From d477e56154a9c9d26522e6e0c898026ec3e57d2c Mon Sep 17 00:00:00 2001 From: JChunX Date: Sun, 10 Jan 2021 15:17:26 -0800 Subject: [PATCH] Add Ex 7.2 --- Chapter 7/Ex7.2.ipynb | 246 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 246 insertions(+) create mode 100644 Chapter 7/Ex7.2.ipynb diff --git a/Chapter 7/Ex7.2.ipynb b/Chapter 7/Ex7.2.ipynb new file mode 100644 index 0000000..7c8a979 --- /dev/null +++ b/Chapter 7/Ex7.2.ipynb @@ -0,0 +1,246 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 166, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import random\n", + "import math\n", + "\n", + "'''\n", + "19-state random walk from example 7.1\n", + "State-value function evaluated with n-step and sum of TD error methods\n", + "Results suggest similar performance across varying parameter values\n", + "'''\n", + "\n", + "def train_nstep_TD_sum(pi, alpha, gamma, n, max_episode):\n", + " '''\n", + " Estimate v using n-step TD error sum\n", + " \n", + " Parameters\n", + " ---------- \n", + " pi : func\n", + " Policy to evaluate\n", + " alpha : float\n", + " Convergence parameter\n", + " gamma : float\n", + " Discount parameter\n", + " n : int\n", + " Puts the n in n-step\n", + " max_episode : int\n", + " maximum number of episodes\n", + " Returns\n", + " -------\n", + " ndarray\n", + " state-value function for pi for every episode\n", + " '''\n", + " vs = []\n", + " v = np.zeros(21)\n", + " episode = 0\n", + " \n", + " while episode < max_episode:\n", + " done = False\n", + " st = 3\n", + " s = [st]\n", + " r = [0] # R_0 = 0\n", + " tau = 0\n", + " T = math.inf\n", + " t = 0\n", + " \n", + " while tau != T - 1:\n", + " if t < T:\n", + " a = pi(st)\n", + " st = st + a\n", + " reward = 0\n", + " if st == 0 or st == 20:\n", + " done = True\n", + " if st == 20:\n", + " reward = 1\n", + " else:\n", + " reward = -1\n", + " s.append(st)\n", + " r.append(reward)\n", + " if done:\n", + " T = t + 1\n", + " tau = t - n + 1\n", + " if tau >= 0:\n", + " gammas = np.array([gamma ** (i - tau) for i in range(tau, min(tau + n - 1, T - 1) + 1)])\n", + " deltas = np.array([r[i + 1] + gamma * v[s[i + 1]] - v[s[i]] for i in range(tau, min(tau + n - 1, T - 1) + 1)])\n", + " error = np.sum(gammas * deltas)\n", + " v[s[tau]] = v[s[tau]] + alpha * error\n", + " t += 1\n", + " \n", + " episode += 1\n", + " vs.append(v.copy()[1:-1])\n", + " \n", + " return np.array(vs)\n", + "\n", + "def train_nstep_TD(pi, alpha, gamma, n, max_episode):\n", + "\n", + " vs = []\n", + " v = np.zeros(21)\n", + " episode = 0\n", + " \n", + " while episode < max_episode:\n", + " done = False\n", + " st = 3\n", + " s = [st]\n", + " r = [0] # R_0 = 0\n", + " tau = 0\n", + " T = math.inf\n", + " t = 0\n", + " \n", + " while tau != T - 1:\n", + " if t < T:\n", + " a = pi(st)\n", + " st = st + a\n", + " reward = 0\n", + " if st == 0 or st == 20:\n", + " done = True\n", + " if st == 20:\n", + " reward = 1\n", + " else:\n", + " reward = -1\n", + " s.append(st)\n", + " r.append(reward)\n", + " if