDP with states, exact offline solution, \n",
    "even by a polynomial-time algorithm, is not possible.\n",
    "\n",
    "<img src=./contraction.png width=500 height=100/>\n",
    "\"\"\"\n",
    "\n",
    "# Lecture notes \n",
    "module8_lecture_notes = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "\n",
    "# Definitions of concepts from Module 8.\n",
    "# You can define any term in the textbook or lecture, \n",
    "# but you most use your own words for the definitions.\n",
    "# Each definition should be at most 25 words long.\n",
    "\n",
    "module8_definitions = {\n",
    "\"utility function\" : \"Your definition here\",\n",
    "\"expected utility\" : \"your definition here\",\n",
    "\"etc.\": \"your definition here\",\n",
    "}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "elCCgY64spuq"
   },
   "source": [
    "## Preview of your notes for Module 8\n",
    "\n",
    "Here's a preview of your how your notes will be displayed.  At the end of this Python notebook, we'll aggregate your notes for all modules together into a single display.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "gYYeNcdM_maE",
    "outputId": "d4a72fc4-c2f5-43a5-c703-7406f8d1811b"
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   "outputs": [
    {
     "data": {
      "text/markdown": [
       "# Module 8: Markov Decision Processes\n",
       "## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n",
       "maximum expected utility (MEU) says that a rational agent should choose the action that maximizes the agent’s expected utility.  \n",
       "  \n",
       "    \n",
       "  \n",
       "$P(\\text{RESULT}(a)=s') = \\sum_s P(s)P(s'|s,a)$  \n",
       "  \n",
       "$EU(a)=\\sum\\limits_{s^{\\prime}}P(result(a)=s^{\\prime})U(s^{\\prime})$\n",
       "\n",
       "\n",
       "## AIMA Chapter 16.2 The Basis of Utility Theory\n",
       " six constraints that we require any reasonable preference relation to obey:  \n",
       "1. orderability: the agent cannot avoid deciding. any A and B is comparable.  \n",
       "2. transitivity: if A>B and B>C then A>C.  \n",
       "3. continuity: if A>B>C, then there is a p such that [p, A;1-p, C]=B.  \n",
       "4. substituability: if A=B, then [p, A;1-p, C]=[p, B;1-p, C].  \n",
       "5. monocity: if A>B, then p>q <=> [p, A;1-p, B]>[q, A;1-q, B].  \n",
       "6. decomposability: [p, A; 1-p, [q, B; (1-q), C]]=[p, A; (1-p)q, B; (1-p)(1-q), C].  \n",
       "  \n",
       "These constraints are known as the axioms of utility theory. Violation of these constraints results in irrationality.  \n",
       "\n",
       "As in game-playing, in a deterministic environment an agent needs only a preference ranking on states—the numbers don’t matter. \n",
       "This is called a value function or ordinal utility function.  \n",
       "  \n",
       "It is important to remember that the existence of a utility function that describes an agent’s preference behavior \n",
       "does not necessarily mean that the agent is explicitly maximizing that utility function in its own deliberations. \n",
       "\n",
       "\n",
       "## AIMA Chapter 16.3 Utility Functions\n",
       "If we want to build a decision-theoretic system that helps a human make decisions or acts\n",
       "on his or her behalf, we must first work out what the human’s utility function is. This\n",
       "process, often called preference elicitation, involves presenting choices to the human and\n",
       "using the observed preferences to pin down the underlying utility function.  \n",
       "  \n",
       "there is no absolute scale for utilities, but it is helpful, nonetheless, \n",
       "to establish some scale on which utilities can be recorded and compared for any particular problem. \n",
       "Usually we use normalized utilities where the best utility we can get is 1 and the worse is 0.  \n",
       "  \n",
       "standard lottery: [p, best; (1-p), worse].  \n",
       "  \n",
       "This tendency for the estimated expected utility of the best choice to be too high as k(number of events) grows is called\n",
       "the optimizer’s curse.  \n",
       "  \n",
       "Decision theory is a normative theory: it describes how a rational agent should act. \n",
       "A descriptive theory, on the other hand, describes how actual agents—for example, humans— really do act.  \n",
       "  \n",
       "Certain effect: people are strongly attracted by gains that are certain.  \n",
       "  \n",
       "ambiguity aversion: Most people elect the known probability rather than the unknown unknowns.  \n",
       "  \n",
       "framing effect: Experiments show that people like a\n",
       "medical procedure that is described as having a “90% survival rate” about twice as much as\n",
       "one described as having a “10% death rate,”  \n",
       "\n",
       "anchoring effect: People feel more comfortable making relative utility judgments rather than absolute ones.\n",
       "\n",
       "\n",
       "## AIMA Chapter 17.1 Sequential Decision Problems\n",
       "Markovian: the probability of reaching s' from s depends only on s and not on the history of earlier states.  \n",
       "  \n",
       "a sequential decision problem for a fully observable, stochastic environment \n",
       "with a Markovian transition model and additive rewards is called a Markov decision process, or MDP.  \n",
       "   \n",
       "dynamic programming: simplifying a problem by recursively breaking it into smaller pieces and remembering the optimal solutions to the pieces.  \n",
       "  \n",
       "A solution to MDP must specify what the agent should do for any state that the agent might reach. A solution of this kind is called a policy.  \n",
       "  \n",
       "An optimal policy is a policy that yields the highest expected utility.  \n",
       "  \n",
       "A policy that depends on the time is called nonstationary.  \n",
       "\n",
       "An optimal action depends only on the current state, and the optimal policy is stationary.  \n",
       "\n",
       "A policy that is guaranteed to reach a terminal state is called a proper policy.  \n",
       "  \n",
       "Bellman equation: $U(s)=\\max\\limits_{a\\in A(s)}\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U(s^{\\prime})]$, $O(|S|^2|A|)$.  \n",
       "  \n",
       "action-utility function, or Q-function: $Q(s, a)=\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U(s^{\\prime})]$,  \n",
       "then we have $U(s)=\\max\\limits_{a\\in A(s)}Q(s, a)$ and $\\pi^{*}=argmax Q(s, a)$\n",
       "\n",
       "\n",
       "## AIMA Chapter 17.2 Algorithms for MDPs\n",
       "\n",
       "Value Iteration:  each step is called a Bellman update: $U_{i+1}(s)=\\max\\limits_{a\\in A(s)}\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U_i(s^{\\prime})]$.  \n",
       "\n",
       "Policy Iteration: each step contains two parts:  \n",
       "1. policy evaluation: given a policy $\\pi_{i}$, we calculate $U_i=U^{\\pi_i}$, the utility of each state under this policy.  \n",
       "2. policy improvement: Calculate a new MEU policy $\\pi_{i+1}$, using one-step look-ahead based on $U_i$.  \n",
       "  \n",
       "Linear Programming: we seek to minimize $U(s)$ for all subject to the inequalities $U(s)\\geq\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U(s^{\\prime})]$.  \n",
       "  \n",
       "Value iteration and policy iteration are offline algorithms: like the A* algorithm, \n",
