DP_practice.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hr2tPjlrf-rP"
      },
      "source": [
        "# Practice Session 1: Policy and Value Iteration\n",
        "\n",
        "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/rlsummerschool/practical-sessions/blob/master/notebooks/DP_practice.ipynb)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "VYZ_hFDkXuY0",
        "outputId": "437f743a-50ca-45c1-b4e5-5211a2b88e2c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m103.1/103.1 kB\u001b[0m \u001b[31m3.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m925.5/925.5 kB\u001b[0m \u001b[31m21.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Building wheel for rlss-practice (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n"
          ]
        }
      ],
      "source": [
        "# Set up the environment (not needed for local installations)\n",
        "!pip install \"git+https://github.com/rlsummerschool/practical-sessions.git\" --quiet\n",
        "\n",
        "import time\n",
        "import random"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CFtCdzEI9gHZ"
      },
      "source": [
        "## RL development in Python\n",
        "\n",
        "Large RL projects are usually developed locally, as any other Python package, in OOP, version controlled by Git (see [example](https://github.com/rlsummerschool/practical-sessions/blob/master/rlss_practice/environments.py)).\n",
        "\n",
        "[Jupyter](https://jupyter.org/) notebooks, like this one, are collections of text cells and code cells, that can be executed with an interactive interpreter.\n",
        "Colab notebooks are Jupyter notebooks whose interpreter runs in a runtime that is hosted by Google."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yqPq-DrFG3se"
      },
      "source": [
        "### Environments and tasks\n",
        "\n",
        "An MDP is a model of Reinforcement Learning tasks. It comprises of:\n",
        "* a **state space** $\\mathcal{S}$\n",
        "* a **action space** $\\mathcal{A}$\n",
        "* a **starting-state distribution** $\\nu_0(s)$\n",
        "* a **reward function** $r: \\mathcal{S}\\times\\mathcal{A}\\rightarrow [0,1]$ (or vector $r\\in[0,1]^{|\\mathcal{S}|\\cdot|\\mathcal{A}|}$)\n",
        "* a **transition function** $p: \\mathcal{S}\\times\\mathcal{A}\\rightarrow \\Delta_{\\mathcal{S}}$ (or matrix $p \\in\\mathbb{R}^{|\\mathcal{S}|\\cdot|\\mathcal{A}|\\times|\\mathcal{S}|}$)\n",
        "\n",
        "where $\\Delta_{\\mathcal{S}} = \\{q\\in\\mathbb{R}^{|\\mathcal{S}|} \\,\\,|\\,\\, \\sum_{s\\in\\mathcal{S}}q(s) = 1,\\, q(s)\\geq 0 \\text{ for } s\\in\\mathcal{S}\\}$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PsQticuSJmdO"
      },
      "source": [
        "Interaction between an agent (or decision maker) and some environment (or task) in some round $t$:\n",
        "\n",
        "<div>\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=11KyhHxuaileBEJ9fFZmIS5-GzncQgyqt\" alt=\"agent-environment interaction\" width=\"600\"/>\n",
        "</div>\n",
        "\n",
        "The agent is equipped with a policy $\\pi$ mapping states to actions (or a distribution over actions)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ob8WriuZLh-g"
      },
      "source": [
        "### The Gym(nasium) interface\n",
        "\n",
        "[Gymnasium](https://gymnasium.farama.org/) is a standard API for Decision Processes, based on OpenAI's Gym library."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "JgaqoJNTOi6o",
        "outputId": "bc17dcdf-7ffc-484c-9f27-200fc2fd00ed",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "pygame 2.4.0 (SDL 2.26.4, Python 3.10.12)\n",
            "Hello from the pygame community. https://www.pygame.org/contribute.html\n"
          ]
        }
      ],
      "source": [
        "# Standard import\n",
        "import gymnasium as gym\n",
        "from gymnasium import Env"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yDwwk5BL1eRQ"
      },
      "source": [
        "The library also defines a number of classic benchmarks [Atari](https://gymnasium.farama.org/environments/atari/) games, [MuJoCo](https://gymnasium.farama.org/environments/mujoco/) simulations, and [ToyText](https://gymnasium.farama.org/environments/toy_text/), minimal environments for debugging.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "DlzPIsH23hpE",
        "outputId": "0cd52d11-297e-47b8-a4d7-359ba407a163",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Discrete(4)\n",
            "Discrete(48)\n"
          ]
        }
      ],
      "source": [
        "# A registered environment (for example Cliff Walking) can be instantiated with\n",
        "env = gym.make(\"CliffWalking-v0\")\n",
        "\n",
        "# Important properties:\n",
        "print(env.action_space)\n",
        "print(env.observation_space)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XXhGGkAI7XEh"
      },
      "source": [
        "We only consider discrete state and action spaces. See the possible alternatives: `dir(gym.spaces)`\n",
        "\n",
        "Environments can be fully observable, partially observable or non-stationary. All these variants fit the same environment interface.\n",
        "We should know which class our environment belongs to.\n",
        "Today, we only consider stationary and fully observable MDPs."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fNcySyOGACgZ"
      },
      "source": [
        "The environment interface allows  to sample initial states and transition with `env.reset()` and `env.step(action)`. Every method is well documented (see `help(gym.Env.step)`).\n",
        "\n",
        "Try it out!"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "Wnymj388egTo",
        "outputId": "550f1eec-8634-468d-c672-ab0dc6ff051f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Initial observation: 36\n",
            "Observation: 24, reward -1\n",
            "Observation: 12, reward -1\n",
            "Observation: 0, reward -1\n"
          ]
        }
      ],
      "source": [
        "observation, info = env.reset()\n",
        "print(f\"Initial observation: {observation}\")\n",
        "\n",
        "action = 0  # any action\n",
        "\n",
        "observation, reward, terminated, truncated, info = env.step(action)\n",
        "print(f\"Observation: {observation}, reward {reward}\")\n",
        "\n",
        "observation, reward, terminated, truncated, info = env.step(action)\n",
        "print(f\"Observation: {observation}, reward {reward}\")\n",
        "\n",
        "observation, reward, terminated, truncated, info = env.step(action)\n",
        "print(f\"Observation: {observation}, reward {reward}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5xffKa7UfiOC"
      },
      "source": [
        "Custom environments can be created by subclassing the `Env` class.\n",
        "\n",
        "Environments can be also modified with wrappers. See the predefined Gymnasium [Wrappers](https://gymnasium.farama.org/api/wrappers/#gymnasium-wrappers)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gHgub_3DH-9V"
      },
      "source": [
        "## Setting up our RL task\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_QotsgLalKv4"
