finite-mdps.ipynb

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   "source": [
    "# Finite Markov Decision Processes\n",
    "\n",
    "Finite because the state and actions are discrete. Markovian because state depends only on the previous state + action pair. "
   ]
  },
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   "source": [
    "from enum import IntEnum\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import plotly.express as px\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "import gymnasium as gym\n",
    "from gymnasium import spaces"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8c695da-4a81-4a57-9382-c2ad8c2eac38",
   "metadata": {},
   "source": [
    "## Q-Learning / Sarsa & Double Q-Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "b3678658-d48d-4f21-bb39-26fcb67678d2",
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   "source": [
    "def one_of_best(values, available_actions=None):\n",
    "    if available_actions is None:\n",
    "        return np.random.choice(np.where(values==np.max(values))[0])\n",
    "    argmaxes = np.where(values==np.max(values[available_actions]))[0]\n",
    "    return np.random.choice(argmaxes[np.isin(argmaxes, available_actions)])\n",
    "\n",
    "class QLearning:\n",
    "    def __init__(self, env, alpha, eps, s_dims, a_dim, sarsa=False, gamma=1):\n",
    "        # I added the env as an argument as a convenience to track state dependent number of actions. \n",
    "        # You could pass the method instead if you don't want to code against a gym class.\n",
    "        self.env = env\n",
    "        self.alpha = alpha\n",
    "        self.eps = eps\n",
    "        self.a_dim = a_dim\n",
    "        self.q = np.zeros(s_dims + [a_dim])\n",
    "        self.sarsa = sarsa\n",
    "        self.gamma = gamma\n",
    "\n",
    "    def init_episode(self, init_s, init_a):\n",
    "        self.s = init_s\n",
    "        self.a = init_a\n",
    "\n",
    "    def sample(self, state):\n",
    "        if np.random.rand() > self.eps:\n",
    "            return one_of_best(self.q[*state], \n",
    "                               np.arange(self.env.action_space.n))\n",
    "        return np.random.choice(self.env.action_space.n)\n",
    "\n",
    "    def update(self, reward, n_state):\n",
    "        if self.sarsa:\n",
    "            n_action = self.sample(n_state)\n",
    "            next_q = self.q[*n_state, n_action]\n",
    "        else:\n",
    "            next_q = np.max(self.q[*n_state])\n",
    "        self.q[*self.s, self.a] += self.alpha*(reward + self.gamma*next_q - self.q[*self.s, self.a])\n",
    "        self.s = n_state\n",
    "        if self.sarsa:\n",
    "            self.a = n_action\n",
    "        else:\n",
    "            self.a = self.sample(n_state)"
   ]
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   "id": "0f5bf5a1-a911-4b41-98cf-d274c49e51cb",
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   "source": [
    "class DQLearning:\n",
    "    def __init__(self, env, alpha, eps, s_dims, a_dim, gamma=1):\n",
    "        self.env = env\n",
    "        self.alpha = alpha\n",
    "        self.eps = eps\n",
    "        self.a_dim = a_dim\n",
    "        self.q1 = np.zeros(s_dims + [a_dim])\n",
    "        self.q2 = np.zeros(s_dims + [a_dim])\n",
    "        self.gamma = gamma\n",
    "\n",
    "    def init_episode(self, init_s, init_a):\n",
    "        self.s = init_s\n",
    "        self.a = init_a\n",
    "\n",
    "    def sample(self, state):\n",
    "        if np.random.rand() > self.eps:\n",
    "            return one_of_best(self.q1[*state] + self.q2[*state], \n",
    "                               np.arange(self.env.action_space.n))\n",
    "        return np.random.choice(self.env.action_space.n)\n",
    "\n",
    "    def update(self, reward, n_state):\n",
    "        if np.random.rand() >= 0.5:\n",
    "            a = one_of_best(self.q1[*n_state], \n",
    "                            np.arange(self.env.action_space.n))\n",
    "            self.q1[*self.s, self.a] += self.alpha*(reward \n",
    "                                                    + self.gamma*self.q2[*n_state, a]\n",
    "                                                    - self.q1[*self.s, self.a])\n",
    "        else:\n",
    "            a = one_of_best(self.q2[*n_state], \n",
    "                            np.arange(self.env.action_space.n))\n",
    "            self.q2[*self.s, self.a] += self.alpha*(reward \n",