       "they generate an optimal solution for the problem, which can then be executed by a simple agent. \n",
       "For sufficiently large MDPs, such as the Tetris MDP with states, exact offline solution, \n",
       "even by a polynomial-time algorithm, is not possible.\n",
       "\n",
       "<img src=./contraction.png width=500 height=100/>\n",
       "\n",
       "\n",
       "## Module 8 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 8 Definitions\n",
       "* **Utility function** - Your definition here\n",
       "* **Expected utility** - your definition here\n",
       "* **Etc.** - your definition here\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Preview of your summary\n",
    "#@markdown You don't need to modify anything in this cell. Just press play.\n",
    "from IPython.display import display, Markdown, Latex\n",
    "\n",
    "module8_sections = [\n",
    "  (\"AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\", chapter16_1),\n",
    "  (\"AIMA Chapter 16.2 The Basis of Utility Theory\", chapter16_2),\n",
    "  (\"AIMA Chapter 16.3 Utility Functions\", chapter16_3),\n",
    "  (\"AIMA Chapter 17.1 Sequential Decision Problems\", chapter17_1),\n",
    "  (\"AIMA Chapter 17.2 Algorithms for MDPs\", chapter17_2),\n",
    "  (\"Module 8 Lecture Notes\", module8_lecture_notes),\n",
    "]\n",
    "\n",
    "\n",
    "def length_check(sections):\n",
    "  warnings = \"\"\n",
    "  for section, summary in sections:\n",
    "    max_word_length = 500\n",
    "    max_character_length = 3000\n",
    "    if \"lecture\" in section.lower():\n",
    "      # It's OK to do longer summaries of the lectures\n",
    "      max_word_length = 2000\n",
    "      max_character_length = 12000  \n",
    "    if (len(summary) > max_character_length or len(summary.split(' ')) > max_word_length):\n",
    "      warnings += \"WARNING: Your summary of '{section}' is too long!\\n\".format(section=section)\n",
    "  return warnings\n",
    "\n",
    "def length_check_definitions(definitions):\n",
    "  warnings = \"\"\n",
    "  for concept, definition in definitions.items():\n",
    "    if(len(definition.split(' ')) > 25):\n",
    "      warnings += \"WARNING: Your definition of '{concept}' is too long!\\n\".format(concept=concept)\n",
    "  return warnings\n",
    "\n",
    "\n",
    "def format_module(module_num, title, sections, definitions, show_placeholder=False):\n",
    "  markdown = \"\"\n",
    "\n",
    "  # Check summary lengths\n",
    "  warnings = length_check(sections)\n",
    "  if warnings != \"\":\n",
    "    markdown += \"## \" + warnings\n",
    "\n",
    "  # Check definition lengths\n",
    "  warnings = length_check_definitions(definitions)\n",
    "  if warnings != \"\":\n",
    "    markdown += \"## \" + warnings\n",
    "\n",
    "  markdown += \"# Module {num}: {title}\\n\".format(num=module_num, title=title)\n",
    "\n",
    "\n",
    "  for section, summary in sections:\n",
    "    if show_placeholder and summary == \" Your summary here \":\n",
    "      summary = placeholder\n",
    "    markdown += \"## {section}\\n{summary}\\n\\n\".format(section=section, summary=summary)\n",
    "  \n",
    "  markdown += \"## Module {num} Definitions\\n\".format(num=module_num)\n",
    "  for concept, definition in definitions.items():\n",
    "    markdown += \"* **{concept}** - {definition}\\n\".format(concept=concept.capitalize(), definition=definition)\n",
    "  return markdown\n",
    "\n",
    "\n",
    "module8_markdown = format_module(8, \"Markov Decision Processes\", module8_sections, module8_definitions)\n",
    "display(Markdown(module8_markdown))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9xRbdqDox2zD"
   },
   "source": [
    "#Module 9 - Reinforcement Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "DpBvu7EMx7sy"
   },
   "outputs": [],
   "source": [
    "# Russell and Norvig, AIMA Section 17.3 “Bandit Problems”\n",
    "chapter17_3 =  \"\"\"a one-armed bandit is a slot machine. A gambler can insert a coin, \n",
    "pull the lever, and collect the winnings (if any). An -armed bandit has levers. \n",
    "Behind each lever is a fixed but unknown probability distribution of winnings; each pull samples from that unknown distribution. \n",
    "This is an example of exploration vs exploitation trade off.  \n",
    "  \n",
    "\n",
    "\"\"\"\n",
    "\n",
    "# Russell and Norvig, AIMA Chapter 22 “Reinforcement Learning” (Sections 22.1-22.5)\n",
    "chapter22_1 =  \"\"\"<img src=./different_ways.png width=500 height=100/>\n",
    "\n",
    "Model-Based Idea:\n",
    "1. Learn an approximate model based on experiences\n",
    "2. Solve for values as if the learned model were correct\n",
    "\n",
    "Step 1: Learn empirical MDP model\n",
    "1. Count outcomes s’ for each s, a\n",
    "2. Normalize to give an estimate of T\n",
    "3. Discover each R when we experience (s, a, s’)\n",
    "\n",
    "Step 2: Solve the learned MDP\n",
    "1. For example, use value iteration, as before\n",
    "\n",
    "MODEL-FREE REINFORCEMENT LEARNING: In these approaches the agent neither\n",
    "knows nor learns a transition model for the environment. \n",
    "Instead, it learns a more direct representation of how to behave. This comes in one of two varieties:\n",
    "1. action-utility learning(Q-learning)\n",
    "2. policy search(reflex agent)\n",
    "\n",
    "passive reinforcement learning: the agent’s policy is fixed and the task is to learn the utilities of states\n",
    "active reinforcement learning: the agent must also figure out what to do.\"\"\"\n",
    "chapter22_2 =  \"\"\"Direct Evaluation:\n",
    "<img src=./direct_evaluation1.png width=500 height=100/>\n",
    "<img src=./direct_evaluation2.png width=500 height=100/>\n",
    "<img src=./direct_evaluation3.png width=500 height=100/>\n",
    "For model-free approaches, we can't use policy iteration because we don't know T and R.\n",
    "\n",
    "Temperal Difference:\n",
    "<img src=./temperal_difference1.png width=500 height=100/>\n",
    "<img src=./temperal_difference2.png width=500 height=100/>\n",
    "<img src=./temperal_difference1.png width=500 height=100/>\n",
    "(we still don't know R and T)\n",
    "\"\"\"\n",
    "chapter22_3 =  \"\"\"\n",
    "Active RL:\n",
    "<img src=./active_RL.png width=500 height=100/>\n",
    "\n",
    "Q-learning:\n",
    "<img src=./Q-learning1.png width=500 height=100/>\n",
    "<img src=./Q-learning2.png width=500 height=100/>\n",
    "<img src=./Q-learning3.png width=500 height=100/>\n",
    "<img src=./regret.png width=500 height=100/>\n",
    "\n",
    "Approx Q-learning:\n",
    "<img src=./approx_Q.png width=500 height=100/>\"\"\"\n",
    "chapter22_4 =  \"\"\" Your summary here \"\"\"\n",
    "chapter22_5 =  \"\"\" Your summary here \"\"\"\n",
    "\n",
    "\n",
    "# Lecture notes \n",
    "module9_lecture_notes = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "# Each definition should be at most 25 words long.\n",
    "module9_definitions = {\n",
    "\"term\" : \"your definition here\",\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "cellView": "form",
    "colab": {
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    {
     "data": {
      "text/markdown": [
       "# Module 9: Reinforcement Learning\n",
       "## AIMA Chapter 17.3 Bandit Problems\n",
       "a one-armed bandit is a slot machine. A gambler can insert a coin, \n",
       "pull the lever, and collect the winnings (if any). An -armed bandit has levers. \n",