      },
      "source": [
        "We experiment with a simple grid-world environment, based on the implementation in [minigrid](https://minigrid.farama.org/environments/minigrid/). The environment is configured and observations are transformed appropriately (you already know how)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "dzPxVxymjlZr",
        "outputId": "894fadd7-38a9-4a9f-c320-d76c6dc3bc74",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "WWWWW\n",
            "W>  W\n",
            "W   W\n",
            "W  GW\n",
            "WWWWW\n"
          ]
        }
      ],
      "source": [
        "from rlss_practice.environments import Room, MinigridBase\n",
        "\n",
        "\n",
        "# Initializing the environment\n",
        "env = Room(\n",
        "    failure=0.0,\n",
        "    agent_start_pos=(1, 1),\n",
        "    agent_start_dir=0,\n",
        "    size=5,\n",
        ")\n",
        "print(env)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AA74pMHsl_be"
      },
      "source": [
        "In this ASCII representation, > is the agent, facing right, G is the goal, and W are walls.\n",
        "\n",
        "Understand you own environment:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "pY4EV-n0mH-d",
        "outputId": "050d45c3-d74d-46af-bb52-0a993319ff50",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Action space: Discrete(3)\n",
            "Observation space: MultiDiscrete([5 5 4])\n",
            "\n"
          ]
        }
      ],
      "source": [
        "print(\"Action space:\", env.action_space)\n",
        "print(\"Observation space:\", env.observation_space, end=\"\\n\\n\")\n",
        "#print(help(MinigridBase))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Tk3VBz-ZmsvM"
      },
      "source": [
        "When you checkout `help(env)`:\n",
        "\n",
        "    class MinigridBase\n",
        "       MinigridBase(minigrid: minigrid.minigrid_env.MiniGridEnv, seed: int, failure=0.0)\n",
        "\n",
        "       Base class for minigrid environments with explicit transition and reward functions.\n",
        "\n",
        "       The agent is rewarded upon reaching the goal location.\n",
        "\n",
        "       Action space:\n",
        "\n",
        "       | Num | Name         | Action       |\n",
        "       |-----|--------------|--------------|\n",
        "       | 0   | left         | Turn left    |\n",
        "       | 1   | right        | Turn right   |\n",
        "       | 2   | forward      | Move forward |\n",
        "\n",
        "       Observation space:\n",
        "\n",
        "       | Name | Description             |\n",
        "       |------|-------------------------|\n",
        "       | x    | x coordinate            |\n",
        "       | y    | y coordinate (downward) |\n",
        "       | dir  | cardinal direction      |\n",
        "\n",
        "       The transition function is stored in `T`,\n",
        "       where `T[state][action][next_state]` is the transition probability.\n",
        "       The reward function is `R`. `R[state][action]` contains a reward."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nOD43HaO2M6X"
      },
      "source": [
        "### Demo\n",
        "\n",
        "Here's a rollout loop, for a single trajectory"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "ugRanvqJo4RW",
        "outputId": "3ebce8c5-3080-4ae3-ddca-e741ded1b5e4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Initial observation: [1 1 0]\n",
            "WWWWW\n",
            "W>  W\n",
            "W   W\n",
            "W  GW\n",
            "WWWWW\n",
            "Action: 1\n",
            "Observation: [1 1 1], reward 0.0, terminated False, truncated False\n",
            "WWWWW\n",
            "WV  W\n",
            "W   W\n",
            "W  GW\n",
            "WWWWW\n",
            "Action: 2\n",
            "Observation: [1 2 1], reward 0.0, terminated False, truncated False\n",
            "WWWWW\n",
            "W   W\n",
            "WV  W\n",
            "W  GW\n",
            "WWWWW\n",
            "Action: 1\n",
            "Observation: [1 2 2], reward 0.0, terminated False, truncated False\n",
            "WWWWW\n",
            "W   W\n",
            "W<  W\n",
            "W  GW\n",
            "WWWWW\n",
            "Invalid action or KeyboardInterrupt\n"
          ]
        }
      ],
      "source": [
        "# Test it\n",
        "done = False\n",
        "observation, info = env.reset()\n",
        "print(\"Initial observation:\", observation)\n",
        "print(env)\n",
        "\n",
        "# Steps\n",
        "while not done:\n",
        "\n",
        "    try:\n",
        "      # Action selection\n",
        "\n",
        "      action = int(input(\"Action: \"))\n",
        "\n",
        "      # Transition\n",
        "      observation, reward, terminated, truncated, info = env.step(action)\n",
        "      done = terminated or truncated\n",
        "\n",
        "      print(f\"Observation: {observation}, reward {reward}, terminated {terminated}, truncated {truncated}\")\n",
        "      print(env)\n",
        "\n",
        "    except:\n",
        "      done = True\n",
        "      print(\"Invalid action or KeyboardInterrupt\")\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X910eylycXEf"
      },
      "source": [
        "We can define a function that performs `n_trajectories` rollouts on the environment with a given policy. We can also compute arbitrary statistics in the meanwhile."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "gU1XQ-ObDqCn"
      },
      "outputs": [],
      "source": [
        "def rollouts(env, policy, n_trajectories, gamma):\n",
        "    \"\"\"Execute policy over env for n_trajectories and compute discounted return.\"\"\"\n",
        "    total_return = 0.0\n",
        "\n",
        "    # Trajectores\n",
        "    for _ in range(n_trajectories):\n",
        "\n",
        "        # Init\n",
        "        discount = 1.0\n",
        "        ret = 0.0\n",
        "        observation, info = env.reset()\n",
        "        done = False\n",
        "\n",
        "        # Steps\n",
        "        while not done:\n",
        "\n",
        "            # Action selection\n",
        "            action = policy(observation)\n",
        "\n",
        "            # Transition\n",
        "            observation, reward, terminated, truncated, info = env.step(action)\n",
        "\n",
        "            done = terminated or truncated\n",
        "            ret += reward * discount\n",
        "            discount *= gamma\n",
        "\n",
        "            if done:\n",
        "                total_return += ret\n",
        "\n",
        "    env.close()\n",
        "    return total_return / n_trajectories"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PmYQPLghM8cy"
      },
      "source": [
        "Since we don't have a policy yet, let's define the uniform one."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "Itk9LgVqL-DD"
      },
      "outputs": [],
      "source": [
        "class UniformPolicy():\n",
        "    def __init__(self, n_actions: int):\n",
        "        self.n_actions = n_actions\n",