    "                                                    + self.gamma*self.q1[*n_state, a]\n",
    "                                                    - self.q2[*self.s, self.a])\n",
    "        self.s = n_state\n",
    "        self.a = self.sample(n_state)"
   ]
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   "source": [
    "def print_opt_policy(q, start, finish):\n",
    "    dims = q.shape[:-1]\n",
    "    for i in range(0, dims[0]):\n",
    "        print('\\n')\n",
    "        for j in range(0, dims[1]):\n",
    "            if [i, j] == start:\n",
    "                print(' 0 ', end=\"\")\n",
    "                continue\n",
    "            if [i, j] == finish:\n",
    "                print(' * ', end=\"\")\n",
    "                continue\n",
    "            bestAction = np.argmax(q[i, j, :])\n",
    "            if bestAction == Action.N:\n",
    "                print(' ↑ ', end=\"\")\n",
    "            elif bestAction == Action.S:\n",
    "                print(' ↓ ', end=\"\")\n",
    "            elif bestAction == Action.W:\n",
    "                print(' ← ', end=\"\")\n",
    "            elif bestAction == Action.E:\n",
    "                print(' → ', end=\"\")"
   ]
  },
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   "cell_type": "markdown",
   "id": "c4bde41f-3294-4cf1-b42e-08b31dcd225f",
   "metadata": {},
   "source": [
    "## First a simple discrete observation space, Windy Grid World from eg. 6.5"
   ]
  },
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   "cell_type": "code",
   "execution_count": 8,
   "id": "2586387d-5ba0-4bc1-b11c-a26a2fb400d2",
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   "source": [
    "class Action(IntEnum):\n",
    "    N = 0\n",
    "    S = 1\n",
    "    W = 2\n",
    "    E = 3\n",
    "\n",
    "class WindyGridworld(gym.Env):\n",
    "    def __init__(self):\n",
    "        self.dims = [7, 10]\n",
    "        \n",
    "        self.action_space = spaces.Discrete(4)\n",
    "        self.observation_space = spaces.Tuple((\n",
    "                spaces.Discrete(self.dims[0]),\n",
    "                spaces.Discrete(self.dims[1])\n",
    "                ))\n",
    "        self.start = [3, 0]\n",
    "        self.goal = [3, 7]\n",
    "        self.wind = [0, 0, 0, 1, 1, 1, 2, 2, 1, 0]\n",
    "\n",
    "        self.reset()\n",
    "\n",
    "    def step(self, action):\n",
    "        \"\"\"\n",
    "        Returns: observation, reward, terminated, truncated, info\n",
    "        \"\"\"\n",
    "        self.t += 1\n",
    "        i, j = self.S\n",
    "\n",
    "        if action == Action.S:\n",
    "            i  = max(min(i + 1 - self.wind[j], self.dims[0] - 1), 0)\n",
    "        elif action == Action.N:\n",
    "            i = max(i - 1 - self.wind[j], 0)\n",
    "        elif action in [Action.W, Action.E]:\n",
    "            i = max(i - self.wind[j], 0)\n",
    "            if action == Action.E:\n",
    "                j = min(j + 1, self.dims[1] - 1)\n",
    "            elif action == Action.W:\n",
    "                j = max(j - 1, 0)\n",
    "\n",
    "        self.S = [i, j]\n",
    "        return self.S, -1, self.S == self.goal, False, {}\n",
    "\n",
    "    def reset(self):\n",
    "        self.S = self.start\n",
    "        self.t = 0\n",
    "        return self.S, {}"
   ]
  },
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   "execution_count": 81,
   "id": "8a98d0f3-612f-455e-b5ed-aa3c298863ed",
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   "outputs": [],
   "source": [
    "env = WindyGridworld()\n",
    "observation = env.reset()\n",
    "dims = [o.n for o in env.observation_space]"
   ]
  },
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    "np.random.seed(seed=123456789)\n",
    "\n",
    "n = 200 \n",
    "\n",
    "ts = np.zeros(n)\n",
    "algo = QLearning(env, 0.5, 0.1, dims, env.action_space.n)\n",
    "for i in range(n):\n",
    "    observation, info = env.reset()\n",
    "    action = algo.sample(observation)\n",
    "    algo.init_episode(observation, action)\n",
    "    t = 1\n",
    "    while True:\n",
    "        observation, reward, terminated, truncated, info = env.step(algo.a)\n",
    "        algo.update(reward, observation)\n",
    "        if terminated:\n",
    "            break\n",
    "        t += 1\n",
    "    ts[i] = t"
   ]
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",
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   "source": [