       "Behind each lever is a fixed but unknown probability distribution of winnings; each pull samples from that unknown distribution. \n",
       "This is an example of exploration vs exploitation trade off.  \n",
       "  \n",
       "\n",
       "\n",
       "\n",
       "## AIMA Chapter 22.1 Learning from Rewards\n",
       "<img src=./different_ways.png width=500 height=100/>\n",
       "\n",
       "Model-Based Idea:\n",
       "1. Learn an approximate model based on experiences\n",
       "2. Solve for values as if the learned model were correct\n",
       "\n",
       "Step 1: Learn empirical MDP model\n",
       "1. Count outcomes s’ for each s, a\n",
       "2. Normalize to give an estimate of T\n",
       "3. Discover each R when we experience (s, a, s’)\n",
       "\n",
       "Step 2: Solve the learned MDP\n",
       "1. For example, use value iteration, as before\n",
       "\n",
       "MODEL-FREE REINFORCEMENT LEARNING: In these approaches the agent neither\n",
       "knows nor learns a transition model for the environment. \n",
       "Instead, it learns a more direct representation of how to behave. This comes in one of two varieties:\n",
       "1. action-utility learning(Q-learning)\n",
       "2. policy search(reflex agent)\n",
       "\n",
       "passive reinforcement learning: the agent’s policy is fixed and the task is to learn the utilities of states\n",
       "active reinforcement learning: the agent must also figure out what to do.\n",
       "\n",
       "## AIMA Chapter 22.2 Passive Reinforcement Learning\n",
       "Direct Evaluation:\n",
       "<img src=./direct_evaluation1.png width=500 height=100/>\n",
       "<img src=./direct_evaluation2.png width=500 height=100/>\n",
       "<img src=./direct_evaluation3.png width=500 height=100/>\n",
       "For model-free approaches, we can't use policy iteration because we don't know T and R.\n",
       "\n",
       "Temperal Difference:\n",
       "<img src=./temperal_difference1.png width=500 height=100/>\n",
       "<img src=./temperal_difference2.png width=500 height=100/>\n",
       "<img src=./temperal_difference1.png width=500 height=100/>\n",
       "(we still don't know R and T)\n",
       "\n",
       "\n",
       "## AIMA Chapter 22.3 Active Reinforcement Learning\n",
       "\n",
       "Active RL:\n",
       "<img src=./active_RL.png width=500 height=100/>\n",
       "\n",
       "Q-learning:\n",
       "<img src=./Q-learning1.png width=500 height=100/>\n",
       "<img src=./Q-learning2.png width=500 height=100/>\n",
       "<img src=./Q-learning3.png width=500 height=100/>\n",
       "<img src=./regret.png width=500 height=100/>\n",
       "\n",
       "Approx Q-learning:\n",
       "<img src=./approx_Q.png width=500 height=100/>\n",
       "\n",
       "## AIMA Chapter 22.4 Generalization in Reinforcement Learning\n",
       " Your summary here \n",
       "\n",
       "## Module 9 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 9 Definitions\n",
       "* **Term** - your definition here\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Preview of your summary\n",
    "#@markdown You don't need to modify anything in this cell. Just press play.\n",
    "\n",
    "module9_sections = [\n",
    "  (\"AIMA Chapter 17.3 Bandit Problems\", chapter17_3),\n",
    "  (\"AIMA Chapter 22.1 Learning from Rewards\", chapter22_1),\n",
    "  (\"AIMA Chapter 22.2 Passive Reinforcement Learning\", chapter22_2),\n",
    "  (\"AIMA Chapter 22.3 Active Reinforcement Learning\", chapter22_3),\n",
    "  (\"AIMA Chapter 22.4 Generalization in Reinforcement Learning\", chapter22_4),\n",
    "  (\"Module 9 Lecture Notes\", module9_lecture_notes),\n",
    "]\n",
    "\n",
    "module9_markdown = format_module(9, \"Reinforcement Learning\", module9_sections, module9_definitions)\n",
    "display(Markdown(module9_markdown))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "46MQLR-Gx8dZ"
   },
   "source": [
    "#Module 10 - Probabilities and Language Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "BN0b1eVYx-nd"
   },
   "outputs": [],
   "source": [
    "# Russell and Norvig, AIMA 4th Edition, AIMA Chapter 12 “Quantifying Uncertainty” (Sections 12.1-12.7)\n",
    "chapter12_1 = \"\"\" Probabilistic inference: compute a desired probability from other known probabilities (e.g. conditional from joint) \n",
    "\n",
    "\"\"\"\n",
    "chapter12_2 = \"\"\" Your summary here \"\"\"\n",
    "chapter12_3 = \"\"\" Your summary here \"\"\"\n",
    "chapter12_4 = \"\"\" Your summary here \"\"\"\n",
    "chapter12_5 = r\"\"\"$P(b|a)=\\frac{P(a|b)P(b)}{P(a)}$\"\"\"\n",
    "chapter12_6 = \"\"\" Your summary here \"\"\"\n",
    "chapter12_7 = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "\n",
    "# Jurafsky and Martin, Speech and Language Processing Chapter 3 “N-Gram Language Models”  (Sections 3.1-3.5,3.7)\n",
    "SLP_chapter3_1 = \"\"\"\n",
    "<img src=./prob_lang_model1.png width=500 height=100/>\n",
    "<img src=./prob_lang_model2.png width=500 height=100/>\n",
    "<img src=./prob_lang_model3.png width=500 height=100/>\n",
    "<img src=./prob_lang_model4.png width=500 height=100/>\n",
    "<img src=./prob_lang_model5.png width=500 height=100/>\"\"\"\n",
    "SLP_chapter3_2 = \"\"\"\n",
    "<img src=./perplexity.png width=500 height=100/>\n",
    "\"\"\"\n",
    "SLP_chapter3_3 = \"\"\" Your summary here \"\"\"\n",
    "SLP_chapter3_4 = \"\"\" Your summary here \"\"\"\n",
    "SLP_chapter3_5 = \"\"\" Your summary here \"\"\"\n",
    "SLP_chapter3_7 = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "\n",
    "# Lecture notes \n",
    "module10_lecture_notes = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "\n",
    "# Each definition should be at most 25 words long.\n",
    "module10_definitions = {\n",
    "\"term\" : \"your definition here\",\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "lvtN3p7ET3Tx",
    "outputId": "9f9760bc-9acd-4df8-8e04-4190000e27b4"
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "# Module 10: Probabilies and Language Models\n",
       "## AIMA Chapter 12.1 Acting under Uncertainty\n",
       " Probabilistic inference: compute a desired probability from other known probabilities (e.g. conditional from joint) \n",
       "\n",
       "\n",
       "\n",
       "## AIMA Chapter 12.2 Basic Probability Notation\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 12.3 Inference Using Full Joint Distributions\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 12.4 Independence\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 12.5 Bayes’ Rule and Its Use\n",
       "$P(b|a)=\\frac{P(a|b)P(b)}{P(a)}$\n",
       "\n",
       "## AIMA Chapter 12.6 Naive Bayes Models\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 12.7 The Wumpus World Revisited\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 3.1 N-Grams\n",
       "\n",
       "<img src=./prob_lang_model1.png width=500 height=100/>\n",
       "<img src=./prob_lang_model2.png width=500 height=100/>\n",
       "<img src=./prob_lang_model3.png width=500 height=100/>\n",
       "<img src=./prob_lang_model4.png width=500 height=100/>\n",
       "<img src=./prob_lang_model5.png width=500 height=100/>\n",
       "\n",
       "## SLP Chapter 3.2 Evaluating Language Models\n",
       "\n",
       "<img src=./perplexity.png width=500 height=100/>\n",
       "\n",
       "\n",