        "\n",
        "    def __call__(self, observation):\n",
        "        return random.randint(0, self.n_actions-1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kQmcdqKt31XT"
      },
      "source": [
        "Let's try:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "qXnOiHr234mn",
        "outputId": "a162d594-7f7b-441a-a8fc-9a374765051b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.06171285861857455\n"
          ]
        }
      ],
      "source": [
        "avg_return = rollouts(env=env,\n",
        "                      policy=UniformPolicy(env.action_space.n),\n",
        "                      n_trajectories=20,\n",
        "                      gamma=0.9)\n",
        "\n",
        "print(avg_return)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qpv9bGrwdtFd"
      },
      "source": [
        "We can also visualize the execution:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "k7_UY2RPOb7v"
      },
      "outputs": [],
      "source": [
        "from rlss_practice.wrappers import Renderer\n",
        "visible_env = Renderer(env)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "P2CieU7A_40i",
        "outputId": "b3071d52-d7a6-4681-d00e-279623677833",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.0\n"
          ]
        }
      ],
      "source": [
        "avg_return = rollouts(env=visible_env,\n",
        "                      policy=UniformPolicy(env.action_space.n),\n",
        "                      n_trajectories=1,\n",
        "                      gamma=0.9)\n",
        "\n",
        "print(avg_return)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "EbdR7lQQXhXu",
        "outputId": "3e2e49a2-8260-4cbc-cfc1-0e114abcf1aa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 181
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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              "<IPython.core.display.HTML object>"
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type=\"video/mp4\"> </video>"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "visible_env.play()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "71rNJIH7xEM2"
      },
      "source": [
        "Finally, a small utility for creating callable objects from state-action mappings"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "4KDwEt06qnHI"
      },
      "outputs": [],
      "source": [
        "def make_policy(policy_dict):\n",
        "  \"\"\"Return the policy dictionary as a callable object\"\"\"\n",
        "\n",
        "  def callable_policy(observation):\n",
        "      return policy_dict[tuple(observation.tolist())]\n",
        "\n",
        "  return callable_policy"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "srQzHwZTe_gd"
      },
      "source": [
        "### Explicit model\n",
        "\n",
        "The algorithms we will implement require that a complete model of the environment is available, in the form of explicit transition and reward functions. This is not part of the gym interface.\n",
        "\n",
        "These two functions are stored in two members:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "DczwaYuUfqHg",
        "outputId": "accfc9d1-ee8f-4bf5-9216-ff81dbaf6cf1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "A few probabilities\n",
            "1.0\n",
            "0.0\n",
            "1.0\n",
            "\n",
            "A few rewards\n",
            "0.0\n",
            "1.0\n"
          ]
        }
      ],
      "source": [
        "# Transition and reward functions\n",
        "T = env.T\n",
        "R = env.R\n",
        "\n",
        "# These are represented as dictionaries (for maximum clarity)\n",
        "#   and indexed as T[state][action][next_state]\n",
        "print(\"A few probabilities\")\n",
        "print(T[(1, 1, 0)][2][(2, 1, 0)])\n",
        "print(T[(1, 1, 0)][2][(1, 1, 1)])\n",
        "print(T[(3, 1, 0)][1][(3, 1, 1)])\n",
        "\n",
        "#   also R[state][action]\n",
        "print(\"\\nA few rewards\")\n",
        "print(R[(1, 1, 0)][2])\n",
        "print(R[(3, 3, 0)][0])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8XYATMt3xEM3"
      },
      "outputs": [],
      "source": [
        "#env.pretty_print_T()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "lQglr5MOiDCp",
        "outputId": "2481cab3-1946-4de0-9cd2-0b6c0c771054",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "States [(1, 1, 0), (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 0), (1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 3, 0), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 0), (2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 2, 0), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 0), (2, 3, 1), (2, 3, 2), (2, 3, 3), (3, 1, 0), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 0), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 0), (3, 3, 1), (3, 3, 2), (3, 3, 3), (0, 0, 0)]\n",
            "Actions [0, 1, 2]\n",
            "Number of states 37\n",
            "Number of actions 3\n"
          ]
        }
      ],
      "source": [
        "# Explicit set of states and actions\n",
        "\n",
        "print(\"States\", env.states)\n",
        "print(\"Actions\", env.actions)\n",
        "print(\"Number of states\", len(env.states))\n",
        "print(\"Number of actions\", len(env.actions))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "XfYfq9HebRHw"
      },
      "outputs": [],
      "source": [
        "# Some classic imports for the rest of the notebook\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib as mpl\n",
        "import math\n",
        "\n",
        "mpl.style.use('seaborn-v0_8')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8L7zlYG8WcPq"
      },
      "source": [
        "## Solving the Minigrid task\n",
        "\n",
        "We would like to find a **stationary deterministic memoryless policy** or mapping from states to actions $\\pi : \\mathcal{S}\\rightarrow \\mathcal{A}$, that is able to arrive at the **goal state** sooner.\n",
        "\n",
        "In other words, our objective is to find $\\pi$ which maximizes the **expected discounted return** from any starting state represented by:\n",
        "\n",
        "\\begin{align*}\n",
        "    \\rho(\\pi) &= \\mathbb{E}_{s_0\\sim\\nu_0, s_{t+1}\\sim p(\\cdot|s_t,\\pi(s_t))}\\left[\\sum_{t=0}^\\infty\\gamma^t r(s_t,\\pi(s_t))\\right]\\\\\n",
        "    &= \\sum_{s}\\nu_0(s) V^{\\pi}(s)\n",
        "\\end{align*}\n",
        "\n",
        "with the **discount factor** $\\gamma\\in[0,1)$.\n",
        "\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "---\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "Recall that the **state value function** for $s\\in \\mathcal{S}$ denoted\n",
        "\n",
        "\\begin{align*}\n",
        "    V^\\pi(s) &= \\mathbb{E}_{s_{t+1}\\sim p(\\cdot|s_t,\\pi(s_t))}\\left[\\sum_{t=0}^\\infty\\gamma^t r(s_t,\\pi(s_t))\\bigg|s_0=s\\right]\\\\\n",
        "    &=  \\sum_{a}\\pi(a|s)Q^{\\pi}(s,a)\n",
        "\\end{align*}\n",
        "\n",
        "represents the value of being in state $s$ and following policy $\\pi$ while the **action-value function** for $s\\in \\mathcal{S}, a\\in \\mathcal{A}$ denoted\n",
        "\n",
