{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# %load /Users/facai/Study/book_notes/preconfig.py\n", "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "sns.set(color_codes=True)\n", "#sns.set(font='SimHei', font_scale=2.5)\n", "#plt.rcParams['axes.grid'] = False\n", "\n", "import numpy as np\n", "\n", "import pandas as pd\n", "#pd.options.display.max_rows = 20\n", "\n", "#import sklearn\n", "\n", "#import itertools\n", "\n", "#import logging\n", "#logger = logging.getLogger()\n", "\n", "#from IPython.display import SVG\n", "from IPython.display import Image" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Chapter 3: Finite Markov Decision Processes \n", "==========\n", "\n", "MDP(Markov Decision Processes): actions influence not just immediate rewards, but also subsequential situations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1 The Agent-Environment Interface" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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uIWwauaJ77+5oWvl5BnS3sWO9N87fSUGjzt3Rv2OTdJu8FjeFaBb/ALv+5PPv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\ngA+dYO2RGzzZVLyzkjvzeq0vOSDasSccFxGS4ffvMmDyyyD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"text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image('./res/fig3_1.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*finite* MDP: the sets of states, actions and rewards all have a finite number of elements.\n", "\n", "\\begin{align}\n", " & p(s', r \\mid s, a) \\doteq \\operatorname{Pr} \\{ S_t = s', R_t = r \\mid S_{t-1} = s, A_{t-1} = a \\} \\\\\n", " & \\displaystyle \\sum_{s' \\in \\mathcal{S}} \\sum_{r \\in \\mathcal{R}} p(s', r \\mid s, a) = 1 \\quad \\text{, for all $s \\in \\mathcal{S}$, $a \\in \\mathcal{A}(s)$}\n", "\\end{align}\n", "\n", "\n", "+ state-transition probabilities:\n", "\n", "\\begin{align*}\n", " p(s' \\mid s, a) & \\doteq \\operatorname{Pr} \\{ S_t = s' \\mid S_{t-1} = s, A_{t-1} = a \\} \\\\\n", " & = \\sum_{r \\in \\mathcal{R}} p(s', r \\mid s, a)\n", "\\end{align*}\n", "\n", "+ expected rewards for state-action paris:\n", "\n", "\\begin{align*}\n", " r(s, a) & \\doteq \\mathbb{E} \\left [ R_t \\mid S_{t-1} = s, A_{t-1} = a \\right ] \\\\\n", " & = \\sum_{r \\in \\mathcal{R}} \\left ( r \\sum_{s' \\in \\mathcal{S}} p(s', r \\mid s, a) \\right )\n", "\\end{align*}\n", "\n", "+ expected rewards for state-action-next-state triples:\n", "\n", "\\begin{align*}\n", " r(s, a, s') & \\doteq \\mathbb{E} \\left [ R_t \\mid S_{t-1} = s, A_{t-1} = a, S_t = s' \\right ] \\\\\n", " & = \\sum_{r \\in \\mathcal{R}} r \\frac{p(s', r \\mid s, a)}{p(s' \\mid s, a)}\n", "\\end{align*}\n", "\n", "agent-environment boundary represents the limit of the agent's *absolute control*, not of its knowledge." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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oU6eOpJrcn6LGR25WqVrBYNw57I35Q1Nv002cA8G4YPkQszcMkCmM/bK/in8z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"text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Transition Graph\n", "Image('./res/ex3_3.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Exercise 3.4\n", "\n", "$r(S_t, a) \\; \\pi(a \\mid S_t)$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2 Goals and Rewards\n", "\n", "goal: to maximize the total amount of reward it receives.\n", "\n", "In particular, the reward signal is not the place to impart to the agent prior knowledge about *how* to achieve what it to do." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.3 Returns and Episodes\n", "\n", "+ episodic tasks: $G_t \\doteq R_{t+1} + R_{t+2} + R_{t+3} + \\cdots + R_T$, $\\quad G_t$ is *expected return*.\n", "+ continuing tasks: $G_t \\doteq R_{t+1} + \\gamma R_{t+2} + \\gamma^2 R_{t+3} + \\cdots = \\displaystyle \\sum_{k=0}^\\infty \\gamma^k R_{t+k+1} = R_{t+1} + \\gamma G_{t+1}$ \n", " - $\\gamma$ is called *discount rate*, and $0 \\leq \\gamma \\leq 1$ \n", " - $G_T = 0$ often makes it easy to compute returns from reward sequences.