       "## SLP Chapter 3.3 Sampling sentences from a language model\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 3.4 Generalization and Zeros\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 3.5 Smoothing\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 3.7 Huge Language Models and Stupid Backoff\n",
       " Your summary here \n",
       "\n",
       "## Module 10 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 10 Definitions\n",
       "* **Term** - your definition here\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Preview of your summary\n",
    "#@markdown You don't need to modify anything in this cell. Just press play.\n",
    "module10_sections = [\n",
    "  (\"AIMA Chapter 12.1 Acting under Uncertainty\", chapter12_1),\n",
    "  (\"AIMA Chapter 12.2 Basic Probability Notation\", chapter12_2),\n",
    "  (\"AIMA Chapter 12.3 Inference Using Full Joint Distributions\", chapter12_3),\n",
    "  (\"AIMA Chapter 12.4 Independence\", chapter12_4),\n",
    "  (\"AIMA Chapter 12.5 Bayes’ Rule and Its Use\", chapter12_5),\n",
    "  (\"AIMA Chapter 12.6 Naive Bayes Models\", chapter12_6),\n",
    "  (\"AIMA Chapter 12.7 The Wumpus World Revisited\", chapter12_7),\n",
    "  (\"SLP Chapter 3.1 N-Grams\", SLP_chapter3_1),\n",
    "  (\"SLP Chapter 3.2 Evaluating Language Models\", SLP_chapter3_2),\n",
    "  (\"SLP Chapter 3.3 Sampling sentences from a language model\", SLP_chapter3_3),\n",
    "  (\"SLP Chapter 3.4 Generalization and Zeros\", SLP_chapter3_4),\n",
    "  (\"SLP Chapter 3.5 Smoothing\", SLP_chapter3_5),\n",
    "  (\"SLP Chapter 3.7 Huge Language Models and Stupid Backoff\", SLP_chapter3_7),\n",
    "  (\"Module 10 Lecture Notes\", module10_lecture_notes),\n",
    "]\n",
    "\n",
    "module10_markdown = format_module(10, \"Probabilies and Language Models\", module10_sections, module10_definitions)\n",
    "display(Markdown(module10_markdown))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WHREsHSSyA-h"
   },
   "source": [
    "#Module 11 - Probabilistic Reasoning and Bayes’ Nets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "tuFC8w7CyCns"
   },
   "outputs": [],
   "source": [
    "# Russell and Norvig, Russell and Norvig, AIMA Chapter 13 “Probabilistic Reasoning” (13.1, 13.2, 13.3)\n",
    "chapter13_1 = \"\"\" Your summary here \"\"\"\n",
    "chapter13_2 = \"\"\"\n",
    "<img src=./bayes_net1.png width=500 height=100/>\n",
    "<img src=./bayes_net2.png width=500 height=100/>\"\"\"\n",
    "chapter13_3 = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "\n",
    "# Lecture notes \n",
    "module11_lecture_notes = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "# Definitions\n",
    "module11_definitions = {\n",
    "\"concept\" : \"definition\",    \n",
    "}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 408
    },
    "id": "vqtEs0gHs9sO",
    "outputId": "2d851c05-1e84-4fb0-cc09-b682a625cf21"
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "# Module 11: Probabilistic Reasoning and Bayes’ Nets\n",
       "## AIMA Chapter 13.1 Representing Knowledge in an Uncertain Domain\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 13.2 The Semantics of Bayesian Networks\n",
       "\n",
       "<img src=./bayes_net1.png width=500 height=100/>\n",
       "<img src=./bayes_net2.png width=500 height=100/>\n",
       "\n",
       "## AIMA 13.3 Exact Inference in Bayesian Networks\n",
       " Your summary here \n",
       "\n",
       "## Module 11 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 11 Definitions\n",
       "* **Concept** - definition\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Preview of your summary\n",
    "#@markdown You don't need to modify anything in this cell. Just press play.\n",
    "module11_sections = [\n",
    "  (\"AIMA Chapter 13.1 Representing Knowledge in an Uncertain Domain\", chapter13_1),\n",
    "  (\"AIMA Chapter 13.2 The Semantics of Bayesian Networks\", chapter13_2),\n",
    "  (\"AIMA 13.3 Exact Inference in Bayesian Networks\", chapter13_3),\n",
    "  (\"Module 11 Lecture Notes\", module11_lecture_notes),\n",
    "]\n",
    "\n",
    "module11_markdown = format_module(11, \"Probabilistic Reasoning and Bayes’ Nets\", \n",
    "                         module11_sections, \n",
    "                         module11_definitions)\n",
    "display(Markdown(module11_markdown))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "F3FPMzG9yUls"
   },
   "source": [
    "#Module 12 - Naive Bayes and Perceptrons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "iEIOpL7vyWcc"
   },
   "outputs": [],
   "source": [
    "# Russell and Norvig, AIMA Chapter 19 “Learning from Examples” (Sections 19.1-19.6)\n",
    "\n",
    "chapter19_1 = \"\"\" Your summary here \"\"\"\n",
    "chapter19_2 = \"\"\" Your summary here \"\"\"\n",
    "chapter19_3 = \"\"\" Your summary here \"\"\"\n",
    "chapter19_4 = \"\"\" Your summary here \"\"\"\n",
    "chapter19_5 = \"\"\" Your summary here \"\"\"\n",
    "chapter19_6 = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "# Speech and Language Processing Chapter 4 “Naive Bayes and Sentiment Classification”\n",
    "slp_chapter4_1 = \"\"\" <img src=./naive_bayes.png width=500 height=100/> \"\"\"\n",
    "slp_chapter4_2 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter4_3 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter4_4 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter4_5 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter4_6 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter4_7 = \"\"\"<img src=./eval_metric.png width=700 height=200/>\"\"\"\n",
    "slp_chapter4_8 = \"\"\"<img src=./train_and_test.png width=500 height=100/>\n",
    "<img src=./laplace_smooth.png width=500 height=100/>\n",
    "<img src=./linear_interpolation.png width=500 height=100/>\n",
    "\"\"\"\n",
    "slp_chapter4_9 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter4_10 = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "# Lecture notes \n",
    "module12_lecture_notes = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "# Definitions\n",
    "module12_definitions = {\n",
    "\"concept\" : \"definition\",    \n",
    "}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "KUc_LgzDvWf-",
    "outputId": "6f0e1c1c-cd15-482b-b806-5d2e6e4f0e5e"
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "# Module 12: Naive Bayes and Perceptrons\n",
       "## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 16.2 The Basis of Utility Theory\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.1 Naive Bayes Classifiers\n",
       " <img src=./naive_bayes.png width=500 height=100/> \n",
       "\n",
       "## SLP Chapter 4.2 Training the Naive Bayes Classifier\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.3 Worked Example\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.4 Optimizing for Sentiment Analysis\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.5 Naive Bayes for other text classification tasks\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.6 Naive Bayes as a Language Model\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.7 Evaluation: Precision, Recall, F-measure\n",
       "<img src=./eval_metric.png width=700 height=200/>\n",
       "\n",
       "## SLP Chapter 4.8 Test sets and Cross-validation\n",
       "<img src=./train_and_test.png width=500 height=100/>\n",
       "<img src=./laplace_smooth.png width=500 height=100/>\n",
       "<img src=./linear_interpolation.png width=500 height=100/>\n",
       "\n",
       "\n",
