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td-gamma.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "TD(\\gamma).ipynb",
"version": "0.3.2",
"provenance": [],
"collapsed_sections": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"[View in Colaboratory](https://colab.research.google.com/gist/kbobyrev/90efb074a4740f8a8a6abf22e58d988a/td-gamma.ipynb)"
]
},
{
"metadata": {
"id": "EQN5Mc28hEpF",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"# TD($\\gamma$)\n",
"\n",
"Implementation of **TD($\\gamma$)** algorithm after the [original paper](https://users.cs.duke.edu/~gdk/pubs/td_gamma.pdf)."
]
},
{
"metadata": {
"id": "6DEOJnl0idB-",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 221
},
"outputId": "6a245787-e497-4d01-d740-b5e24079ac24"
},
"cell_type": "code",
"source": [
"!pip install --upgrade gym\n",
"!pip install --upgrade seaborn\n",
"!pip install --upgrade tqdm"
],
"execution_count": 2,
"outputs": [
{
"output_type": "stream",
"text": [
"Requirement already up-to-date: gym in /usr/local/lib/python3.6/dist-packages (0.10.5)\n",
"Requirement not upgraded as not directly required: requests>=2.0 in /usr/local/lib/python3.6/dist-packages (from gym) (2.18.4)\n",
"Requirement not upgraded as not directly required: numpy>=1.10.4 in /usr/local/lib/python3.6/dist-packages (from gym) (1.14.3)\n",
"Requirement not upgraded as not directly required: pyglet>=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym) (1.3.2)\n",
"Requirement not upgraded as not directly required: six in /usr/local/lib/python3.6/dist-packages (from gym) (1.11.0)\n",
"Requirement not upgraded as not directly required: chardet<3.1.0,>=3.0.2 in /usr/local/lib/python3.6/dist-packages (from requests>=2.0->gym) (3.0.4)\n",
"Requirement not upgraded as not directly required: certifi>=2017.4.17 in /usr/local/lib/python3.6/dist-packages (from requests>=2.0->gym) (2018.4.16)\n",
"Requirement not upgraded as not directly required: urllib3<1.23,>=1.21.1 in /usr/local/lib/python3.6/dist-packages (from requests>=2.0->gym) (1.22)\n",
"Requirement not upgraded as not directly required: idna<2.7,>=2.5 in /usr/local/lib/python3.6/dist-packages (from requests>=2.0->gym) (2.6)\n",
"Requirement not upgraded as not directly required: future in /usr/local/lib/python3.6/dist-packages (from pyglet>=1.2.0->gym) (0.16.0)\n",
"Requirement already up-to-date: seaborn in /usr/local/lib/python3.6/dist-packages (0.8.1)\n",
"Requirement already up-to-date: tqdm in /usr/local/lib/python3.6/dist-packages (4.23.3)\n"
],
"name": "stdout"
}
]
},
{
"metadata": {
"id": "bJJA9jdyijPw",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"import matplotlib\n",
"import tensorflow\n",
"import gym\n",
"import seaborn\n",
"import numpy\n",
"import tqdm"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "T8s0n_HvIZsT",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"seaborn.set()"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "yoscc2kUhZRP",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"This experiment is based on Shangtong Zhang's code used to create a figure for the Reinforcement Learning: An Introduction book (Chatper 12)."
]
},
{
"metadata": {
"id": "up6KZR8XqeOU",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 756862
},
"outputId": "71886eb2-d0f4-46f8-bdb3-9cfa914d3823"
},
"cell_type": "code",
"source": [
"#######################################################################\n",
"# Copyright (C) #\n",
"# 2016 Shangtong Zhang(zhangshangtong.cpp@gmail.com) #\n",
"# 2016 Kenta Shimada(hyperkentakun@gmail.com) #\n",
"# Permission given to modify the code as long as you keep this #\n",
"# declaration at the top #\n",
"#######################################################################\n",
"\n",
"from __future__ import print_function\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# all states\n",
"N_STATES = 19\n",
"\n",
"# all states but terminal states\n",
"states = np.arange(1, N_STATES + 1)\n",
"\n",
"# start from the middle state\n",
"START_STATE = 10\n",
"\n",
"# two terminal states\n",
"# an action leading to the left terminal state has reward -1\n",
"# an action leading to the right terminal state has reward 1\n",
"END_STATES = [0, N_STATES + 1]\n",
"\n",
"# true state values from Bellman equation\n",
"realStateValues = np.arange(-20, 22, 2) / 20.0\n",
"realStateValues[0] = realStateValues[N_STATES + 1] = 0.0\n",
"\n",
"# base class for lambda-based algorithms in this chapter\n",
"# In this example, we use the simplest linear feature function, state\n",
"# aggregation. And we use exact 19 groups, so the weights for each group is\n",
"# exact the value for that state\n",
"class ValueFunction:\n",
" # @rate: lambda, as it's a keyword in python, so I call it rate\n",
" # @stepSize: alpha, step size for update\n",
" def __init__(self, rate, stepSize):\n",
" self.rate = rate\n",
" self.stepSize = stepSize\n",
" self.weights = np.zeros(N_STATES + 2)\n",
"\n",
" # the state value is just the weight\n",
" def value(self, state):\n",
" return self.weights[state]\n",
"\n",
" # feed the algorithm with new observation\n",
" # derived class should override this function\n",
" def learn(self, state, reward):\n",
" return\n",
"\n",
" # initialize some variables at the beginning of each episode\n",
" # must be called at the very beginning of each episode\n",
" # derived class should override this function\n",
" def newEpisode(self):\n",
" return\n",
"\n",
"# TD(lambda) algorithm\n",
"class TemporalDifferenceLambda(ValueFunction):\n",
" def __init__(self, rate, stepSize):\n",
" ValueFunction.__init__(self, rate, stepSize)\n",
" self.newEpisode()\n",
"\n",
" def newEpisode(self):\n",
" # initialize the eligibility trace\n",
" self.eligibility = np.zeros(N_STATES + 2)\n",
" # initialize the beginning state\n",
" self.lastState = START_STATE\n",
"\n",
" def learn(self, state, reward):\n",
" # update the eligibility trace and weights\n",
" self.eligibility *= self.rate\n",
" self.eligibility[self.lastState] += 1\n",
" delta = reward + self.value(state) - self.value(self.lastState)\n",
" delta *= self.stepSize\n",
" self.weights += delta * self.eligibility\n",
" self.lastState = state\n",
"\n",
"# 19-state random walk\n",
"def randomWalk(valueFunction):\n",
" valueFunction.newEpisode()\n",
" currentState = START_STATE\n",
" while currentState not in END_STATES:\n",
" newState = currentState + np.random.choice([-1, 1])\n",
" if newState == 0:\n",
" reward = -1\n",
" elif newState == N_STATES + 1:\n",
" reward = 1\n",
" else:\n",
" reward = 0\n",
" valueFunction.learn(newState, reward)\n",
" currentState = newState\n",
"\n",
"def figure_(valueFunctionGenerator, runs, lambdas, alphas):\n",
" # play for 10 episodes for each run\n",
" episodes = 10\n",
" # track the rms errors\n",
" errors = [np.zeros(len(alphas_)) for alphas_ in alphas]\n",
" for run in range(runs):\n",
" for lambdaIndex, rate in zip(range(len(lambdas)), lambdas):\n",
" for alphaIndex, alpha in zip(range(len(alphas[lambdaIndex])),\n",
" alphas[lambdaIndex]):\n",