    "px.line(x=np.cumsum(ts), y=np.arange(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "0fead195-2cd5-44be-bde6-d2943a9dc71e",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 0, 0, 1, 1, 1, 2, 2, 1, 0]\n",
      "\n",
      "\n",
      " ↑  →  →  →  →  →  →  →  →  ↓ \n",
      "\n",
      " →  →  →  →  →  →  →  →  →  ↓ \n",
      "\n",
      " ↑  →  →  →  →  →  →  ↑  →  ↓ \n",
      "\n",
      " 0  →  →  →  →  →  ↑  *  →  ↓ \n",
      "\n",
      " ←  ↓  →  →  →  →  ↑  ↓  ←  ← \n",
      "\n",
      " ↓  →  ↓  →  →  ↑  ↑  ↑  ←  ↓ \n",
      "\n",
      " →  →  ↓  →  ↑  ↑  ↑  ↑  ↑  ↓ "
     ]
    }
   ],
   "source": [
    "## visualize optimal move for windy grid world: follow the arrows from 0 to * but imagine the wind lifting you\n",
    "## upward!\n",
    "print(env.wind)\n",
    "print_opt_policy(algo.q, env.start, env.goal)"
   ]
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   "cell_type": "markdown",
   "id": "23d2e59c-ccb0-4e8b-9b1c-b40c3dc17bb8",
   "metadata": {
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    "slideshow": {
     "slide_type": ""
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    "tags": []
   },
   "source": [
    "## Cliff Walking to illustrate differences between Sarsa and Q-Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b351336b-71cd-4988-9750-04b277b2e60b",
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   "source": [
    "class CliffWalking(gym.Env):\n",
    "    def __init__(self):\n",
    "        self.dims = [4, 12]\n",
    "        \n",
    "        self.action_space = spaces.Discrete(4)\n",
    "        self.observation_space = spaces.Tuple((\n",
    "                spaces.Discrete(self.dims[0]),\n",
    "                spaces.Discrete(self.dims[1])\n",
    "                ))\n",
    "        self.start = [0, 0]\n",
    "        self.goal = [0, 11]\n",
    "\n",
    "        self.reset()\n",
    "\n",
    "    def step(self, action):\n",
    "        \"\"\"\n",
    "        Returns: observation, reward, terminated, truncated, info\n",
    "        \"\"\"\n",
    "        self.t += 1\n",
    "        i, j = self.S\n",
    "\n",
    "        if action == Action.S:\n",
    "            i  = min(i + 1, self.dims[0] - 1)\n",
    "        elif action == Action.N:\n",
    "            i = max(i - 1, 0)\n",
    "        if action == Action.E:\n",
    "            j = min(j + 1, self.dims[1] - 1)\n",
    "        elif action == Action.W:\n",
    "            j = max(j - 1, 0)\n",
    "\n",
    "        self.S = [i, j]\n",
    "        reward = -100 if (i==0 and 0<j<11) else -1\n",
    "        return self.S, reward, i==0 and j>0, False, {}\n",
    "\n",
    "    def reset(self):\n",
    "        self.S = self.start\n",
    "        self.t = 0\n",
    "        return self.S, {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "c8e0e8cc-fab2-4683-bc21-194ce2e0a573",
   "metadata": {},
   "outputs": [],
   "source": [
    "env = CliffWalking()\n",
    "observation = env.reset()\n",
    "dims = [o.n for o in env.observation_space]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "954f6fb9-9a18-493a-9dbc-f9a895b6502a",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=123456789)\n",
    "\n",
    "runs = 200\n",
    "n = 200 \n",
    "\n",
    "r_qlearning = np.zeros((runs, n))\n",
    "r_sarsa = np.zeros((runs, n))\n",
    "\n",
    "for j in range(runs):\n",
    "    algo_q = QLearning(env, 0.5, 0.1, dims, env.action_space.n)\n",
    "    for i in range(n):\n",
    "        observation, info = env.reset()\n",
    "        action = algo_q.sample(observation)\n",
    "        algo_q.init_episode(observation, action)\n",
    "        r = 0\n",
    "        while True:\n",
    "            observation, reward, terminated, truncated, info = env.step(algo_q.a)\n",
    "            algo_q.update(reward, observation)\n",
    "            r += reward\n",
    "            if terminated:\n",
    "                break\n",
    "        r_qlearning[j, i] = r\n",
    "        \n",
    "    algo = QLearning(env, 0.5, 0.1, dims, env.action_space.n, sarsa=True)\n",
    "    for i in range(n):\n",
    "        observation, info = env.reset()\n",
    "        action = algo.sample(observation)\n",
    "        algo.init_episode(observation, action)\n",
    "        r = 0\n",
    "        while True:\n",
    "            observation, reward, terminated, truncated, info = env.step(algo.a)\n",
    "            algo.update(reward, observation)\n",
    "            r += reward\n",
    "            if terminated:\n",