       "## SLP Chapter 4.9 Statistical Significance Testing\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.10 Avoiding Harms in Classification\n",
       " Your summary here \n",
       "\n",
       "## Module 12 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 12 Definitions\n",
       "* **Concept** - definition\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Preview of your summary\n",
    "#@markdown You don't need to modify anything in this cell. Just press play.\n",
    "module12_sections = [\n",
    "  (\"AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\", chapter19_5),\n",
    "  (\"AIMA Chapter 16.2 The Basis of Utility Theory\", chapter19_6),\n",
    "  (\"SLP Chapter 4.1 Naive Bayes Classifiers\", slp_chapter4_1),\n",
    "  (\"SLP Chapter 4.2 Training the Naive Bayes Classifier\", slp_chapter4_2),\n",
    "  (\"SLP Chapter 4.3 Worked Example\", slp_chapter4_3),\n",
    "  (\"SLP Chapter 4.4 Optimizing for Sentiment Analysis\", slp_chapter4_4),\n",
    "  (\"SLP Chapter 4.5 Naive Bayes for other text classification tasks\", slp_chapter4_5),\n",
    "  (\"SLP Chapter 4.6 Naive Bayes as a Language Model\", slp_chapter4_6),\n",
    "  (\"SLP Chapter 4.7 Evaluation: Precision, Recall, F-measure\", slp_chapter4_7),\n",
    "  (\"SLP Chapter 4.8 Test sets and Cross-validation\", slp_chapter4_8),\n",
    "  (\"SLP Chapter 4.9 Statistical Significance Testing\", slp_chapter4_9),\n",
    "  (\"SLP Chapter 4.10 Avoiding Harms in Classification\", slp_chapter4_10),\n",
    "  (\"Module 12 Lecture Notes\", module12_lecture_notes),\n",
    "]\n",
    "\n",
    "module12_markdown = format_module(12, \"Naive Bayes and Perceptrons\", \n",
    "                         module12_sections, \n",
    "                         module12_definitions)\n",
    "display(Markdown(module12_markdown))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qVSQhTVSyYYO"
   },
   "source": [
    "# Module 13 - Neural Networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "id": "Wm4mfW82yaRH"
   },
   "outputs": [],
   "source": [
    "# Jurafsky and Martin, Speech and Language Processing Chapter 5 “Logistic Regression” (5.1-5.6)\n",
    "\n",
    "slp_chapter5_1 = \"\"\"<img src=./perceptron.png width=500 height=100/> \n",
    "We can also update perceptron with a decrease learning rate.\n",
    "<img src=./min_correct_update.png width=500 height=100/>\n",
    "<img src=./comparison.png width=500 height=100/>\"\"\"\n",
    "slp_chapter5_2 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter5_3 = \"\"\"<img src=./ce.png width=500 height=100/> \"\"\"\n",
    "slp_chapter5_4 = \"\"\"<img src=./ce_grad.png width=500 height=100/>\"\"\"\n",
    "slp_chapter5_5 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter5_6 = \"\"\"<img src=./computation_graph.png width=500 height=100/> \"\"\"\n",
    "\n",
    "# Jurafsky and Martin, Chapter 7 “Neural Networks and Neural Language Models”\n",
    "\n",
    "slp_chapter7_1 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter7_2 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter7_3 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter7_4 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter7_5 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter7_6 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter7_7 = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "# Lecture notes \n",
    "module13_lecture_notes = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "# Definitions\n",
    "module13_definitions = {\n",
    "\"concept\" : \"definition\",    \n",
    "}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "kKWbCsbfxL3R",
    "outputId": "7c42a025-092a-4522-b305-6a5e7d884055"
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "# Module 13: Neural Networks\n",
       "## SLP Chapter 5.1 Classification: the sigmoid\n",
       "<img src=./perceptron.png width=500 height=100/> \n",
       "We can also update perceptron with a decrease learning rate.\n",
       "<img src=./min_correct_update.png width=500 height=100/>\n",
       "<img src=./comparison.png width=500 height=100/>\n",
       "\n",
       "## SLP Chapter 5.2 Learning in Logistic Regression\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 5.3 The cross-entropy loss function\n",
       "<img src=./ce.png width=500 height=100/> \n",
       "\n",
       "## SLP Chapter 5.4 Gradient Descent\n",
       "<img src=./ce_grad.png width=500 height=100/>\n",
       "\n",
       "## SLP Chapter 5.5 Regularization\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 5.6 Multinomial logistic regression\n",
       "<img src=./computation_graph.png width=500 height=100/> \n",
       "\n",
       "## SLP Chapter 7.1 Units\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.2 The XOR problem\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.3 Feedforward Neural Networks\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.4 Feedforward networks for NLP: Classification\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.5 Feedforward Neural Language Modeling\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.6 Training Neural Nets\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.7 Training the neural language model\n",
       " Your summary here \n",
       "\n",
       "## Module 13 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 13 Definitions\n",
       "* **Concept** - definition\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Preview of your summary\n",
    "#@markdown You don't need to modify anything in this cell. Just press play.\n",
    "module13_sections = [\n",
    "  (\"SLP Chapter 5.1 Classification: the sigmoid\", slp_chapter5_1),\n",
    "  (\"SLP Chapter 5.2 Learning in Logistic Regression\", slp_chapter5_2),\n",
    "  (\"SLP Chapter 5.3 The cross-entropy loss function\", slp_chapter5_3),\n",
    "  (\"SLP Chapter 5.4 Gradient Descent\", slp_chapter5_4),\n",
    "  (\"SLP Chapter 5.5 Regularization\", slp_chapter5_5),\n",
    "  (\"SLP Chapter 5.6 Multinomial logistic regression\", slp_chapter5_6),\n",
    "\n",
    "  (\"SLP Chapter 7.1 Units\", slp_chapter7_1),\n",
    "  (\"SLP Chapter 7.2 The XOR problem\", slp_chapter7_2),\n",
    "  (\"SLP Chapter 7.3 Feedforward Neural Networks\", slp_chapter7_3),\n",
    "  (\"SLP Chapter 7.4 Feedforward networks for NLP: Classification\", slp_chapter7_4),\n",
    "  (\"SLP Chapter 7.5 Feedforward Neural Language Modeling\", slp_chapter7_5),\n",
    "  (\"SLP Chapter 7.6 Training Neural Nets\", slp_chapter7_6),\n",
    "  (\"SLP Chapter 7.7 Training the neural language model\", slp_chapter7_7),\n",
    "  (\"Module 13 Lecture Notes\", module13_lecture_notes),\n",
    "]\n",
    "\n",
    "module13_markdown = format_module(13, \"Neural Networks\", \n",
    "                         module13_sections, \n",
    "                         module13_definitions)\n",
    "display(Markdown(module13_markdown))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RYESi2kMybL8"
   },
   "source": [
    "# Module 14 - Natural Language Processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "id": "qIRJ4YYCzNHL"
   },
   "outputs": [],
   "source": [
    "# Jurafsky and Martin, Chapter 9 “Sequence Processing with Recurrent Networks” (Sections 9.1-9.3)\n",
    "\n",
    "slp_chapter9_1 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter9_2 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter9_3 = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "# Jurafsky and Martin, Chapter 6 “Vector Semantics and Embeddings” (6.1-6.4, 6.8, 6.10-6.12)\n",