done:\n", + " T = t + 1\n", + " tau = t - n + 1\n", + " if tau >= 0:\n", + " gammas = np.array([gamma ** (i - tau - 1) for i in range(tau + 1, min(tau + n, T) + 1)])\n", + " r_sub = np.array(r[tau + 1:len(gammas) + tau + 1])\n", + " g = np.sum(r_sub * gammas)\n", + " if tau + n < T:\n", + " g += gamma ** n * v[s[tau + n]]\n", + " v[s[tau]] = v[s[tau]] + alpha * (g - v[s[tau]])\n", + " t += 1\n", + "\n", + " episode += 1\n", + " vs.append(v.copy()[1:-1])\n", + " \n", + " return np.array(vs)\n", + "\n", + "def parameter_analysis(alphas, ns, v, repeat=100, max_episode=10, gamma=1):\n", + " '''\n", + " Calculate RMS error for varying n, alpha\n", + " \n", + " Each (n,alpha) will be run times\n", + " RMS error for (n,alpha) will be over 19 states, episodes, and runs\n", + " '''\n", + " def pi(st):\n", + " # Use a stochastic policy\n", + " return random.choice([-1, 1])\n", + " \n", + " rms1 = np.zeros((len(ns), alphas.size))\n", + " rms2 = np.zeros((len(ns), alphas.size))\n", + " for i, n in enumerate(ns):\n", + " for j, alpha in enumerate(alphas):\n", + " for k in range(repeat):\n", + " vs1 = train_nstep_TD(pi, alpha, gamma, n, max_episode)\n", + " vs2 = train_nstep_TD_sum(pi, alpha, gamma, n, max_episode)\n", + " rms1[i, j] = rms1[i, j] + (np.sum([np.sqrt(np.sum(np.square(val-v))/5) for val in vs1]) / 19 - rms1[i, j]) / (k + 1)\n", + " rms2[i, j] = rms2[i, j] + (np.sum([np.sqrt(np.sum(np.square(val-v))/5) for val in vs2]) / 19 - rms2[i, j]) / (k + 1)\n", + " \n", + " return rms1, rms2\n", + "\n", + "if __name__ == '__main__':\n", + " # Find ground-truth state-values\n", + " d = np.ones((1, 18))[0] / 2\n", + " M = np.diag(d, -1) + np.diag(d, 1)\n", + " M = np.vstack((M, np.zeros((2,19))))\n", + " M = np.hstack((M, np.zeros((21,2))))\n", + " M[19,0] = 0.5\n", + " M[20,18] = 0.5\n", + " M[-1,-1] = 1\n", + " M[-2,-2] = 1\n", + " R = M[19:, :19]\n", + " Q = M[:19, :19]\n", + " It = np.eye(19)\n", + " v = np.matmul(R, np.linalg.inv(It - Q))[1,:] + np.matmul(R, np.linalg.inv(It - Q))[0,:] * -1\n", + " \n", + " # Parameters\n", + " alphas = np.linspace(0.2,0.8,10)\n", + " ns = [1,2,4,8]\n", + " \n", + " rms1, rms2 = parameter_analysis(alphas, ns, v)\n", + " \n", + " plt.figure()\n", + " for i in range(len(ns)):\n", + " plt.plot(alphas, rms1[i,:], label='n={}'.format(ns[i]))\n", + "\n", + " plt.legend(loc='upper right')\n", + " plt.xlabel('alpha')\n", + " plt.ylabel('Avg. RMS error over 19 states & 10 episodes')\n", + " plt.title('n-step method RMS')\n", + " plt.show()\n", + "\n", + " plt.figure()\n", + " for i in range(len(ns)):\n", + " plt.plot(alphas, rms2[i,:], label='n={}'.format(ns[i]))\n", + "\n", + " plt.legend(loc='upper right')\n", + " plt.xlabel('alpha')\n", + " plt.ylabel('Avg. RMS error over 19 states & 10 episodes')\n", + " plt.title('n-step TD error sum method RMS')\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "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": "3.7.7" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}