    "                break\n",
    "        r_sarsa[j, i] = r"
   ]
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   ],
   "source": [
    "px.line(y=[np.mean(r_sarsa, axis=0), np.mean(r_qlearning, axis=0)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0945a11c-1a18-4daf-b80a-462cd3fd3439",
   "metadata": {},
   "source": [
    "I don't quite the same drop in rewards for Q-Learning than Sarsa (because Sutton/Barto do not restart episodes after the agent falls off the cliff; their simulation is more Groundhog Day style with the day restarting over and over until the agent gets it right). \n",
    "\n",
    "Sarsa generally chooses the safer but longer path (follow the arrows from 0 to *):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f46cd365-60af-4127-8334-db866f047cd3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      " 0  ↑  ↑  ↑  ↑  ↑  ↑  ↑  ↑  ↑  ↑  * \n",
      "\n",
      " ↓  ↓  ↓  ↓  ←  ↓  ←  ←  →  →  →  ↑ \n",
      "\n",
      " →  ↓  ↓  →  →  ↓  ↓  ↓  ↓  →  ↑  ↑ \n",
      "\n",
      " →  →  →  →  →  →  →  →  →  ↑  →  ↑ "
     ]
    }
   ],
   "source": [
    "print_opt_policy(algo.q, env.start, env.goal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a17b4cb4-664c-4cb8-ac2c-dc0156e528b3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      " 0  ↑  ↑  ↑  ↑  ↑  ↑  ↑  ↑  ↑  ↑  * \n",
      "\n",
      " →  →  →  →  →  →  →  →  →  →  →  ↑ \n",
      "\n",
      " →  ↑  →  ↑  →  →  ↑  ↑  →  ↑  ↑  ↑ \n",
      "\n",
      " ←  →  ↑  →  →  →  ↓  ↑  ←  ←  →  ↑ "
     ]
    }
   ],
   "source": [
    "print_opt_policy(algo_q.q, env.start, env.goal)"
   ]
  },
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   "cell_type": "markdown",
   "id": "4079c2bb-68e2-41e8-80b4-8e256b989c7a",
   "metadata": {},
   "source": [
    "## Eg. 6.7 to illustrate bias issues in Q-Learning and the merits of Double Q-Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "939a6f0a-d805-4866-97e4-7ae6d76c301b",
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   "source": [
    "class Action2D(IntEnum):\n",
    "    R = 0\n",
    "    L = 1\n",
    "\n",
    "class MaxBiasEg(gym.Env):\n",
    "    def __init__(self):\n",
    "        self.observation_space = spaces.Discrete(13)\n",
    "        self.start = 0\n",
    "        self.end = 1  # B = 2; left of B is 3:13\n",
    "        self._actions = [spaces.Discrete(1) for i in range(13)]\n",
    "        self._actions[0] = spaces.Discrete(2)\n",
    "        self._actions[2] = spaces.Discrete(10)\n",
    "        self.max_action_space_n = 10\n",
    "\n",
    "        self.reset()\n",
    "\n",
    "    def step(self, action):\n",
    "        self.t += 1\n",
    "        terminated = False\n",
    "        reward = 0\n",
    "        if self.S == [0]:\n",
    "            if action == Action2D.L:\n",
    "                self.S = [2]\n",
    "            elif action == Action2D.R:\n",
    "                self.S = [1]\n",
    "                terminated = True\n",
    "                \n",
    "        elif self.S == [2]:\n",
    "            self.S = [action + 2]\n",
    "            reward = np.random.normal(-0.1, 1)\n",
    "            terminated = True\n",
    "        return self.S, reward, terminated, False, {}\n",
    "\n",
    "    @property\n",
    "    def action_space(self):\n",
    "        return self._actions[self.S[0]]\n",
    "\n",
    "    def reset(self):\n",
    "        self.S = [self.start]\n",
    "        self.t = 0\n",
    "        return self.S, {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "0a06a7ca-500a-4786-bcac-193d47e6ded8",
   "metadata": {
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   "source": [
    "np.random.seed(seed=123456789)\n",
    "\n",
    "env = MaxBiasEg()\n",
    "dims = [env.observation_space.n]\n",
    "\n",
    "runs = 1000\n",
    "n = 300 \n",
    "\n",
    "ls = np.zeros((runs, n))\n",
    "dls = np.zeros((runs, n))\n",
    "for j in range(runs):\n",
    "    algo = DQLearning(env, 0.1, 0.1, dims, env.max_action_space_n)\n",
    "    for i in range(n):\n",
    "        observation, info = env.reset()\n",
    "        action = algo.sample(observation)\n",
    "        if action == Action2D.L:\n",
    "            dls[j, i] = 1\n",
    "        algo.init_episode(observation, action)\n",
    "        while True:\n",
    "            observation, reward, terminated, truncated, info = env.step(action)\n",
    "            algo.update(reward, observation)\n",
    "            if terminated:\n",
    "                break\n",