    "\n",
    "slp_chapter6_1 = \"\"\" <img src=./NLP1.png width=500 height=100/> \n",
    "<img src=./NLP2.png width=500 height=100/>\n",
    "<img src=./NLP3.png width=500 height=100/>\n",
    "<img src=./NLP4.png width=500 height=100/>\n",
    "<img src=./TD-IDF.png width=500 height=100/>\"\"\"\n",
    "slp_chapter6_2 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter6_3 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter6_4 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter6_8 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter6_10 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter6_11 = \"\"\" Your summary here \"\"\"\n",
    "slp_chapter6_12 = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "\n",
    "\n",
    "# Lecture notes \n",
    "module14_lecture_notes = \"\"\" Your summary here \"\"\"\n",
    "\n",
    "# Definitions\n",
    "module14_definitions = {\n",
    "\"concept\" : \"definition\",    \n",
    "}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 939
    },
    "id": "lXNcHuKjyNXa",
    "outputId": "c714234d-cfdc-4f50-ec61-47425f7f15e5"
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "# Module 14: Natural Language Processing\n",
       "## SLP Chapter 9.1 Language Models Revisited\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 9.2 Recurrent Neural Networks\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 9.3 RNNs as Language Models\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.1 Lexical Semantics\n",
       " <img src=./NLP1.png width=500 height=100/> \n",
       "<img src=./NLP2.png width=500 height=100/>\n",
       "<img src=./NLP3.png width=500 height=100/>\n",
       "<img src=./NLP4.png width=500 height=100/>\n",
       "<img src=./TD-IDF.png width=500 height=100/>\n",
       "\n",
       "## SLP Chapter 6.2 Vector Semantics\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.3 Words and Vectors\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.4 Cosine for measuring similarity\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.8 Word2vec\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.10 Semantic properties of embeddings\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.11 Bias and Embeddings\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.12 Evaluating Vector Models\n",
       " Your summary here \n",
       "\n",
       "## Module 13 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 14 Definitions\n",
       "* **Concept** - definition\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Preview of your summary\n",
    "#@markdown You don't need to modify anything in this cell. Just press play.\n",
    "module14_sections = [\n",
    "  (\"SLP Chapter 9.1 Language Models Revisited\", slp_chapter9_1),\n",
    "  (\"SLP Chapter 9.2 Recurrent Neural Networks\", slp_chapter9_2),\n",
    "  (\"SLP Chapter 9.3 RNNs as Language Models\", slp_chapter9_3),\n",
    "\n",
    "  (\"SLP Chapter 6.1 Lexical Semantics\", slp_chapter6_1),\n",
    "  (\"SLP Chapter 6.2 Vector Semantics\", slp_chapter6_2),\n",
    "  (\"SLP Chapter 6.3 Words and Vectors\", slp_chapter6_3),\n",
    "  (\"SLP Chapter 6.4 Cosine for measuring similarity\", slp_chapter6_4),\n",
    "  (\"SLP Chapter 6.8 Word2vec\", slp_chapter6_8),\n",
    "  (\"SLP Chapter 6.10 Semantic properties of embeddings\", slp_chapter6_10),\n",
    "  (\"SLP Chapter 6.11 Bias and Embeddings\", slp_chapter6_11),\n",
    "  (\"SLP Chapter 6.12 Evaluating Vector Models\", slp_chapter6_12),\n",
    "  (\"Module 13 Lecture Notes\", module13_lecture_notes),\n",
    "]\n",
    "\n",
    "module14_markdown = format_module(14, \"Natural Language Processing\", \n",
    "                         module14_sections, \n",
    "                         module14_definitions)\n",
    "display(Markdown(module14_markdown))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vX7lbnJd4sT5"
   },
   "source": [
    "# Your Exam Notes\n",
    "\n",
    "Here are your full set of exam notes that you can use on your midterm.  Choose **Runtime > Run all**, then your notes will be displayed.\n",
    "\n",
    "If you are taking the exam in person, then you must print a copy of your notes for yourself.   Here's how to print:\n",
    "* Run the cell below. \n",
    "* Click its \"Mirror cell in tab\" button (this is located in the upper right corner of the cell, immediately to the right of the trash can).  This will open the cell.  \n",
    "* In Chrome, you can then print your notes using the **File > Print** option from the browser's menu.  \n",
    "* In the print options, change the layout from Landscape to Portrait. \n",
    "* Clicking the Save, will save a PDF that you can then print.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
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       "# Module 8: Markov Decision Processes\n",
       "## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n",
       "maximum expected utility (MEU) says that a rational agent should choose the action that maximizes the agent’s expected utility.  \n",
       "  \n",
       "    \n",
       "  \n",
       "$P(\\text{RESULT}(a)=s') = \\sum_s P(s)P(s'|s,a)$  \n",
       "  \n",
       "$EU(a)=\\sum\\limits_{s^{\\prime}}P(result(a)=s^{\\prime})U(s^{\\prime})$\n",
       "\n",
       "\n",
       "## AIMA Chapter 16.2 The Basis of Utility Theory\n",
       " six constraints that we require any reasonable preference relation to obey:  \n",
       "1. orderability: the agent cannot avoid deciding. any A and B is comparable.  \n",
       "2. transitivity: if A>B and B>C then A>C.  \n",
       "3. continuity: if A>B>C, then there is a p such that [p, A;1-p, C]=B.  \n",
       "4. substituability: if A=B, then [p, A;1-p, C]=[p, B;1-p, C].  \n",
       "5. monocity: if A>B, then p>q <=> [p, A;1-p, B]>[q, A;1-q, B].  \n",
       "6. decomposability: [p, A; 1-p, [q, B; (1-q), C]]=[p, A; (1-p)q, B; (1-p)(1-q), C].  \n",
       "  \n",
       "These constraints are known as the axioms of utility theory. Violation of these constraints results in irrationality.  \n",
       "\n",
       "As in game-playing, in a deterministic environment an agent needs only a preference ranking on states—the numbers don’t matter. \n",
       "This is called a value function or ordinal utility function.  \n",
       "  \n",
       "It is important to remember that the existence of a utility function that describes an agent’s preference behavior \n",
       "does not necessarily mean that the agent is explicitly maximizing that utility function in its own deliberations. \n",
       "\n",
       "\n",
       "## AIMA Chapter 16.3 Utility Functions\n",
       "If we want to build a decision-theoretic system that helps a human make decisions or acts\n",
       "on his or her behalf, we must first work out what the human’s utility function is. This\n",
       "process, often called preference elicitation, involves presenting choices to the human and\n",
       "using the observed preferences to pin down the underlying utility function.  \n",
       "  \n",
       "there is no absolute scale for utilities, but it is helpful, nonetheless, \n",
       "to establish some scale on which utilities can be recorded and compared for any particular problem. \n",
       "Usually we use normalized utilities where the best utility we can get is 1 and the worse is 0.  \n",
       "  \n",
       "standard lottery: [p, best; (1-p), worse].  \n",
       "  \n",