\n", " \n", " \n", "##### exercise 3.8\n", "\n", "0 for escaping from the maze and -1 at all other times\n", "\n", "##### exercise 3.10\n", "\n", "$G_1 = \\frac{7}{1 - r} = 70$\n", "\n", "$G_0 = R_1 + 0.9 G_1 = 65$\n", "\n", "##### exercise 3.11\n", "\n", "\\begin{align}\n", " G_t &= \\sum_{k=0}^\\infty r^k \\\\\n", " &= 1 + r \\sum_{k=0}^\\infty r^k \\\\\n", " &= 1 + r G_t \\\\\n", " &= \\frac1{1 - r}\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.4 Unified Notation for Episodic and Continuing Tasks\n", "\n", "$G_t \\doteq \\sum_{k=t+1}^T \\gamma^{k-t-1} R_k$, including the possibility that $T = \\infty$ or $\\gamma = 1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.5 Policies and Value Functions\n", "\n", "+ value functions: estimate *how good* it is for the agent to be in a given state.\n", "+ policy $\\pi$: a mapping from states to probabilities of selecting each possible action.\n", "+ The *value* of a state $s$ under a policy $\\pi$, denoted $v_\\pi(s)$, is the expected return when starting in $s$ and following $\\pi$ thereafter: \n", " $v_\\pi(s) \\doteq \\mathbb{E}_\\pi [ G_t \\mid S_t = s ]$\n", " - $v_\\pi$: state-value function for policy $\\pi$\n", "+ $q_\\pi$: action-value function for policy $\\pi$, $q_\\pi(s, a) \\doteq \\mathbb{E}_\\pi [ G_t \\mid S_t = s, A_t = a]$\n", "\n", "Bellman equation for $v_\\pi$:\n", "\n", "\\begin{equation}\n", " v_\\pi(s) \\doteq \\displaystyle \\sum_a \\pi(a \\mid s) \\sum_{s', r} p(s', r \\mid s, a) \\left [ r + \\gamma v_\\pi(s') \\right ] \\quad \\text{, for all $s \\in \\mathcal{S}$}\n", "\\end{equation}\n", "\n", "The value functions $v_\\pi$ and $q_\\pi$ can be estimated from experience, say Monte Carlo methods (average)." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { 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" ], "text/plain": [ " 0 1 2 3 4\n", "0 2.253150 9.592586 4.524364 6.244556 1.271214\n", "1 1.420013 3.970976 3.260312 2.897431 0.840299\n", "2 0.455929 1.610993 1.648482 1.244556 0.192553\n", "3 -0.207290 0.368589 0.478065 0.239763 -0.314645\n", "4 -0.653676 -0.407414 -0.344568 -0.448925 -0.690892" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Example 3.5\n", "from scipy.signal import convolve2d\n", "\n", "reward_matrix = np.zeros((5, 5))\n", "# kernel\n", "kernel = np.array([[0, 1, 0],\n", " [1, 0, 1],\n", " [0, 1, 0]])\n", "\n", "iteration_nums = 100\n", "\n", "for _ in range(iteration_nums):\n", " reward = convolve2d(reward_matrix, kernel, mode='same', boundary='fill', fillvalue=-1)\n", " reward /= 4.0\n", " # A -> A'\n", " reward[0, 1] = 10 + reward[-1, 1]\n", " # B -> B'\n", " reward[0, -2] = 5 + reward[2, -2]\n", " reward_matrix = reward\n", " \n", "pd.DataFrame(reward_matrix)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### exercise 3.12\n", "\n", "(2.3 + 0.4 - 0.4 + 0.7) / 4 = 0.75\n", "\n", "\n", "##### exercise 3.13\n", "\n", "\n", "##### exercise 3.14\n", "\n", "$\\sum_{k=0}^\\infty \\gamma^k C = \\frac{C}{1 - r}$ = constant offset" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.6 Optimal Policies and Optimal Value Functions\n", "\n", "optimal policy: \n", "\n", "\\begin{align}\n", " v_\\ast(s) & \\doteq \\displaystyle \\max_\\pi v_\\pi(s) \\quad \\text{ for all } s \\in \\mathcal{S} \\\\\n", " & = \\max_a \\sum_{s', r} p(s', r \\mid s, a) \\left [ r + \\gamma v_\\ast(s') \\right ] \\\\\n", "\\end{align}\n", "\n", "Any policy that is *greedy* with respect to the optimal evaluation function $v_\\ast$ is an optimal policy.\n", "\n", "optimal action-value function: \n", "\n", "\\begin{align}\n", " q_\\ast(s, a) & \\doteq \\max_\\pi q_\\pi(s, a) \\quad \\text{ for all $s \\in \\mathcal{S}$ and $a \\in \\mathcal{A}(s)$} \\\\\n", " & = \\mathbb{E} [ R_{t+1} + \\gamma v_\\ast(S_{t+1}) \\mid S_t = s, A_t = a ] \\\\\n", " & = \\sum_{s', r} p(s', r \\mid s, a) \\left [ r + \\gamma \\max_{a'} q_\\ast (s', a') \\right ] \\\\\n", "\\end{align}\n", "\n", "\n", "Explicitly solving the Bellman optimality equation relies on at least three assumptions that are rarely true in practice:\n", "\n", "1. we accurately know the dynamics of the environment;\n", "2. we have enough computational resources;\n", "3. the Markov property." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.7 Optimality and Approximation\n", "\n", "extreme computational cost, memory => approximations\n", "\n", "put more effort into learning to make good decisions for frequently encountered states, at the expense of less effort for infrequently encountered states." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }