1_Basics_of_RL_Environments_and_Agents.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "1 - Basics of RL: Environments and Agents.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pNGaH_p3ivyj"
      },
      "source": [
        "Basic tutorial of RL environment classes and agent classes completed February 2021 by Annik Carson"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "39Xqcc-5OqH6"
      },
      "source": [
        "# basic imports for this notebook\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fMccmakD4cG9"
      },
      "source": [
        "# Fundamental Building Blocks of the Reinforcement Learning Problem\n",
        "A reinforcement learning problem is one where we are interested in how an agent learns from its interaction with the environment it operates in. The agent gets information from the environment about what state it is in, and chooses how to act in that state. The learning problem is about how to make better and better choices with the information you have. \n",
        "\n",
        "When the agent chooses an action, this has some effect on the environment. The agent tells the environment \"Ok, I choose to go left,\" and the environment gives it feedback about the consequences of that action. This feedback is in the form of information about:\n",
        "* What new state does this action take the agent to. For example, from state 1 taking action \"up\" might take you to state 2. \n",
        "* How good or bad that state and/or action selection was in the form of a reward signal. For example, the environment might tell the agent that the reward from taking action \"up\" from state 1 was worth +10 points.   "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x66wfAXW34uD"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rDBjFJ90a2zO"
      },
      "source": [
        "Here we need to make an environment which has the following functionality:\n",
        "* A defined size/shape\n",
        "* A rule for the consequences of actions\n",
        "  - Given the current state and action, produce a new state for the agent \n",
        "  - Given the current state, produce a reward signal upon leaving that state\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zTk_9HNaEFxh"
      },
      "source": [
        "# Making the Environment Class"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "code",
        "id": "ji25p-QqafuQ"
      },
      "source": [
        "# this class includes all the attributes and functions that define the environment \n",
        "# some sections will need to be completed\n",
        "class BasicEnv(object):\n",
        "  def __init__(self, env_shape, nactions):\n",
        "    self.shape    = env_shape                    # tuple describing dimensions of environment (row, column)\n",
        "    self.nstates  = self.shape[0]*self.shape[1]  # integer number of states \n",
        "    self.nactions = nactions                     # integer number of actions available \n",
        "\n",
        "    self.T = self.transition_function()          # a tensor of dimension (nstates x nstates x nactions)\n",
        "    \n",
        "    self.R = self.reward_function()              # a vector of length nstates - one reward for each state\n",
        "                                                  # a more complex reward function would be action dependent, \n",
        "                                                  # making it a matrix of dimension (nstates x nactions)\n",
        "\n",
        "  #checks to make sure all the probabilities for a certain action add up to 1\n",
        "  def check_transition_prob(self, transition_matrix):\n",
        "    action=0\n",
        "    check= True\n",
        "    for action in range(self.nactions):\n",
        "      for state in range(self.nstates):\n",
        "        sum=0\n",
        "        for state2 in range(self.nstates):\n",
        "          sum+=transition_matrix[state, state2, action]\n",
        "          if state2==self.nstates-1:\n",
        "            if \"%.*f\" % (1,sum)!= \"%.*f\" % (1,1):\n",
        "              check=False\n",
        "              break\n",
        "    return check\n",
        "\n",
        "  def transition_function(self):\n",
        "    # write a function that controls transitions between states\n",
        "\n",
        "    # initialize a tensor of the desired shape \n",
        "    T = np.zeros((self.nstates, self.nstates, self.nactions))\n",
        "\n",
        "    # the number at position T[s1, s2, a]\n",
        "    # describes a probability of moving FROM state s1 TO state s2 given an action a \n",
        "    \n",
        "    # check that all transitions probabilities out of one state sum to 1 - \n",
        "    #if self.check_transition_prob(T):\n",
        "    #  return T\n",
        "    #else:\n",
        "    #  raise Exception(\"transition prob does not sum to 1 \") \n",
        "    return T\n",
        "\n",
        "  def reward_function(self):\n",
        "    # write a function that controls reward\n",
        "    pass\n",
        "\n",
        "  def move(self, current_state, selected_action): \n",
        "    # write a function that returns a new state and reward for taking a \n",
        "    # particular action in a particular state\n",
        "    \n",
        "    done=False\n",
        "\n",
        "    # get next state \n",
        "    probabilities = self.T[current_state, : ,selected_action]\n",
        "    next_state = np.random.choice(np.arange(self.nstates), p=probabilities)\n",
        "    \n",
        "    # get reward\n",
        "    reward=self.R[current_state,0]\n",
        "\n",
        "    # set condition for when the agent is finished its trial in the environment\n",
        "    if reward != -1: ### NOTE: This is a poorly defined condition for done -- FIX THIS\n",
        "      done=True\n",
        "\n",
        "    return next_state, reward, done"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Eo1DVq1mSEOJ"
      },
      "source": [
        "## TASK: Write your own environment class"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TTMRI50oSLpj"
      },
      "source": [
        "class MyEnv(object):\n",
        "  def __init__(self):\n",
        "    pass"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_FEWBgcWa1IS"
      },
      "source": [
        "# Making a subclass of BasicEnv - BoundedGridworld"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nJ9DeKB3anvK"
      },
      "source": [
        "class BoundedGridworld(BasicEnv):\n",
        "  # this class inherits everything form the BasicEnv class \n",
        "  # here we will rewrite the class with specific transition rules which dictate\n",
        "  # that the agent can move around freely within the grid but moving into a boundary \n",
        "  # will have no effect \n",
        "  def __init__(self, env_shape, nactions):\n",
        "    super(BoundedGridworld,self).__init__(env_shape, nactions)        # this calls the init function of BasicEnv so we get self.nstates, etc.\n",
        "\n",
        "    # here we write over self.T and self.R defined in the BasicEnv.__init__() \n",
        "    # using the transition_function and reward_function defined in this class, BoundedGridworld\n",
        "    self.T = self.grid_transition_bounded()          # a tensor of dimension (nstates x nstates x nactions)\n",
        "    \n",
        "    self.R = self.reward_function()              # a vector of length nstates - one reward for each state\n",
        "                                                 # a more complex reward function would be action dependent, \n",
        "                                                 # making it a matrix of dimension (nstates x nactions)\n",
        "  def grid_transition_bounded(self):\n",
        "    # initialize\n",
        "    T = np.zeros((self.nstates, self.nstates, self.nactions))  # down, up, right, left\n",
        "\n",
        "    # add neighbor connections and jumps, remove for endlines\n",
        "    #T [starting_state, ending_state, action]\n",
        "    T[list(range(0, self.nstates-self.shape[1])), list(range(self.shape[1],self.nstates)), 0] = 1     #down\n",
        "    T[list(range(self.shape[1],self.nstates)),  list(range(0, self.nstates-self.shape[1])),1] = 1     # up\n",
        "    T[list(range(0, self.nstates-1)),               list(range(1, self.nstates)),              2] = 1     # right\n",
        "    T[list(range(1, self.nstates)),               list(range(0, self.nstates-1)),              3] = 1     # left\n",
        "\n",
        "    #remove endlines\n",
        "    T[list(range(self.shape[1]-1, self.nstates-1, self.shape[1])), list(range(self.shape[1], self.nstates, self.shape[1])),  2 ] = 0    # remove transitions from endlines on right action\n",
        "    T[list(range(0,self.nstates-self.shape[1]+1, self.shape[1])) , list(range(-1,self.nstates-self.shape[1], self.shape[1])), 3] = 0    # remove transitions from endlines on left action\n",
        "    # include self transitions \n",
        "    #T[start_state, end_state, action]\n",
        "    T[list(range(self.nstates-self.shape[1],self.nstates)),list(range(self.nstates-self.shape[1], self.nstates)), 0] = 1\n",
        "    T[list(range(self.shape[1])),list(range(self.shape[1])), 1] = 1    \n",
        "    T[list(range(self.shape[1]-1, self.nstates, self.shape[1])), list(range(self.shape[1]-1, self.nstates, self.shape[1])),  2 ] = 1\n",
        "    T[list(range(0,self.nstates-self.shape[1]+1, self.shape[1])) , list(range(0,self.nstates-self.shape[1]+1, self.shape[1])), 3] = 1\n",
        "\n",
        "    if self.check_transition_prob(T) == True:\n",
        "      return T\n",
        "    else:\n",
        "      raise Exception(\"transition prob does not sum to 1 \") \n",
        "  \n",
        "  def reward_function(self):\n",
        "    R = np.ones((self.nstates, 1))*-1 # reward is -1 in all states for all actions\n",
        "    R[-1] = 100                       # reward is 100 in last state \n",
        "    return R \n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dTIBA9BBEvJm"
      },
      "source": [
        "# Another Subclass - EdgewrapGridworld"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tNbTFV6CEykT"
      },
      "source": [
        "class EdgewrapGridworld(BasicEnv):\n",
        "  # this class inherits everything form the BasicEnv class \n",
        "  # here we will rewrite the class with specific transition rules which dictate\n",
        "  # that the agent can move around freely within the grid and that moving off the\n",
        "  # grid on one side will return you to the other side of the grid (ex. pacman)\n",
        "\n",
        "  def __init__(self, env_shape, nactions):\n",
        "    super().__init__(env_shape, nactions)        # this calls the init function of BasicEnv so we get self.nstates, etc.\n",
        "\n",
        "    # here we write over self.T and self.R defined in the BasicEnv.__init__() \n",
        "    # using the grid_transition_edgeWrapping and reward_function defined in this class, EdgewrapGridworld\n",
        "    self.T = self.grid_transtion_edgeWrapping()\n",
        "    \n",
        "    self.R = self.reward_function()\n",
        "    \n",
        "  #creates transition matrix for edge-wrapping environment\n",
        "  def grid_transtion_edgeWrapping(self):    \n",
        "    # initialize\n",
        "    T = np.zeros((self.nstates, self.nstates, self.nactions))  #T [starting_state, ending_state, action]\n",
        "\n",
        "    # add neighbor connections \n",
        "    T[list(range(0, self.nstates-self.shape[1])), list(range(self.shape[1],self.nstates)), 0] = 1     #down\n",
        "    T[list(range(self.shape[1],self.nstates)),  list(range(0, self.nstates-self.shape[1])),1] = 1     # up\n",
        "    T[list(range(0, self.nstates-1)),               list(range(1, self.nstates)),              2] = 1     # right\n",
        "    T[list(range(1, self.nstates)),               list(range(0, self.nstates-1)),              3] = 1     # left\n",
        "\n",
        "    #remove endlines\n",
        "    T[list(range(self.shape[1]-1, self.nstates-1, self.shape[1])), list(range(self.shape[1], self.nstates, self.shape[1])),  2 ] = 0 # remove transitions from endlines on right action\n",
        "    T[list(range(0,self.nstates-self.shape[1]+1, self.shape[1])) , list(range(-1,self.nstates-self.shape[1], self.shape[1])), 3] = 0 # remove transitions from endlines on left action\n",
        "    \n",
        "    #add in connections to wrap around environment - return you to same line you were in on the other side\n",
        "    T[list(range(self.nstates-self.shape[1],self.nstates)),list(range(self.shape[1])), 0] = 1\n",
        "    T[list(range(self.shape[1])),list(range(self.nstates-self.shape[1],self.nstates)), 1] = 1    \n",
        "    T[list(range(self.shape[1]-1, self.nstates, self.shape[1])),list(range(0,self.nstates-self.shape[1]+1, self.shape[1])) ,  2 ] = 1 \n",
        "    T[list(range(0,self.nstates-self.shape[1]+1, self.shape[1])) , list(range(self.shape[1]-1, self.nstates, self.shape[1])), 3] = 1\n",
        "    \n",
        "    if self.check_transition_prob(T) == True:\n",
        "      return T\n",
        "    else:\n",
        "      raise Exception(\"transition prob does not sum to 1 \") \n",
        "  \n",
        "  def reward_function(self):\n",
        "    R = np.ones((self.nstates, 1))*-1 # reward is -1 in all states for all actions\n",
        "    R[-1] = 100                       # reward is 100 in last state \n",
        "    return R "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m9av-1yVF3RD"
      },
      "source": [
        "# Another Subclass - CliffWorld \n",
        "This environment is used to highlight the differences in tabular Q learning and SARSA (Sutton and Barto section 6.5 example 6.6 - Cliff walking)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5HfIQcjEF2D8"
      },
      "source": [
        "class CliffWorld(BasicEnv):\n",
        "  def __init__(self, env_shape, nactions):\n",
        "    super().__init__(env_shape, nactions)        # this calls the init function of BasicEnv so we get self.nstates, etc.\n",
        "\n",
        "    # here we write over self.T and self.R defined in the BasicEnv.__init__() \n",
        "    # using the transition_function and reward_function defined in this class, CliffWorld\n",
        "    self.T = self.grid_transtion_cliff_bottom()\n",
        "    \n",
        "    self.R = self.set_cliff_reward()\n",
        "\n",
        "  #creates transition vector for cliff environment\n",
        "  def grid_transtion_cliff_bottom(self):\n",
        "    T = np.zeros((self.nstates, self.nstates, self.nactions)) #T [starting_state, ending_state, action]\n",
        "\n",
        "    # add neighbor connections and jumps, remove for endlines\n",
        "    T[list(range(0, self.nstates-2*self.shape[1])), list(range(self.shape[1],self.nstates-self.shape[1])), 0] = 1     #down\n",
        "    T[list(range(self.shape[1],self.nstates)),  list(range(0, self.nstates-self.shape[1])),1] = 1     # up\n",
        "    T[list(range(0, self.nstates-1)),               list(range(1, self.nstates)),              2] = 1     # right\n",
        "    T[list(range(1, self.nstates)),               list(range(0, self.nstates-1)),              3] = 1     # left\n",
        "\n",
        "    #remove endlines\n",
        "    T[list(range(self.shape[1]-1, self.nstates-1, self.shape[1])), list(range(self.shape[1], self.nstates, self.shape[1])),  2 ] = 0    # remove transitions from endlines on right action\n",
        "    T[list(range(0,self.nstates-self.shape[1]+1, self.shape[1])) , list(range(-1,self.nstates-self.shape[1], self.shape[1])), 3] = 0    # remove transitions from endlines on left action\n",
        "    # include self transitions \n",
        "    #T[start_state, end_state, action]\n",
        "    T[list(range(self.nstates-self.shape[1],self.nstates)),list(range(self.nstates-self.shape[1], self.nstates)), 0] = 1\n",
        "    T[list(range(self.shape[1])),list(range(self.shape[1])), 1] = 1    \n",
        "    T[list(range(self.shape[1]-1, self.nstates, self.shape[1])), list(range(self.shape[1]-1, self.nstates, self.shape[1])),  2 ] = 1\n",
        "    T[list(range(0,self.nstates-self.shape[1]+1, self.shape[1])) , list(range(0,self.nstates-self.shape[1]+1, self.shape[1])), 3] = 1\n",
        "\n",
        "    #moving into the cliff states, takes agent back to start \n",
        "    T[list(range((self.shape[1]*(self.shape[0]-2))+1,(self.shape[1]*(self.shape[0]-1))-1)), self.nstates-self.shape[1], 0] = 1 #when taking down action from states above cliff states\n",
        "    T[(self.shape[1]*(self.shape[0]-2)),self.nstates-self.shape[1], 0]=1\n",
        "    T[(self.shape[1]*(self.shape[0]-1))-1,self.nstates-1, 0]=1\n",
        "    T[self.nstates-self.shape[1], self.nstates-self.shape[1]+1, 2] = 0\n",
        "    T[self.nstates-self.shape[1], self.nstates-self.shape[1], 2] = 1 #from the left of cliff states\n",
        "    T[self.nstates-1, self.nstates-2, 3] = 0\n",
        "    T[self.nstates-1, self.nstates-self.shape[1], 3] = 1 #from the right of cliff states\n",
        "\n",
        "    if self.check_transition_prob(T) == True:\n",
        "      return T\n",
        "    else:\n",
        "      raise Exception(\"transition prob does not sum to 1 \") \n",
        "  \n",
        "  #creates reward vector for the cliff evironment where all cliff states are worth -100 and terminal state is 100\n",
        "  def set_cliff_reward(self):\n",
        "    R=np.ones((self.nstates,1))*-1\n",
        "    R[-1] = 100\n",
        "    R[list(range((self.shape[1]*(self.shape[0]-2))+1,(self.shape[1]*(self.shape[0]-1))-1))] = -100\n",
        "    return R"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sgYCWZVOIylO"
      },
      "source": [
        "# Create an Environment and test the move() function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jb3waOAGKw03"
      },
      "source": [
        "env_shape = (10,10)\n",
        "num_actions = 4\n",
        "named_actions = ['Down', 'Up', 'Right','Left']\n",
        "bounded_env = BoundedGridworld(env_shape, num_actions)\n",
        "wrapped_env = EdgewrapGridworld(env_shape, num_actions)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IlZKDHeXLcQq",
        "outputId": "bc09ab3a-aa9c-42f6-f0cb-3a6c3bce7ada"
      },
      "source": [
        "start_state = 0\n",
        "action      = np.random.choice(num_actions)\n",
        "next_state, reward, done  = bounded_env.move(start_state, action)\n",
        "print(f'Started in state {start_state}, took action {action}:{named_actions[action]}, moved to state {next_state}')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Started in state 0, took action 0:Down, moved to state 10\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x6rZ_vdmVLOA"