       "This tendency for the estimated expected utility of the best choice to be too high as k(number of events) grows is called\n",
       "the optimizer’s curse.  \n",
       "  \n",
       "Decision theory is a normative theory: it describes how a rational agent should act. \n",
       "A descriptive theory, on the other hand, describes how actual agents—for example, humans— really do act.  \n",
       "  \n",
       "Certain effect: people are strongly attracted by gains that are certain.  \n",
       "  \n",
       "ambiguity aversion: Most people elect the known probability rather than the unknown unknowns.  \n",
       "  \n",
       "framing effect: Experiments show that people like a\n",
       "medical procedure that is described as having a “90% survival rate” about twice as much as\n",
       "one described as having a “10% death rate,”  \n",
       "\n",
       "anchoring effect: People feel more comfortable making relative utility judgments rather than absolute ones.\n",
       "\n",
       "\n",
       "## AIMA Chapter 17.1 Sequential Decision Problems\n",
       "Markovian: the probability of reaching s' from s depends only on s and not on the history of earlier states.  \n",
       "  \n",
       "a sequential decision problem for a fully observable, stochastic environment \n",
       "with a Markovian transition model and additive rewards is called a Markov decision process, or MDP.  \n",
       "   \n",
       "dynamic programming: simplifying a problem by recursively breaking it into smaller pieces and remembering the optimal solutions to the pieces.  \n",
       "  \n",
       "A solution to MDP must specify what the agent should do for any state that the agent might reach. A solution of this kind is called a policy.  \n",
       "  \n",
       "An optimal policy is a policy that yields the highest expected utility.  \n",
       "  \n",
       "A policy that depends on the time is called nonstationary.  \n",
       "\n",
       "An optimal action depends only on the current state, and the optimal policy is stationary.  \n",
       "\n",
       "A policy that is guaranteed to reach a terminal state is called a proper policy.  \n",
       "  \n",
       "Bellman equation: $U(s)=\\max\\limits_{a\\in A(s)}\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U(s^{\\prime})]$, $O(|S|^2|A|)$.  \n",
       "  \n",
       "action-utility function, or Q-function: $Q(s, a)=\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U(s^{\\prime})]$,  \n",
       "then we have $U(s)=\\max\\limits_{a\\in A(s)}Q(s, a)$ and $\\pi^{*}=argmax Q(s, a)$\n",
       "\n",
       "\n",
       "## AIMA Chapter 17.2 Algorithms for MDPs\n",
       "\n",
       "Value Iteration:  each step is called a Bellman update: $U_{i+1}(s)=\\max\\limits_{a\\in A(s)}\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U_i(s^{\\prime})]$.  \n",
       "  \n",
       "Policy Iteration: each step contains two parts:  \n",
       "1. policy evaluation: given a policy $\\pi_{i}$, we calculate $U_i=U^{\\pi_i}$, the utility of each state under this policy.  \n",
       "2. policy improvement: Calculate a new MEU policy $\\pi_{i+1}$, using one-step look-ahead based on $U_i$.  \n",
       "  \n",
       "Linear Programming: we seek to minimize $U(s)$ for all subject to the inequalities $U(s)\\geq\\sum\\limits_{s^{\\prime}}P(s^{\\prime}|s, a)[R(s, a, s^{\\prime})+\\gamma U(s^{\\prime})]$.  \n",
       "  \n",
       "Value iteration and policy iteration are offline algorithms: like the A* algorithm, \n",
       "they generate an optimal solution for the problem, which can then be executed by a simple agent. \n",
       "For sufficiently large MDPs, such as the Tetris MDP with states, exact offline solution, \n",
       "even by a polynomial-time algorithm, is not possible.\n",
       "\n",
       "\n",
       "## Module 8 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 8 Definitions\n",
       "* **Utility function** - Your definition here\n",
       "* **Expected utility** - your definition here\n",
       "* **Etc.** - your definition here\n",
       "\n",
       "\n",
       "# Module 9: Reinforcement Learning\n",
       "## AIMA Chapter 17.3 Bandit Problems\n",
       "a one-armed bandit is a slot machine. A gambler can insert a coin, \n",
       "pull the lever, and collect the winnings (if any). An -armed bandit has levers. \n",
       "Behind each lever is a fixed but unknown probability distribution of winnings; each pull samples from that unknown distribution. \n",
       "This is an example of exploration vs exploitation trade off.  \n",
       "  \n",
       "\n",
       "\n",
       "\n",
       "## AIMA Chapter 22.1 Learning from Rewards\n",
       "<img src=./different_ways.png width=500 height=100/>\n",
       "\n",
       "Model-Based Idea:\n",
       "1. Learn an approximate model based on experiences\n",
       "2. Solve for values as if the learned model were correct\n",
       "\n",
       "Step 1: Learn empirical MDP model\n",
       "1. Count outcomes s’ for each s, a\n",
       "2. Normalize to give an estimate of T\n",
       "3. Discover each R when we experience (s, a, s’)\n",
       "\n",
       "Step 2: Solve the learned MDP\n",
       "1. For example, use value iteration, as before\n",
       "\n",
       "MODEL-FREE REINFORCEMENT LEARNING: In these approaches the agent neither\n",
       "knows nor learns a transition model for the environment. \n",
       "Instead, it learns a more direct representation of how to behave. This comes in one of two varieties:\n",
       "1. action-utility learning(Q-learning)\n",
       "2. policy search(reflex agent)\n",
       "\n",
       "passive reinforcement learning: the agent’s policy is fixed and the task is to learn the utilities of states\n",
       "active reinforcement learning: the agent must also figure out what to do.\n",
       "\n",
       "## AIMA Chapter 22.2 Passive Reinforcement Learning\n",
       "Direct Evaluation:\n",
       "<img src=./direct_evaluation1.png width=500 height=100/>\n",
       "<img src=./direct_evaluation2.png width=500 height=100/>\n",
       "<img src=./direct_evaluation3.png width=500 height=100/>\n",
       "For model-free approaches, we can't use policy iteration because we don't know T and R.\n",
       "\n",
       "Temperal Difference:\n",
       "<img src=./temperal_difference1.png width=500 height=100/>\n",
       "<img src=./temperal_difference2.png width=500 height=100/>\n",
       "<img src=./temperal_difference1.png width=500 height=100/>\n",
       "(we still don't know R and T)\n",
       "\n",
       "\n",
       "## AIMA Chapter 22.3 Active Reinforcement Learning\n",
       "\n",
       "Active RL:\n",
       "<img src=./active_RL.png width=500 height=100/>\n",
       "\n",
       "Q-learning:\n",
       "<img src=./Q-learning1.png width=500 height=100/>\n",
       "<img src=./Q-learning2.png width=500 height=100/>\n",
       "<img src=./Q-learning3.png width=500 height=100/>\n",
       "<img src=./regret.png width=500 height=100/>\n",
       "\n",
       "Approx Q-learning:\n",
       "<img src=./approx_Q.png width=500 height=100/>\n",
       "\n",
       "## AIMA Chapter 22.4 Generalization in Reinforcement Learning\n",
       " Your summary here \n",
       "\n",
       "## Module 9 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 9 Definitions\n",
       "* **Term** - your definition here\n",
       "\n",
       "\n",
       "# Module 10: Probabilies and Language Models\n",