" valueFunction = valueFunctionGenerator(rate, alpha)\n",
" for episode in range(episodes):\n",
" print('run:', run, 'lambda:', rate, 'alpha:', alpha,\n",
" 'episode:', episode)\n",
" randomWalk(valueFunction)\n",
" stateValues = [valueFunction.value(state)\n",
" for state in states]\n",
" errors[lambdaIndex][alphaIndex] += np.sqrt(np.mean(\n",
" np.power(stateValues - realStateValues[1: -1], 2)))\n",
"\n",
" # average over runs and episodes\n",
" for error in errors:\n",
" error /= episodes * runs\n",
" plt.figure()\n",
" for i in range(len(lambdas)):\n",
" plt.plot(alphas[i], errors[i], label='lambda = ' + str(lambdas[i]))\n",
" plt.xlabel('learning rate')\n",
" plt.ylabel('RMSE')\n",
" \n",
"# Figure: TD(lambda) algorithm\n",
"def td_figure():\n",
" lambdas = [0.0, 0.4, 0.8, 0.9, 0.95, 0.975, 0.99, 1]\n",
" alphas = [np.arange(0, 1.1, 0.1),\n",
" np.arange(0, 1.1, 0.1),\n",
" np.arange(0, 0.99, 0.09),\n",
" np.arange(0, 0.55, 0.05),\n",
" np.arange(0, 0.33, 0.03),\n",
" np.arange(0, 0.22, 0.02),\n",
" np.arange(0, 0.11, 0.01),\n",
" np.arange(0, 0.044, 0.004)]\n",
" figure_(TemporalDifferenceLambda, 50, lambdas, alphas)\n",
"\n",
"\n",
"td_figure()\n",
"plt.savefig('td_lambda_random_walk.jpeg')"
],
"execution_count": 5,
"outputs": [
{
"output_type": "stream",
"text": [
"run: 0 lambda: 0.0 alpha: 0.0 episode: 0\n",
"run: 0 lambda: 0.0 alpha: 0.0 episode: 1\n",
"run: 0 lambda: 0.0 alpha: 0.0 episode: 2\n",
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"run: 0 lambda: 0.0 alpha: 0.1 episode: 0\n",
"run: 0 lambda: 0.0 alpha: 0.1 episode: 1\n",
"run: 0 lambda: 0.0 alpha: 0.1 episode: 2\n",
"run: 0 lambda: 0.0 alpha: 0.1 episode: 3\n",
"run: 0 lambda: 0.0 alpha: 0.1 episode: 4\n",
"run: 0 lambda: 0.0 alpha: 0.1 episode: 5\n",
"run: 0 lambda: 0.0 alpha: 0.1 episode: 6\n",
"run: 0 lambda: 0.0 alpha: 0.1 episode: 7\n",
"run: 0 lambda: 0.0 alpha: 0.1 episode: 8\n",
"run: 0 lambda: 0.0 alpha: 0.1 episode: 9\n",
"run: 0 lambda: 0.0 alpha: 0.2 episode: 0\n",
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"run: 0 lambda: 0.0 alpha: 0.2 episode: 3\n",
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"run: 0 lambda: 0.0 alpha: 0.2 episode: 9\n",
"run: 0 lambda: 0.0 alpha: 0.30000000000000004 episode: 0\n",
"run: 0 lambda: 0.0 alpha: 0.30000000000000004 episode: 1\n",
"run: 0 lambda: 0.0 alpha: 0.30000000000000004 episode: 2\n",
"run: 0 lambda: 0.0 alpha: 0.30000000000000004 episode: 3\n",
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"run: 0 lambda: 0.0 alpha: 0.30000000000000004 episode: 8\n",
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"run: 0 lambda: 0.0 alpha: 0.4 episode: 0\n",
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"run: 0 lambda: 0.4 alpha: 0.7000000000000001 episode: 1\n",
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"text": [
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},
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"text": [
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},
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},
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},
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"name": "stdout"
},
{
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"text": [
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},
{
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},
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},
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"name": "stdout"
},
{
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"text": [
" alpha: 0.0 episode: 8\n",
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],
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},
{
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],
"name": "stdout"
},
{
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"text": [
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