        "$$ Q^\\pi(s,a) = r(s,a) + \\gamma\\sum_{s'\\in\\mathcal{S}}p(s'|s,a)V^{\\pi}(s')$$\n",
        "\n",
        "is the value of first taking an action $a$ in state $s$ then following policy $\\pi$.\n",
        "\n",
        "By standard notation, the **Bellman operator** of policy $\\pi$ acting on functions $V : \\mathcal{S}\\rightarrow \\mathbb{R}$ (or vectors $V\\in\\mathbb{R}^{|\\mathcal{S}|}$) is given as:\n",
        "\n",
        "$$(T^{\\pi}V)(s) =  \\sum_{a}\\pi(a|s)\\bigg[r(s,a) + \\gamma\\sum_{s'\\in\\mathcal{S}}p(s'|s,a)V(s')\\bigg],\\quad s\\in\\mathcal{S}$$\n",
        "\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "---\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "Ideally, we would like to find an **optimal policy** $\\pi^*$ with:\n",
        "\n",
        "$$ \\pi^*(s) \\in \\underset{a\\in\\mathcal{A}}{\\arg\\max} \\bigg\\{r(s,a) + \\gamma\\sum_{s'\\in\\mathcal{S}}p(s'|s,a)V^{\\pi^*}(s')\\bigg\\},\\quad s\\in\\mathcal{S}$$\n",
        "\n",
        "that maximizes our immediate reward and future return.\n",
        "\n",
        "The Bellman operator of $\\pi^*$ (a.k.a the **Bellman optimality operator**) acting on functions $V : \\mathcal{S}\\rightarrow \\mathbb{R}$ (or vectors $V\\in\\mathbb{R}^{|\\mathcal{S}|}$) is given as:\n",
        "\n",
        "$$(T^{*}V)(s) =  \\max_{a}\\bigg\\{r(s,a) + \\gamma\\sum_{s'\\in\\mathcal{S}}p(s'|s,a)V(s')\\bigg\\},\\quad s\\in\\mathcal{S}$$\n",
        "\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "---\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "With the transition and reward function of the grid-world task available to us, we attempt to find an optimal policy via **Dynamic programming**. Precisely, we implement **Policy Iteration** and **Value iteration** methods introduced in the first lecture.\n",
        "\n",
        "&nbsp;"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qMWFCbNN7F8l"
      },
      "source": [
        "### Notation\n",
        "\n",
        "*   $r_{\\pi}\\in\\mathbb{R}^{|\\mathcal{S}|}$ so that for $s\\in\\mathcal{S}$, $r_{\\pi}(s) = r(s,\\pi(s))$.\n",
        "*   $p_{\\pi}\\in\\mathbb{R}^{|\\mathcal{S}|\\times|\\mathcal{S}|}$ so that for $s,s'\\in\\mathcal{S}$, $p_{\\pi}(s'|s) = p(s'|s,\\pi(s))$.\n",
        "*   $\\sum_{r}p(s',r|s,a)  = p(s'|s,a)r(s,a)$ since rewards are deterministic.\n",
        "*   $n_{k}$ is the number of loops required to compute $V_{k}$\n",
        "*   $\\Delta$ is a threshold on the accuracy of value estimation [[3]](#scrollTo=XqJPFe6f6gFV&line=5&uniqifier=1)\n",
        "\n",
        "&nbsp;"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6nljnBe4bZTf"
      },
      "source": [
        "### Policy Iteration (PI) Recap\n",
        "\n",
        "**Idea**\n",
        "\n",
        "Gradually advance to $\\pi^{*}$ from an initial guess $\\pi_0$ through a series of **policy evaluation** and **policy improvement** steps.\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "**Policy Evaluation step**\n",
        "\n",
        "Given a policy $\\pi_k$, compute $V^{\\pi_k}$ as\n",
        "\n",
        "* $V^{\\pi_k} = (I - \\gamma\\, p_{\\pi_k})^{-1}r_{\\pi_k}$\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "**Policy Improvement step**\n",
        "\n",
        "Obtain $\\pi_{k+1}$ as the greedy policy w.r.t $V^{\\pi_k}$ (or $V_{k}$). That is,\n",
        "$$ \\pi_{k+1}(s) \\in \\underset{a\\in\\mathcal{A}}{\\arg\\max} \\bigg\\{r(s,a) + \\gamma\\sum_{s'\\in\\mathcal{X}}p(s'|s,a)V^{\\pi_{k}}(s')\\bigg\\},\\quad s\\in\\mathcal{S}$$\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "#### Putting everything together\n",
        "\n",
        "Starting from an arbitrary stationary deterministic markovian policy $\\pi_{0}$, for $k = 0,1,2,\\cdots, K$ do:\n",
        "* Compute $V^{\\pi_k}$\n",
        "* Obtain $\\pi_{k+1}$ as the greedy policy w.r.t $V^{\\pi_k}$\n",
        "* Terminate loop if policy is stable (i.e $\\pi_{k+1}(s) = \\pi_{k}(s)$ for all $s\\in\\mathcal{S}$) and return $\\pi_{k+1}$.\n",
        "\n",
        "\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "#### Theoretical guarantee [[1,2]](#scrollTo=XqJPFe6f6gFV&line=5&uniqifier=1)\n",
        "\n",
        "PI finds an optimal policy after $K = \\mathcal{\\tilde{O}}(\\mathcal{SA}/(1-\\gamma))$ iterations.\n",
        "\n",
        "<!---\n",
        "Explicitly $K = \\mathcal{\\tilde{O}}((\\mathcal{SA - S})/(1-\\gamma))$ iterations.\n",
        "-->"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "NFYLOHtPKwsG"
      },
      "outputs": [],
      "source": [
        "# Don't look at the solutions! This module contains the functions you should write\n",
        "from rlss_practice import dp_solutions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "id": "Woh49RAfbieB"
      },
      "outputs": [],
      "source": [
        "class PolicyIteration:\n",
        "  \"\"\"\n",
        "  Implements policy iteration\n",
        "  \"\"\"\n",
        "  def __init__(self, env: Env, gamma: float, initial_policy = None):\n",
        "    # Store\n",
        "    self.env = env\n",
        "    self.states = self.env.states\n",
        "    self.n_states = len(self.states)\n",
        "    self.actions = self.env.actions\n",
        "    self.n_actions = len(self.actions)\n",
        "    self.gamma = gamma\n",
        "    self.policy = initial_policy\n",
        "\n",
        "    # Default policy\n",
        "    if self.policy == None:\n",
        "      np.random.seed(4)\n",
        "      self.policy = {state: np.random.randint(0, self.n_actions-1) for state in self.states}\n",
        "\n",
        "    self.policy_stable = False\n",
        "    self.V = {state: 0.0 for state in env.states}\n",
        "    self.V_logs = []\n",
        "\n",
        "  def _evaluate_policy(self):\n",
        "    \"\"\"\n",
        "    Given 'policy' π_{k} compute V^{π_{k}}. Let,\n",
        "\n",
        "      A = (I - \\gamma p_{π_{k}})\n",
        "      b = r_{π_{k}}\n",
        "      x = V^{π_{k}}\n",
        "\n",
        "    solve the system of linear equations Ax=b\n",
        "\n",
        "    :return x: a |S|x1 array\n",
        "    \"\"\"\n",
        "    # Task: complete this and return x instead of using the line \"return dp_solutions...\"\n",
        "    A = np.identity(len(self.states)) - self.gamma * self.get_p_pi()\n",
        "    b = self.get_r_pi()\n",
        "\n",
        "    return np.linalg.solve(A,b)\n",
        "\n",
        "\n",
        "  def evaluate_policy(self):\n",
        "    \"\"\"\n",
        "    Collect state values in dict\n",
        "    \"\"\"\n",
        "    V_array = self._evaluate_policy()\n",
        "\n",
        "    # Assign values to holder as dictionary\n",
        "    self.V = {state: V_array[i].item() for i, state in enumerate(self.states)}\n",
        "\n",
        "    # Append values to log for plots\n",
        "    self.V_logs.append(self.V.copy())\n",
        "\n",
        "\n",
        "  def get_policy(self):\n",
        "    \"\"\"\n",
        "    Get the greedy policy:\n",
        "\n",
        "      π_{k+1}(s) = argmax_{a\\in A} Q^{\\pi_{k}}(s,a)\n",
        "\n",
        "    where\n",
        "\n",
        "      Q^{\\pi_{k}}(s,a) = r(s,a) + gamma * <P(.|s,a),V^{\\pi_{k}}>\n",