       "## AIMA Chapter 12.1 Acting under Uncertainty\n",
       " Probabilistic inference: compute a desired probability from other known probabilities (e.g. conditional from joint) \n",
       "\n",
       "\n",
       "\n",
       "## AIMA Chapter 12.2 Basic Probability Notation\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 12.3 Inference Using Full Joint Distributions\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 12.4 Independence\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 12.5 Bayes’ Rule and Its Use\n",
       "$P(b|a)=\\frac{P(a|b)P(b)}{P(a)}$\n",
       "\n",
       "## AIMA Chapter 12.6 Naive Bayes Models\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 12.7 The Wumpus World Revisited\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 3.1 N-Grams\n",
       "\n",
       "<img src=./prob_lang_model1.png width=500 height=100/>\n",
       "<img src=./prob_lang_model2.png width=500 height=100/>\n",
       "<img src=./prob_lang_model3.png width=500 height=100/>\n",
       "<img src=./prob_lang_model4.png width=500 height=100/>\n",
       "<img src=./prob_lang_model5.png width=500 height=100/>\n",
       "\n",
       "## SLP Chapter 3.2 Evaluating Language Models\n",
       "\n",
       "<img src=./perplexity.png width=500 height=100/>\n",
       "\n",
       "\n",
       "## SLP Chapter 3.3 Sampling sentences from a language model\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 3.4 Generalization and Zeros\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 3.5 Smoothing\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 3.7 Huge Language Models and Stupid Backoff\n",
       " Your summary here \n",
       "\n",
       "## Module 10 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 10 Definitions\n",
       "* **Term** - your definition here\n",
       "\n",
       "\n",
       "# Module 11: Probabilistic Reasoning and Bayes’ Nets\n",
       "## AIMA Chapter 13.1 Representing Knowledge in an Uncertain Domain\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 13.2 The Semantics of Bayesian Networks\n",
       "\n",
       "<img src=./bayes_net1.png width=500 height=100/>\n",
       "<img src=./bayes_net2.png width=500 height=100/>\n",
       "\n",
       "## AIMA 13.3 Exact Inference in Bayesian Networks\n",
       " Your summary here \n",
       "\n",
       "## Module 11 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 11 Definitions\n",
       "* **Concept** - definition\n",
       "\n",
       "\n",
       "# Module 12: Naive Bayes and Perceptrons\n",
       "## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n",
       " Your summary here \n",
       "\n",
       "## AIMA Chapter 16.2 The Basis of Utility Theory\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.1 Naive Bayes Classifiers\n",
       " <img src=./naive_bayes.png width=500 height=100/> \n",
       "\n",
       "## SLP Chapter 4.2 Training the Naive Bayes Classifier\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.3 Worked Example\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.4 Optimizing for Sentiment Analysis\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.5 Naive Bayes for other text classification tasks\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.6 Naive Bayes as a Language Model\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.7 Evaluation: Precision, Recall, F-measure\n",
       "<img src=./eval_metric.png width=700 height=200/>\n",
       "\n",
       "## SLP Chapter 4.8 Test sets and Cross-validation\n",
       "<img src=./train_and_test.png width=500 height=100/>\n",
       "<img src=./laplace_smooth.png width=500 height=100/>\n",
       "<img src=./linear_interpolation.png width=500 height=100/>\n",
       "\n",
       "\n",
       "## SLP Chapter 4.9 Statistical Significance Testing\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 4.10 Avoiding Harms in Classification\n",
       " Your summary here \n",
       "\n",
       "## Module 12 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 12 Definitions\n",
       "* **Concept** - definition\n",
       "\n",
       "\n",
       "# Module 13: Neural Networks\n",
       "## SLP Chapter 5.1 Classification: the sigmoid\n",
       "<img src=./perceptron.png width=500 height=100/> \n",
       "We can also update perceptron with a decrease learning rate.\n",
       "<img src=./min_correct_update.png width=500 height=100/>\n",
       "<img src=./comparison.png width=500 height=100/>\n",
       "\n",
       "## SLP Chapter 5.2 Learning in Logistic Regression\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 5.3 The cross-entropy loss function\n",
       "<img src=./ce.png width=500 height=100/> \n",
       "\n",
       "## SLP Chapter 5.4 Gradient Descent\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 5.5 Regularization\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 5.6 Multinomial logistic regression\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.1 Units\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.2 The XOR problem\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.3 Feedforward Neural Networks\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.4 Feedforward networks for NLP: Classification\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.5 Feedforward Neural Language Modeling\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.6 Training Neural Nets\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 7.7 Training the neural language model\n",
       " Your summary here \n",
       "\n",
       "## Module 13 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 13 Definitions\n",
       "* **Concept** - definition\n",
       "\n",
       "\n",
       "# Module 14: Natural Language Processing\n",
       "## SLP Chapter 9.1 Language Models Revisited\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 9.2 Recurrent Neural Networks\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 9.3 RNNs as Language Models\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.1 Lexical Semantics\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.2 Vector Semantics\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.3 Words and Vectors\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.4 Cosine for measuring similarity\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.8 Word2vec\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.10 Semantic properties of embeddings\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.11 Bias and Embeddings\n",
       " Your summary here \n",
       "\n",
       "## SLP Chapter 6.12 Evaluating Vector Models\n",
       " Your summary here \n",
       "\n",
       "## Module 13 Lecture Notes\n",
       " Your summary here \n",
       "\n",
       "## Module 14 Definitions\n",
       "* **Concept** - definition\n"
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    "# This will generate the full set of notes that you can use for your exam.\n",
    "full_markdown = \"\\n\\n\".join([module8_markdown, \n",
    "                             module9_markdown, \n",
    "                             module10_markdown, \n",
    "                             module11_markdown, \n",
    "                             module12_markdown,\n",
    "                             module13_markdown,\n",
    "                             module14_markdown,]\n",
    "                       )\n",
    "display(Markdown(full_markdown))"
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