      },
      "source": [
        "# Make a basic \"agent\"\n",
        "An agent takes in information of state and produces an action\n",
        "The most basic agent will just choose actions randomly"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jb7zSOIWVcwh"
      },
      "source": [
        "class RandomAgent(object):\n",
        "  def __init__(self, num_actions):\n",
        "    self.num_actions = num_actions\n",
        "  def select_action(self, state):\n",
        "    # state actually does nothing in this agent, but we will want our action selection\n",
        "    # in later agents to be based on the state we're in\n",
        "    action = np.random.choice(self.num_actions)\n",
        "    return action\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2fF68ljjV64s"
      },
      "source": [
        "# Take a step in the environment with your agent\n",
        "This is identical to what we did above, but now we're wrapping it up in an agent class"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eTO0KwA3WTNk",
        "outputId": "1f339d84-de62-4068-e1f6-fb67fb00da6f"
      },
      "source": [
        "# make agent \n",
        "agent = RandomAgent(num_actions)\n",
        "\n",
        "start_state = 0\n",
        "### here we select the action with the agent instead\n",
        "action      = agent.select_action(start_state)\n",
        "next_state, reward, done  = bounded_env.move(start_state, action)\n",
        "print(f'Started in state {start_state}, took action {action}:{named_actions[action]}, moved to state {next_state}')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Started in state 0, took action 1:Up, moved to state 0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f5tGjk-eP11M"
      },
      "source": [
        "# Take multiple steps in the environment with your random agent \n",
        "Write a function to take random actions in the environment for some number of trials (trial end when done=True)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hooZ1p8HPdPd"
      },
      "source": [
        "def navigate_env(env, agent, num_trials, random_start=False):\n",
        "  reward_per_trial = []\n",
        "  for trial in range(num_trials):\n",
        "    total_reward = 0\n",
        "    done = False\n",
        "\n",
        "    if random_start:\n",
        "      start = np.random.choice(env.nstates)\n",
        "    else: \n",
        "      state = 0 \n",
        "    while not done:\n",
        "      # randomly sample an action \n",
        "      action = agent.select_action(state)\n",
        "\n",
        "      # take a step in the environment\n",
        "      next_state, reward, done = env.move(state, action)\n",
        "\n",
        "      # keep running total of rewards observed\n",
        "      total_reward += reward\n",
        "\n",
        "      if done:\n",
        "        break\n",
        "\n",
        "      state = next_state\n",
        "    reward_per_trial.append(total_reward)\n",
        "    # every 50 trials print something:\n",
        "    if trial%50==0:\n",
        "      print(f'Trial: {trial}, Total Reward = {total_reward}')\n",
        "  return reward_per_trial"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SYozMdE_RVHF",
        "outputId": "79d4e843-a902-47f6-c5cd-59900fc0e809"
      },
      "source": [
        "# the navigate function takes an environment as an object, so you can pass either bounded_env or wrapped_env\n",
        "num_trials = 100\n",
        "\n",
        "## bounded_env, wrapped_env, and agent all instantiated above \n",
        "bounded_rewards =navigate_env(bounded_env, agent, num_trials, random_start=False)\n",
        "wrapped_rewards = navigate_env(wrapped_env,agent, num_trials, random_start=False)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Trial: 0, Total Reward = -921.0\n",
            "Trial: 50, Total Reward = -8.0\n",
            "Trial: 0, Total Reward = 98.0\n",
            "Trial: 50, Total Reward = 96.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n0x2iVIDUNAs"
      },
      "source": [
        "Plot the results of random action selection. Which does better? Why? "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "yZZifpLnRajg",
        "outputId": "8bd30407-0350-4bb2-ae73-ddf1fb1fff55"
      },
      "source": [
        "plt.figure()\n",
        "plt.plot(bounded_rewards, label='bounded')\n",
        "plt.plot(wrapped_rewards, label='wrapped')\n",
        "plt.legend(bbox_to_anchor=(1.05,0.95))\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Mcj-7QRTUDw0"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}