    "\n",
    "    algo = QLearning(env, 0.1, 0.1, dims, env.max_action_space_n)\n",
    "    for i in range(n):\n",
    "        observation, info = env.reset()\n",
    "        action = algo.sample(observation)\n",
    "        if action == Action2D.L:\n",
    "            ls[j, i] = 1\n",
    "        algo.init_episode(observation, action)\n",
    "        while True:\n",
    "            observation, reward, terminated, truncated, info = env.step(action)\n",
    "            algo.update(reward, observation)\n",
    "            if terminated:\n",
    "                break"
   ]
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   "source": [
    "px.line(y=[np.mean(ls, axis=0), np.mean(dls, axis=0)])"
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   "source": [
    "## Cart Pole with a continuous action space that must be discretized"
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  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "f52be1b4-bdea-42df-a1e8-96d22df292ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Box([-4.8000002e+00 -3.4028235e+38 -4.1887903e-01 -3.4028235e+38], [4.8000002e+00 3.4028235e+38 4.1887903e-01 3.4028235e+38], (4,), float32),\n",
       " Discrete(2))"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env = gym.make(\"CartPole-v1\")\n",
    "observation, _ = env.reset()\n",
    "\n",
    "env.observation_space, env.action_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "f525fbc1-054d-4d03-96d0-96441e6bbb30",
   "metadata": {},
   "outputs": [],
   "source": [
    "dims = [3, 3, 9, 5]\n",
    "bins = [\n",
    "    np.linspace(-2.4, 2.4, dims[0]), \n",
    "    np.linspace(-3, 3, dims[1]),\n",
    "    np.linspace(-.2095, .2095, dims[2]),\n",
    "    np.linspace(-3, 3, dims[3])\n",
    "    ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "0cecd1d2-3bae-4db0-b459-989dede8cc11",
   "metadata": {},
   "outputs": [],
   "source": [
    "def _discretize(observation, bins):\n",
    "    return [np.digitize(o, b) - 1 for o, b in zip(observation, bins)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "a546990d-35a3-43e8-a2c4-93130e8ec421",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 4, 1]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_discretize(observation, bins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "6f91beac-c222-46a2-88fb-150c740be165",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=123456789)\n",
    "\n",
    "n = 3000\n",
    "\n",
    "ts = np.zeros(n)\n",
    "algo = DQLearning(env, 0.25, 0.05, dims, env.action_space.n)\n",
    "for i in range(n):\n",
    "    observation, info = env.reset()\n",
    "    observation = _discretize(observation, bins)\n",
    "    action = algo.sample(observation)\n",
    "    algo.init_episode(observation, action)\n",
    "    t = 1\n",
    "    while True:\n",
    "        observation, reward, terminated, truncated, info = env.step(algo.a)\n",
    "        observation = _discretize(observation, bins)\n",
    "        algo.update(reward, observation)\n",
    "        if terminated:\n",
    "            break\n",
    "        t += 1\n",
    "    ts[i] = t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "5857ddae-ffb3-41a9-8af7-e2818ea280f8",
   "metadata": {},
   "outputs": [
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     "metadata": {},
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    }
   ],
   "source": [
    "px.line(np.convolve(ts, np.ones(10)/10, \"valid\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "2e0f1e72-0cac-4af8-ad77-fa1e1fb6f5da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "657.03\n"
     ]
    }
   ],
   "source": [
    "## evaluate cart pole with entirely greedy policy\n",
    "n= 200\n",
    "\n",
    "algo.eps = 0\n",
    "ts = np.zeros(n)\n",
    "for i in range(n):\n",
    "    observation, info = env.reset()\n",
    "    t = 0\n",
    "    while True:\n",
    "        observation = _discretize(observation, bins)\n",
    "        action = algo.sample(observation)\n",
    "        observation, reward, terminated, truncated, info = env.step(action)\n",
    "        t += 1\n",
    "        if terminated:\n",
    "            break\n",
    "    ts[i] = t\n",
    "print(np.mean(ts))"
   ]
  },
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   "execution_count": null,
   "id": "826dc80f-1df2-4f2a-b6cf-94618ec32af1",
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   "outputs": [],
   "source": []
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