        "\n",
        "    assign new policy to self.policy\n",
        "    update self.policy_stable\n",
        "    \"\"\"\n",
        "    self.policy_stable = True\n",
        "    for state in self.states:\n",
        "      best_q = -np.inf\n",
        "      tmp_a = self.policy[state]\n",
        "      best_a = 0\n",
        "      for action in self.actions:\n",
        "        q = self.get_expected_update(state, action)\n",
        "        if q > best_q:\n",
        "          best_q = q\n",
        "          best_a = action\n",
        "      self.policy[state] = best_a\n",
        "      if self.policy[state] != tmp_a:\n",
        "        self.policy_stable = False\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "  def get_expected_update(self, state, action):\n",
        "    \"\"\"\n",
        "    Compute:\n",
        "\n",
        "      Q(s,a) = r(s,a) + gamma <p(.|s,a),V>\n",
        "\n",
        "    :param state\n",
        "    :param action\n",
        "\n",
        "    :return Q(s,a): float\n",
        "    \"\"\"\n",
        "    # TODO: Solve this and return Q(s,a) instead\n",
        "    dot_product = sum([self.V[state_next] * self.env.T[state][action][state_next] for state_next in self.states])\n",
        "    return self.env.R[state][action] + self.gamma * dot_product\n",
        "\n",
        "\n",
        "  def get_p_pi(self):\n",
        "    \"\"\"\n",
        "    Given π_{k}, compute p_{π_{k}}\n",
        "    \"\"\"\n",
        "    p_pi = np.zeros((self.n_states,self.n_states))\n",
        "\n",
        "    for s_index, s in enumerate(self.states):\n",
        "      for snext_index, snext in enumerate(self.states):\n",
        "        p_pi[s_index, snext_index] = self.env.T[s][self.policy[s]][snext]\n",
        "\n",
        "    return p_pi\n",
        "\n",
        "\n",
        "  def get_r_pi(self):\n",
        "    \"\"\"\n",
        "    Given π_{k}, compute r_{π_{k}}\n",
        "    \"\"\"\n",
        "    r_pi = np.zeros((self.n_states,1))\n",
        "\n",
        "    for i, state in enumerate(self.states):\n",
        "      r_pi[i][0] = self.env.R[state][self.policy[state]]\n",
        "\n",
        "    return r_pi"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2pTZRo-jxBxQ"
      },
      "source": [
        "Let's try it out"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "id": "zKL72UxrxFJl"
      },
      "outputs": [],
      "source": [
        "# Run policy iteration\n",
        "PI_planner1 = PolicyIteration(env, gamma=0.9)\n",
        "\n",
        "while not PI_planner1.policy_stable:\n",
        "  PI_planner1.evaluate_policy()\n",
        "  PI_planner1.get_policy()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rQkER_MsJiCK"
      },
      "source": [
        "Visualization"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "id": "6btXwfrRJev2"
      },
      "outputs": [],
      "source": [
        "def visualize(vlogs, state, grid_size):\n",
        "  grid_size -= 2   # walls\n",
        "\n",
        "  # Initial state values\n",
        "  fig1 = plt.figure(figsize=(4, 3))\n",
        "  ax1 = fig1.subplots()\n",
        "  ax1.set_ylabel(\"value of (1,1,0)\")\n",
        "  ax1.set_xlabel(\"iterations\")\n",
        "  initial_state_values = [value[(1, 1, 0)] for value in PI_planner1.V_logs]\n",
        "  ax1.plot(range(len(initial_state_values)), initial_state_values)\n",
        "\n",
        "  # States values over time\n",
        "  some_values_over_time = [\n",
        "    {(x, y): values[(x, y, o)] for (x, y, o) in env.states if o == 0}  # o is a fixed agent orientation\n",
        "    for values in vlogs\n",
        "  ]\n",
        "  values_over_time = [\n",
        "    np.array([[values[(x+1, y+1)] for x in range(grid_size)] for y in range(grid_size)])\n",
        "    for values in some_values_over_time\n",
        "  ]\n",
        "  vmids = [(values.max() + values.min()) / 2 for values in values_over_time]\n",
        "  vmin = min([values.min() for values in values_over_time])\n",
        "  vmax = max([values.max() for values in values_over_time])\n",
        "\n",
        "  steps = len(values_over_time)\n",
        "  fig2 = plt.figure(figsize=(4 * steps, 3))\n",
        "  axs2 = fig2.subplots(1, steps)\n",
        "  if isinstance(axs2, plt.Axes):\n",
        "    axs2 = [axs2]\n",
        "    multistep = False\n",
        "  else:\n",
        "    multistep = True\n",
        "\n",
        "  for i, ax in enumerate(axs2):\n",
        "    ax.set_title(f\"values at step {i}\" if multistep else \"values\")\n",
        "    ax.imshow(values_over_time[i], cmap=\"Blues\", vmin=vmin, vmax=vmax)\n",
        "    ax.xaxis.set_visible(False)\n",
        "    ax.yaxis.set_visible(False)\n",
        "    for x in range(grid_size):\n",
        "      for y in range(grid_size):\n",
        "        val = values_over_time[i][y,x]\n",
        "        ax.text(x, y, f\"{val:.2f}\", ha=\"center\", va=\"center\", color=\"w\" if val > vmids[i] else \"k\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "id": "XvCmq5bQQqEi",
        "outputId": "accb4e66-1350-47b8-d6bc-c05fb8b83c07",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2400x300 with 6 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ],
      "source": [
        "visualize(PI_planner1.V_logs, (1, 1, 0), 5)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "meYQb9VOTnDT"
      },
      "source": [
        "We can also test the policy."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "id": "3C-WmCiVT6op",
        "outputId": "f7ae5509-f6da-4f4b-e2fe-17cf6013621c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.5904900000000003\n"
          ]
        }
      ],
      "source": [
        "avg_return = rollouts(env=visible_env,\n",
        "                      policy=make_policy(PI_planner1.policy),\n",
        "                      n_trajectories=20,\n",
        "                      gamma=0.9)\n",
        "\n",
        "print(avg_return)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "id": "LGxMz5yZEZ-N",
        "outputId": "09dc8b8e-9a78-4ef1-f217-1d32a6eaf95e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 181
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
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            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "visible_env.play()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ymYjjFBYbiy-"
      },
      "source": [
        "What if we have failure probabilities now?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "id": "8EcH0mS2bt1N",
        "outputId": "4bff9f3e-a68d-400c-c2a9-ebbe89f3cdef",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "WWWWWW\n",
            "WV   W\n",
            "W    W\n",
            "W    W\n",
            "W   GW\n",
            "WWWWWW\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/gymnasium/wrappers/record_video.py:87: UserWarning: \u001b[33mWARN: Overwriting existing videos at /content/videos-dir folder (try specifying a different `video_folder` for the `RecordVideo` wrapper if this is not desired)\u001b[0m\n",
            "  logger.warn(\n"
          ]
        }
      ],
      "source": [
        "# Define\n",
        "env = Room(\n",
        "    failure=0.2,\n",
        "    agent_start_pos=(1, 1),\n",
        "    agent_start_dir=1,\n",
        "    size=6,\n",
        ")\n",
        "visible_env = Renderer(env)\n",
        "print(env)\n",
        "\n",
        "# Plan\n",
        "PI_planner1 = PolicyIteration(env, gamma=0.9)\n",
        "\n",
        "while not PI_planner1.policy_stable:\n",
        "  PI_planner1.evaluate_policy()\n",
        "  PI_planner1.get_policy()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gvuqeY88cCW2"
      },
      "outputs": [],
      "source": [
        "# Visualize\n",
        "avg_return = rollouts(\n",
        "    env=visible_env,\n",
        "    policy=make_policy(PI_planner1.policy),\n",
        "    n_trajectories=80,\n",
        "    gamma=0.9\n",
        ")\n",
        "print(avg_return)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "I-hHn_KXcKaS"
      },
      "outputs": [],
      "source": [
        "visible_env.play()\n",
        "\n",
        "visualize(PI_planner1.V_logs, (1, 1, 1), 6)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uzJ9fQ8ceZIB"
      },
      "source": [
        "But matrix inversions can be quite expensive. Consider iterative policy evaluation instead.\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "### Modified Policy Iteration (MPI) Recap\n",
        "\n",
        "**Idea**\n",
        "\n",
        "Same as PI but with **truncated policy evaluation**\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "**Truncated Policy Evaluation step**\n",
        "\n",
        "Given a policy $\\pi_k$, estimate $V^{\\pi_k}$ as $V_{k}$ with the following iterations\n",
        "\n",
        "  * Initialize $V$ as $\\mathbf{0}$ when $k = 0$ and $V_{k-1}$ otherwise, let $\\pi = \\pi_k$\n",
        "\n",
        "    <div>\n",
        "    <img src=\"https://drive.google.com/uc?export=view&id=1QaMg7a6HELjYycAnm6RE9vnzHD_fnaCn\" alt=\"iterative policy evaluation\" width=\"600\"/>\n",
        "    </div>\n",
        "\n",
        "    Return $V_k = V$. <!--$(T^{\\pi_{k}})^{n_{k}}V_{k-1}$-->\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "#### Putting everything together\n",
        "\n",
        "Starting from an arbitrary stationary deterministic markovian policy $\\pi_{0}$, for $k = 0,1,2,\\cdots, K$ do:\n",
        "* Estimate $V^{\\pi_k}$ with $V_{k}=(T^{\\pi_{k}})^{n_{k}}V_{k-1}$\n",
        "* Obtain $\\pi_{k+1}$ as the greedy policy w.r.t $V^{\\pi_k}$\n",
        "* Terminate loop if policy is stable (i.e $\\pi_{k+1}(s) = \\pi_{k}(s)$ for all $s\\in\\mathcal{S}$) and return $\\pi_{k+1}$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "id": "nFkMVMI3syvt"
      },
      "outputs": [],
      "source": [
        "class ModifiedPolicyIteration(PolicyIteration):\n",
        "  \"\"\"\n",
        "  Implements policy iteration with truncated policy evaluation\n",
        "  \"\"\"\n",
        "  def __init__(self,\n",
        "              env: Env,\n",
        "              gamma: float,\n",
        "              theta: float,\n",
        "              initial_policy = None):\n",
        "\n",
        "    super().__init__(env, gamma, initial_policy)\n",
        "    self.theta = theta\n",
        "    self.V = {state: 0.0 for state in env.states}\n",
        "\n",
        "\n",
        "  def evaluate_policy(self):\n",
        "    \"\"\"\n",
        "    Given 'policy' π_{k},\n",
        "    Starting from a previous guess 'V_{k-1}',\n",
        "    iteratively estimate V^{π_{k}} as T^{π_{k}}V_{k-1}.\n",
        "\n",
        "    assign new state values to self.V\n",
        "    \"\"\"\n",
        "    # Task: Complete this and delete line *\n",
        "\n",
        "    # Set Delta\n",
        "    delta = np.inf\n",
        "\n",
        "    # Main loop for iterative value update\n",
        "    while delta > self.theta:\n",
        "      # Initialize Delta\n",
        "      delta = 0\n",
        "      for state in self.states:\n",
        "        v = self.V[state]\n",
        "        sum_ = 0\n",
        "        for s_next in self.states:\n",
        "          sum_ += self.env.T[state][self.policy[state]][s_next] * (self.env.R[state][self.policy[state]] + self.gamma * self.V[s_next])\n",
        "        self.V[state] = sum_\n",
        "        delta = max(delta, abs(v - self.V[state]))\n",
        "      # ToDo: Loop over states\n",
        "\n",
        "        #ToDo: Update the state value\n",
        "\n",
        "        #ToDo: Update Delta\n",
        "\n",
        "    dp_solutions.ModifiedPolicyIteration._evaluate_policy(self)    #*\n",
        "\n",
        "    self.V_logs.append(self.V.copy())\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KofhGOYGhckf"
      },
      "source": [
        "Now we run Modified policy iteration"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "id": "D9uBUwD-hhSF"
      },
      "outputs": [],
      "source": [
        "MPI_planner = ModifiedPolicyIteration(env,\n",
        "                                      gamma = 0.9, # Same as PI\n",
        "                                      theta = 0.01)\n",
        "\n",
        "while not MPI_planner.policy_stable:\n",
        "  MPI_planner.evaluate_policy()\n",
        "  MPI_planner.get_policy()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "70ieiSAZqR6H",
        "outputId": "07744e70-54e1-4f7b-9f80-03ab81934059",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.3562100496439758\n"
          ]
        }
      ],
      "source": [
        "avg_return = rollouts(env=visible_env,\n",
        "                      policy=make_policy(MPI_planner.policy),\n",
        "                      n_trajectories=80,\n",
        "                      gamma=0.9)\n",
        "\n",
        "print(avg_return)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "id": "cCueLRiiqvaQ",
        "outputId": "0a40d632-4a40-4ba2-c8d3-06b35253d7a2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 778
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
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              "<video  controls autoplay> <source 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type=\"video/mp4\"> </video>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x300 with 1 Axes>"
            ],
            "image/png": 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D0K9nECOvudLJEQnRtKQQCHGBM8Yy1n2aAUAHjRdTx/SWfgHR5kkhEOI8k9nCms2HKKswo1apmDkuBj8fD2eHJUSTk0IgxHmb9mRy8nT1vBS3DutO+JUBTo5IiOYhhUAI4ODxc3z2w28ARIcFctN13ZwckRDNRwqBcHn6wnLe+fgIABpfT6aPjUYt/QLChUghEC7NbLGwdtthisuqUAH3jo0iwNfT2WEJ0awcfkLm6NGjfPnll2RkZKDX6wEIDAykV69eDB8+nMjISLv3lZOTw5IlSzh48CDt2rVjzJgxPPTQQ6htTAC+ceNG3nvvPc6cOUPXrl2ZO3cuo0aNAuDRRx9l69atuLn9MRCYl5cX+/btc/TwhIvZ9vVJjv1mBGDMoG5Eh2mdG5AQTmB3ITh27BjLli3j66+/pn379kRERKDVVv+nOXfuHO+++y4vv/wygwcP5u9//7tdBWHu3LlER0eTlpZGfn4+M2fOJCgoiKlTp9Zab+fOnaxcuZK33nqLPn36sHnzZubNm8cnn3xCly5dAJg9ezZz58515NiFizvyq4FtX58EIPzKAMZf3925AQnhJHYVgi1btrB48WJGjBjBBx98QExMTJ17qxVFIT09nXXr1jFp0iSeeuopxo8fX+8+09PTycjIICUlBX9/f/z9/UlOTmbdunV1CkF5eTkLFizgmmuuAWDixImsWLGCAwcOWAuBEI4oLKlk7TYdCuDr7c7MsdG42bgSFcIV2FUIXnvtNdavX09sbGy966hUKvr06cPKlSs5dOgQ8+fPv2gh0Ol0hIaGEhDwxy160dHRZGVlUVxcjJ+fn3V5YmJirW0LCwspKSkhJOSPGaK+/fZbPv/8c3799Vd69OjB4sWLiYmJsefwAFCrVajVjnUQup2fq9ZN5qytoyXnxqIovLvjCAXFlQDcOy6akA7tmuW9W3JenE1yY1tz5MWuQvCf//wHf3/7x1qJiYnho48+uug6RqMRjUZTa1lNUTAYDLUKwYUURWHRokX07duXgQMHAtClSxfUajUPPvggvr6+vP7669xzzz3s3LmTwMBAu2LWan0v+wlSjUbmra1PS8zNR7t/4efMfADGXn8VI+PCmj2GlpiXlkJyY1tT5sWuQlBTBPbu3cv69es5ePAgRqMRAK1WS79+/Zg6dSr9+/evs83FKIriULBVVVU8+uijHD9+nPXr11uX33fffbXWe/jhh9m+fTtpaWlMnDjRrn3r9SWXdUWg0fhQWFiG2WxxaNu2rqXm5vipAtbvqL5VNKyjP+OHhGEwlDTb+7fUvLQEkhvbGpKXwED7JlGyu7N469at/OMf/+CGG24gOTnZ+k3bYDCwf/9+pkyZwiuvvGK9k+dStFqttZjUMBqNqFQqayf0hcrLy5kzZw5lZWVs2LDhot/03dzc6NSpE2fOnLH38LBYFCwWxwpTDbPZgskkH1xbWlJuSsurePM/6ZgtCl6ebswcF40KnBJfS8pLSyO5sa0p82J3IUhJSeHVV19l5MiRNl/fvn07q1atsrsQxMTEkJubi16vt57409PTCQ8Px9e3dhVTFIX58+fj7u7Oe++9h5eXV63XXnjhBW699VZ69eoFQGVlJdnZ2dKRLKwURSHlkwzOFZQDcPfoSEK0zdMvIERLZ3fvQ3Z2NsOHD6/39RtvvJGTJ0/a/cZRUVHExsaycuVKiouLyczMJCUlhaSkJAASEhKszwFs27aN48eP8+qrr9YqAlDdSX3q1CmWLFlCXl4eJSUlrFixAg8PD7uLkmj79vyUw/6jZwEY2qcT10V3dHJEQrQcdheC4OBgjh49Wu/rx44ds9mkczGrVq3izJkzDBkyhClTpjB+/HgmT54MQFZWFqWlpQB8+OGH5OTkMHDgQGJjY61/Fi1aBMCzzz5LWFgYEyZMYPDgwRw5coR169bRrp184xOQnVfExs+PA9CpQzvuGBXh5IiEaFnsbhoaPXo0s2bNYurUqfTp04f27dsD1e36Bw4c4L333rOexO3VsWNH/vnPf9p87cKis27duovup3379jz//PMOvbdwDeWVJtZs0WEyW/BwVzN7fAxenm6X3lAIF2J3IXjwwQfx8PDg7bffRq/XW2+1VBSFoKAgkpOTmT59epMFKsTleP+zY5zWV19ZJo3qyZXBtm9LFsKV2V0I1Go1999/P/fffz/Z2dnWcYY6dOggnbKiRfo6PZdvDp0GYECvKxjet7OTIxKiZXJ40DmArl270rVr18aORYhGk5tfwvufHQMguL03dyf0kiknhajHZRUCWxYsWEBubi4BAQEMHjyYKVOmNNauhXBIlcnM6s06KqrMuKlVzEqMoZ13o33UhWhzGm3witDQUMLCwnj++edtDiMtRHP5967jnDpbDMDEG3rQvZPmElsI4doa7WvSQw89ZP35zjvvbKzdCuGQfRln2P1jDgB9e3TgLwOk/0qIS2nUr+4yEYxwpnPGMlI+yQAg0N+Le27uLf0CQtihUQvBtGnTGnN3QtjNZLbw1lYdZRUmVCqYOS4a/3Yy5aQQ9mjUQuDoaKJCNJb/fHmCzN8LAUgc2p2ILu2dG5AQrYjdfQQX9gHUx2w2NygYIS5H+ol8PvkuG4De3QK5ZVCYcwMSopWxuxDs3r2b0NBQ69AStsgVgWhuhqIK3t5+GAD/dh7cOzbK4XklhHB1dheChQsX8umnn9aaEObP+vbt2yhBCWEPi0Xhn9t0FJVWATD9lija+3ldYishxJ/Z3UcwefJk1Go1b7/9dr3ryBWBaE7b954kI9sIwE1xXYm9qoNzAxKilXLoOYK1a9dSUVFR7+vPPPNMgwMSwh5Hsw1s+SoLgB6dNdw67ConRyRE6+VQIfD09MTTs/5b8hITExsckBCXUlRaydpth1EUaOflzsxx0bi7ydPsQlyuRnuyOCcnB5PJREBAwEU7lIVoCEVRePfjIxiKqq9Mp47pRVB7HydHJUTr1miFYPr06Zw8eZLhw4dTUFDAxo0bG2vXQlj994ffOJiZD0B8/1CuibzCyREJ0fo1WiFYtmwZ5eXlDBw40DpXgRCNKSu3kA/2ZALQ5Qo/Jo0Id3JEQrQNjVYI+vTpY/3Z0bmLhbiU0nITa7YcwmxR8PJwY1ZiNB7uMuWkEI2hUXvYnnzySYfWz8nJYcaMGcTFxREfH8/y5cuxWCw21924cSOjR4+mX79+JCYmkpaWZn3NYrHw8ssvM3LkSAYMGMC0adP47bffGnQsouVQFIX1OzM4aywH4M4bI+jUwdfJUQnRdjRqIdiyZYtD68+dO5eQkBDS0tJISUkhLS3N5kT1O3fuZOXKlTz33HN8//333HnnncybN896st+wYQPbtm1j7dq17N69m7CwMO677z55rqGN+PLg73x/5AwAg2M6MiS2k5MjEqJtsbsQVFZWXvKPI9LT08nIyGDhwoX4+/sTFhZGcnIyqampddYtLy9nwYIFXHPNNXh4eDBx4kR8fX05cOAAAKmpqSQnJ9OjRw/8/PyYP38+mZmZHDx40KGYRMtz6mwx/0r7BYCO2nbceWOEkyMSou2xu4+gT58+jTq2u06nIzQ0lICAAOuy6OhosrKyKC4uxs/Pz7r8z88nFBYWUlJSQkhICOXl5Rw/fpyoqCjr635+fnTr1o309HSuvvpqu+JRq1UOj1Hjdv7edTe5h72OxshNRaWZNVt0VJkseLipuf+vsfi18qGl5TNTP8mNbc2RF7sLQa9evejRowdDhw61+bqiKA71ERiNRjSa2lMI1hQFg8FQqxD8+X0WLVpE3759GThwIHl5eSiKUqug1OzLYDDYHY9W63vZhU6jkfvY69OQ3KxK/Ynfz5UAMC0xhr69OjZWWE4nn5n6SW5sa8q82F0IXnjhBe69914ee+wxgoKCbK6zZMkSh97c0Tb8qqoqHn30UY4fP15n8LuG9gfo9SWXdUWg0fhQWFiG2Wy7k9tVNTQ33xw6zX+/rx5aekCvKxjUOxiDoaSxw2x28pmpn+TGtobkJTDQvpsqHLoimD17Njt27GDKlCk213HkZKzVajEajbWWGY1GVCqVzdtPy8vLmTNnDmVlZWzYsIHAwEAA2rdvj1qttrmvDh3sH4TMYlGwWC6vmJjNFkwm+eDacjm5ydOXkrLjCAAdNN7cnRCJ2awAbafzXz4z9ZPc2NaUeXHoOYLJkydf9PWff/7Z7n3FxMSQm5uLXq+3nvjT09MJDw/H17d2FVMUhfnz5+Pu7s57772Hl9cfQw17eXnRs2dPdDodAwcOBKr7ELKzs2s92yBahyqThTVbdFRUmnFTq5iVGE07bw9nhyVEm2ZX78PHH3/s8I537Nhx0dejoqKIjY1l5cqVFBcXk5mZSUpKCklJSQAkJCSwb98+ALZt28bx48d59dVXaxWBGklJSaxfv57MzEyKi4tZsWIFvXv3JjY21uG4hXN9sPs4v+YVATBh2FX0CA24xBZCiIay64pg5cqVfPfddzzwwAP19g/U0Ov1vPLKK3z11VeMGTPmouuuWrWKJ554giFDhuDn58ekSZOsVx1ZWVmUlpYC8OGHH5KTk2P9xl8jMTGRpUuXMmnSJM6ePctdd91FSUkJcXFxvP766/YcmmhBfjp2lrT9pwCI6a5ldFxXJ0ckhGtQKXY07Ov1eubNm8fPP//MTTfdxLBhw4iKirK20xsMBo4cOcKXX37JJ598QmxsLK+88kqrGmri7Nkih7dxd1cTGOiLwVAibZp/4mhu8gvKWZzyPSXlJgL8PFkydSAa39Z9q6gt8pmpn+TGtobkJTjY3773sGclrVbL+vXr2blzJ++++y5btmyp0zGsUqmIjY3lhRdeYPTo0Q4FK1yb2WLhrW06SspNqIAZY6PbZBEQoqVyqLN49OjRjB49GqPRyNGjR62jjGq1WiIiIqxXCEI4YvP/sjh+qgCAsUPC6N1NPkdCNKfLGn20ffv2xMXFNXYswgXpTurZsfdXACK6tGfskDDnBiSEC5JnuYXTFJRU8s9th1EAPx8PZo6Lxk0tH0khmpv8rxNOYVEU3t6mo7CkerDCaTf3JtC/7q3BQoimJ4VAOMUn3/6K7mT1WFA3DuhC3/CL35YshGg6dhWCf//739afN2zY0GTBCNfwyykj//kyC4Dunfy57YYeTo5ICNdmVyF44YUXOHfuHAAvvvhikwYk2rbisire2qrDoij4eLkxMzEGdxl2WAinsuuuoaioKEaMGIFGo6GioqLeoagBvvrqq0YLTrQtiqKQsuMI+sIKAO5O6MUV7WXIYSGcza5C8Prrr/Pxxx9TUFDA6tWrmTRpUlPHJdqgz/ef4qdfqq8sh1/dmYG9Q5wckRACHHiy+K677gIgLy+P+++/v0mDEm3Pr6eL+H+7jwMQGuxL0sieTo5ICFHD4QfKnnnmGYqKiti1a5d18virrrqK+Ph4fHzkMl/UVVZhYvWWQ5jMCp7uamYlxuDp4ebssIQQ5zlcCHQ6Hffccw9FRUUEBQVhsVjIz88nODiYjRs3Ehoa2hRxilZKURT+77OjnDGUAXDHXyIIDbJv1iQhRPNw+HaN5cuXM2LECPbu3cuXX37JV199xddff82AAQNYtmxZU8QoWrH/HczlW10eANdFhTC0TycnRySE+DOHC8HPP//MokWLak0Wr9VqefLJJ/nxxx8bNTjRumWfLmT9pxkAXBHow12jI1GpHJsXWgjR9BwuBF5eXjb/M3t6emIymRolKNH6VVaZefH/9lFpsuDupmJ2Ygw+Xpc1xqEQook5XAiioqJ46aWXqKystC6rqKhgxYoVREZGNmpwovXa8Nkxfj1dPdnPxPhwunW0b4IMIUTzc/gr2t///nemTJnC5s2b6dq1eirB7OxsVCoV77zzTqMHKFqf74/ksfunHAD6RwQz6pornRyREOJiHC4EkZGR/Pe//2Xr1q1kZ2dTUVHBuHHjuOWWWy45n7Fo+84Yy1h3vl8gqL0P08dGSb+AEC3cZTXaajQa7rzzzga/eU5ODkuWLOHgwYO0a9eOMWPG8NBDD6G2MSZ9SUkJTz31FNu2bWPHjh306PHHQGUjRozgzJkztU44Q4YMYc2aNQ2OUdjPZLawZvMhyirMqFUqHr7zGvx8PGT+WSFaOKf23s2dO5fo6GjS0tLIz89n5syZBAUFMXXq1Frr5eXlMWXKFK6++up69/XOO+/IrGlOtmlPJifP9wtMGH4VUd07YDCUODkqIcSlOG3Yx/T0dDIyMli4cCH+/v6EhYWRnJxMampqnXUNBgMPP/wwc+fOdUKkwh4Hj5/jsx+qnzSPCgvkFplyUohWw2lXBDqdjtDQ0FrPI0RHR5OVlUVxcTF+fn7W5b169aJXr16cOnWq3v2tX7+exx9/nPz8fK6//nqeeuopOnToYHc8arUKtdqxtmy388Mnu7n4MMr6wnLe+fgIABpfT2aNj8HDvXoICVfPzZ/JZ6Z+khvbmiMvTisERqMRjUZTa1lNUTAYDLUKwaX07t2bPn368OKLL1JYWMgjjzzCgw8+yPvvv2/3PrRa38vu1NRoXHeMJbPZwrJ//URxWRUqFSy84xq6d9FaX3fl3FyM5KV+khvbmjIvl1UI9u7dy5YtW/j9999Zv349FouFTz/9lDFjxji0H0VRLuft63jjjTesP/v6+vLUU08xZswYsrOzrbe4XopeX3JZVwQajQ+FhWWYza7ZIfrRF5noTuQDcMugMMKu8MVgKJHc1EPyUj/JjW0NyUtgoH3jejlcCHbs2MHf//53hg4dyk8//QTA6dOnefLJJykpKWHixIl27Uer1WI0GmstMxqNqFQqtFqt7Y3sVDPw3ZkzZ+wuBBaLgsVyeYXJbLa45J0xR341sOV/1VNOhl8ZwLihYXXy4Kq5uRTJS/0kN7Y1ZV4cbnRas2YNy5cvZ82aNdamlM6dO/Pqq6/y7rvv2r2fmJgYcnNz0ev11mXp6emEh4fj62v/6JQ5OTk89dRTtZ50zszMBKBLly5270c4prCkkrXbdCiAr7c7M8dG42bjtl8hRMvn8P/c7OxsbrzxRoBabeqDBg26aGfun0VFRREbG8vKlSspLi4mMzOTlJQUkpKSAEhISGDfvn2X3E+HDh3YtWsXL7zwAqWlpeTl5fH8888THx9PSIjMgNUULIrC2x8fpqC4uvjec3NvOgR4OzkqIcTlcrgQBAYGkp+fX2d5VlaWQ9/kAVatWsWZM2cYMmQIU6ZMYfz48UyePNm6v9LSUgDefPNNYmNjSUhIACAxMZHY2FjefPNNvL29efvtt8nKymLYsGHcfPPNdOnShRdffNHRQxN22vl9NodOVF/JjbrmSvr1DHZyREKIhlApDvbYPv744+Tl5fHII49w22238cUXX3Do0CGWLVtGTEwMzz//fFPF2qTOni1yeBt3dzWBgdWdo67SppmZU8ALG37EbFHoFuLPP+66Bg/3ut8nXDE39pC81E9yY1tD8hIcbN9gjw5fETzyyCOUl5czduxYKioqGDRoENOnT6dz5848+uijju5OtCKl5VW8tVWH2aLg5enGrMRom0VACNG6OHzXkEaj4f333ycjI4MTJ07g7e1N9+7d6d69e1PEJ1oIRVFI+SSDcwXlANw9OpIQbTsnRyWEaAyX/UBZzdO+wjXs+SmH/UfPAjC0Tyeui+7o5IiEEI3F4ULQq1eviz6Be+TIkQYFJFqe7LwiNn5+HIBOHdpxx6gIJ0ckhGhMDheCp556qlYhMJvNZGVl8cUXXzBnzpxGDU44X3mliTVbdJjMFjzc1cweH4OXp5uzwxJCNCKHC0HNff5/duONN5Kamsqtt97a4KBEy7Hhs2Oc1lffxps0qidXBts/BpQQonVotFs+BgwYwBdffNFYuxMtwNfpuXx96DQAA3pdwfC+nZ0ckRCiKTRaIfj8889xd3fqPDeiEeXml/D+Z8cACG7vzd0JF+8bEkK0Xg6fuYcOHVpnWXl5OSUlJfU2G4nWpcpkZvVmHRVVZtzUKmYlxtDOW4q8EG2Vw/+7//a3v9X5Zujl5UWPHj0YMWJEowUmnOffu45z6mwxALfd0IPunTSX2EII0Zo5XAhkusi2bV/GGXb/mANAnx4duHGAjOAqRFtnVyF46aWX7N7hggULLjsY4VznjGWkfJIBQKC/F9Nu7i39AkK4ALsKwfbt2+3amUqlkkLQSpnMFt7aqqOswoRKBTPGRuHfztPZYQkhmoFdhWDXrl127ezPM46J1uM/X54g8/dCABKHdCeya6CTIxJCNJdGu320pKSE0aNHN9buRDNKP5HPJ99lA9Cra3tuGRzm3ICEEM3K4c5ivV7Ps88+y4EDB6ioqLAuLy4ubvBcw6L5GYoqeHv7YQD823lw79ho1GrpFxDClTh8RbB06VJ++eUXbr75ZgwGAxMnTqRnz5706tWL9evXN0WMoolYLAr/3KajqLQKgOm3RBHo7+XkqIQQzc3hQvDdd9/xzjvvsGDBAtzd3XnwwQdJSUlh0KBBpKWlNUWMools33uSjGwjAAlxXYm9qoNzAxJCOIXDhaC4uJjg4Oo5alUqFSaTCYApU6awbt26xo1ONJmj2Qa2fJUFwFWdNUwYdpWTIxJCOIvDhaBr16588sknAISEhPD1118D1TNYFRQUOLSvnJwcZsyYQVxcHPHx8SxfvhyLxfacnCUlJSxcuJDIyEgyMzNrvWY0Gpk3bx6DBw9m6NChPP7445SXlzt6aC6jqLSStdsOoyjg4+XOrHHRuLvJlJNCuCqH//dPnz6dBQsWYDQaGTt2LPPnz2fmzJncfvvt9OvXz6F9zZ07l5CQENLS0khJSSEtLc3mVUVeXh4TJkzAzc32OPhPPPEEZWVlbN++nQ8//JDMzExWrFjh6KG5BEVRePfjIxiKqjv6p97Ui6D2Pk6OSgjhTA4XgsTERD744APat2/Pfffdx/Tp0zGbzQwfPpxly5bZvZ/09HQyMjJYuHAh/v7+hIWFkZycTGpqap11DQYDDz/8sM3hLc6dO0daWhrz589Hq9USEhLCnDlz+PDDD6mqqnL08Nq8//7wGwcz8wGI7xfKtb2ucHJEQghnc/j20Q8//JCbbroJqO4juNxZyXQ6HaGhoQQEBFiXRUdHk5WVRXFxMX5+f0yAUjM/8qlTp+rs58iRI7i5uREZGVlrP6WlpZw4caLW8otRq1UO3zbpdr45xa2VNKuc+L2QD/ZUN6t1ucKPO0ZH4O7eNLG3ttw0F8lL/SQ3tjVHXhwuBE8//TRLly5l9OjRTJgwgYEDB17WGxuNRjSa2qNa1hQFg8FQqxBcaj9+fn61xsS5cD/20mp9L3tcHY2m5TetlJRVsWbLIcwWBW9PN/4xdSAhwf5N/r6tITfOIHmpn+TGtqbMi8OF4Ouvv+azzz5j+/btJCcn07lzZ8aPH8+tt95KaGioQ/tSFMXRt2+y/ej1JZd1RaDR+FBYWIbZbLuTuyVQFIU3/3OI0/nVU05OSYjE10ONwVDSZO/ZWnLT3CQv9ZPc2NaQvAQG+tq1nsOFwM/PjwkTJjBhwgTOnj3Lxx9/zKeffsrq1au59tpr7b6FVKvV1hmbyGg0olKpHHpCWavVUlxcjNlstnYm1+y3Qwf774u3WBQslssrKGazBZOp5X5wvziQw3eH8wAYHNOR66I6Nlu8LT03ziJ5qZ/kxramzEuDGp2Cg4P529/+xpQpUxgwYADff/+93dvGxMSQm5uLXq+3LktPTyc8PBxfX/uqGEDv3r1RFIWMjIxa+9FoNHTv3t3u/bRVp84W86+0XwDoqG3HnTdGODkiIURLc1mFoLKyks8++8x67/6zzz5LREQEmzZtsnsfUVFRxMbGsnLlSoqLi8nMzCQlJcU63WVCQgL79u275H60Wi2jR4/mlVdeQa/Xc/r0ad544w1uu+02l59DuaLSzJotOqpMFtzd1MxKjMbb07VzIoSoy+GzwkMPPcSePXuoqqoiPj6el156iWHDhtV7j//FrFq1iieeeIIhQ4bg5+fHpEmTmDx5MgBZWVmUlla3ab/55pusXr3a2heQmJiISqVi9uzZzJkzh6effpqnnnqKkSNH4uHhwS233ML8+fMdjqet2ZB2jN/PVfcDTBoZTteQpu8cFkK0PirFwZ7WpKQkxo8fz5gxY/D3bzsnlrNnixzext1dTWCgLwZDSYtr0/xWd5q126pHFb0mMpg542OadbaxlpwbZ5K81E9yY1tD8hJs552BDl8RbNy40dFNRDPL05eybudRADpovJl6Uy+ZclIIUS95cqONqTJZWLNFR0WlGTe1ilmJ0bTz9nB2WEKIFkwKQRvzwe7j/JpX3cw1YdhV9AgNuMQWQghXJ4WgDfnp2FnS9lcPwxHTXcvouK5OjkgI0RpIIWgj8gvKeXfHEQAC/DyZfksUaukXEELYQQpBG2C2WHhrm46SchMqYMYtUWh8PZ0dlhCilZBC0AZs/l8Wx09VTwp0y+AweofZP0SHEEJIIWjldCf17Nj7KwARVwYwbmiYcwMSQrQ6UghasYKSSv657TAK4OfjwYxx0bip5Z9UCOEYOWu0UhZF4e1tOgpLKgG45+beaDXeTo5KCNEaSSFopT759ld0J6sn3rlxQBeuDg9yckRCiNZKCkEr9MspI//5MguAsI7+3HZDDydHJIRozaQQtDLFZVW8tVWHRamecnJWYjTuMserEKIB5AzSiiiKQsqOI+gLKwBIvqkXVwS2c3JUQojWTgpBK/L5/lP89Ms5AIb17czA3iFOjkgI0RZIIWglfj1dxP/bfRyA0CBfkkb1dHJEQoi2QgpBK1BWYWL1lkOYzAqe7mpmjY/By8PxGeGEEMIWKQQtnKIo/N9nRzljKANg8l8iCA3ydXJUQoi2RApBC/dVei7f6vIAuC4qhOv7dHJyREKItsaphSAnJ4cZM2YQFxdHfHw8y5cvx2KxPSfn+vXrGT16NP379ycpKYlDhw5ZX7vrrruIjo4mNjbW+mfcuHHNdRhNJudcCRv+ewyAKwJ9uGt0pEw5KYRodA7PWdyY5s6dS3R0NGlpaeTn5zNz5kyCgoKYOnVqrfV27drFa6+9xttvv01kZCTr169n1qxZfPbZZ7RrV3375DPPPMOECROccRhNorLKzJoth6issuDupmJ2Ygw+Xk795xJCtFFOuyJIT08nIyODhQsX4u/vT1hYGMnJyaSmptZZNzU1lQkTJtC3b1+8vb2ZPn06ALt3727usJvNxs9/IedsCQAT48Pp1tHfyREJIdoqp33F1Ol0hIaGEhDwx5y60dHRZGVlUVxcjJ+fX611x4wZY/1drVbTu3dv0tPTufnmmwHYsWMHb7/9Nrm5ufTt25enn36arl3tn6pRrVahVjvW7OJ2/olet0Z+sve7w3l8ceB3APpHBJMQ17XVNQk1VW5aO8lL/SQ3tjVHXpxWCIxGIxqNptaymqJgMBhqFQKj0VirYNSsazBUD7rWo0cPfHx8WLFiBRaLhaVLlzJ9+nS2b9+Op6d9M3Vptb6XfbLVaHwuaztbTueXkHJ+ysmg9j4svOta/Nu13tnGGjM3bYnkpX6SG9uaMi9ObXRWFKVR1l28eHGt359++mni4uLYv38/gwYNsmv/en3JZV0RaDQ+FBaWYTbb7uR2hMls4bn39lFabkKtUjErMRpTRRWGiqoG77u5NXZu2grJS/0kN7Y1JC+Bgfbdau60QqDVajEajbWWGY1GVCoVWm3tqRYDAwNtrtuzp+2na/38/AgICCAvL8/ueCwWBYvF/sJ0IbPZgsnU8A/uvz//hazcQgDGX9+dqzppGmW/ztRYuWlrJC/1k9zY1pR5cVpjXExMDLm5uej1euuy9PR0wsPD8fX1rbOuTqez/m42mzl8+DB9+/aluLiYxYsX1zrp6/V69Ho9Xbp0afoDaSQHj5/jsx9+AyAqLJAxg7o5OSIhhKtwWiGIiooiNjaWlStXUlxcTGZmJikpKSQlJQGQkJDAvn37AEhKSmLz5s0cOHCAsrIyVq9ejaenJzfccAN+fn4cPHiQpUuXYjQaKSgoYMmSJURGRtKvXz9nHZ5D9IXlvPNxdb+App0H994ShbqVdQ4LIVovp3bPr1q1ijNnzjBkyBCmTJnC+PHjmTx5MgBZWVmUlpYCMGzYMBYsWMC8efMYOHAg33zzDWvXrsXbu3pqxjfeeANFURg9ejQ33HADVVVVrF27FnUrmL/XbLGwdtthisuqUAH3jo0mwM/L2WEJIVyISnGkx7YNO3u2yOFt3N3VBAb6YjCUXHbb3eb/nWDr1ycBuHlQN/46vG3MNtYYuWmLJC/1k9zY1pC8BAfb9/xRy//K3IYd+dXAtvNFIDw0gPHXd3duQEIIlySFwEkKSypZu02HAvh6uzNzXDRuraApSwjR9siZxwksisLbHx+moLgSgKljetMhwNvJUQkhXJUUAifY+X02h05U3zY78por6R8R7OSIhBCuTApBM8vMKeCjL04A0DXEj9vjw50ckRDC1UkhaEal5VW8tVWH2aLg5enG7MQYPNzln0AI4VxyFmomiqKQ8kkG5wrKAZgyOpIQbTsnRyWEEFIIms2en3LYf/QsAENjOzEouqOTIxJCiGpSCJpBdl4RGz8/DkCnDu244y8RTo5ICCH+IIWgiZVXmlizRYfJbMHDXc3sxBi8PN2cHZYQQlhJIWhiGz47xml99ZhJSSN7cuUVfpfYQgghmpcUgib0dXouXx86DcC1va5g+NWdnRyREELUJYWgieTml/D+Z8cACArwJjmhV6ubd1gI4RqkEDSBKpOZ1Zt1VFSZcVOrmJUYQztvp84KKoQQ9ZJC0AT+ves4p84WA/DX4T24qrPGyREJIUT9pBA0sn0ZZ9j9Yw4AfXp04MaBrWe6TCGEa5JC0IjOGctI+SQDgEB/L6bd3FumnBRCtHhSCBqJyWzhra06yipMqFQwY2wU/u08nR2WEEJckhSCRvKfL0+Q+XshAIlDuhPZNdDJEQkhhH2cWghycnKYMWMGcXFxxMfHs3z5ciwW23Nyrl+/ntGjR9O/f3+SkpI4dOiQ9bWKigqefPJJhg0bRlxcHA888AAGg6G5DoOfM8/xyXfZAPTq2p5bBoc123sLIURDObUQzJ07l5CQENLS0khJSSEtLY1169bVWW/Xrl289tprvPjii3zzzTfEx8cza9YsSkurn9h9+eWX0el0pKamsnPnThRF4bHHHmuWY8gvKOOtLToA/Nt5cO/YaNRq6RcQQrQeTisE6enpZGRksHDhQvz9/QkLCyM5OZnU1NQ666ampjJhwgT69u2Lt7c306dPB2D37t2YTCY2bdrEnDlz6NSpE+3bt2fevHns2bOHvLy8Jj0Gi0XhpX/9SFFpFQDTb4ki0N+rSd9TCCEam9OectLpdISGhhIQEGBdFh0dTVZWFsXFxfj5+dVad8yYMdbf1Wo1vXv3Jj09nd69e1NUVER0dLT19R49euDt7Y1OpyMkJMSueNRqlcPf5NP2neLn4+cAGDOoG/1kykkrNzd1rb9FNclL/SQ3tjVHXpxWCIxGIxpN7QetaoqCwWCoVQiMRmOtglGzrsFgwGg0AtTZl0ajcaifQKv1dXgIiHOF1ZPMRHYN5N5b++AuH+A6NBofZ4fQIkle6ie5sa0p8+LUcQ8URWm0dR3Zly16fYnDVwTjh3YnpkcQkVdqKCosa9D7tzVubmo0Gh8KC8swm23fAOCKJC/1k9zY1pC8BAb62rWe0wqBVqu1fpuvYTQaUalUaLXaWssDAwNtrtuzZ0/rukajEV/fPw66oKCADh062B2PxaJgsThWTLw93bj+6lAMhhJMJvng2mI2WyQ3Nkhe6ie5sa0p8+K0toyYmBhyc3PR6/XWZenp6YSHh9c6odesq9PprL+bzWYOHz5M37596dKlCwEBAbVeP3bsGJWVlcTExDT9gQghRCvntEIQFRVFbGwsK1eupLi4mMzMTFJSUkhKSgIgISGBffv2AZCUlMTmzZs5cOAAZWVlrF69Gk9PT2644Qbc3Ny4/fbbWbNmDbm5uRgMBl566SX+8pe/EBQU5KzDE0KIVsOpfQSrVq3iiSeeYMiQIfj5+TFp0iQmT54MQFZWlvU5gWHDhrFgwQLmzZtHfn4+sbGxrF27Fm9vbwAeeOABSkpKSExMxGQyER8fz+LFi511WEII0aqolIb2srYRZ88WObyNu7uawEBf6SOwQXJjm+SlfpIb2xqSl+Bgf7vWk/sdhRDCxUkhEEIIFyeFQAghXJwUAiGEcHHSWSyEEC5OrgiEEMLFSSEQQggXJ4VACCFcnBQCIYRwcVIIhBDCxUkhEEIIFyeFQAghXJwUAiGEcHFSCIQQwsVJIRBCCBcnheAScnJymDFjBnFxccTHx7N8+XIsFttjgq9fv57Ro0fTv39/kpKSOHToUDNH27zszc1rr71G7969iY2NrfXn3LlzToi6efzvf/9j8ODBzJ8//6LrWSwWXn75ZUaOHMmAAQOYNm0av/32WzNF2fzszcujjz5qncWw5s+1117bTFE2v5ycHO677z7i4uIYPHgwjz76KIWFhTbX3bFjB2PHjqVfv35MmDCBr776qsHvL4XgEubOnUtISAhpaWmkpKSQlpbGunXr6qy3a9cuXnvtNV588UW++eYb4uPjmTVrlnWWtbbI3twAJCYmkp6eXutPW51K9J///CdLly6lW7dul1x3w4YNbNu2jbVr17J7927CwsK47777aItDgDmSF4DZs2fX+rzUTF3bFs2aNQuNRsOuXbv46KOP+OWXX1i2bFmd9Y4cOcIjjzzCwoUL+fbbb0lOTub+++/n9OnTDXp/KQQXkZ6eTkZGBgsXLsTf35+wsDCSk5NJTU2ts25qaioTJkygb9++eHt7M336dAB2797d3GE3C0dy42q8vLzYtGmTXSe81NRUkpOT6dGjB35+fsyfP5/MzEwOHjzYDJE2L0fy4koKCwuJiYnhoYcewtfXl44dO3LrrbfaLHwffPABw4cPZ/jw4Xh5eTFu3DgiIiLYunVrg2KQQnAROp2O0NBQAgICrMuio6PJysqiuLi4zrpRUVHW39VqNb179yY9Pb3Z4m1OjuQG4OjRo0yaNIn+/ftz8803N8rlbEs1ZcoU/P0vPUVgeXk5x48fr/W58fPzo1u3bm3yc2NvXmp8++23jB8/nn79+nHbbbe12aZWjUbD888/X+sKOTc3lyuuuKLOun8+zwBERUU1+PMiheAijEYjGo2m1rKaE5/BYKiz7oUnxZp1/7xeW+FIbjp27EiXLl1YtmwZX3/9NRMnTmTWrFmcOHGi2eJtiQoKClAUxaU+N/bq0qUL3bp146233uJ///sf1157Lffcc49L5CU9PZ3333+f2bNn13mtqc4zUgguwZG22rbYrnsx9h7vxIkTWbVqFd26dcPHx4fk5GR69+7d4MvZtsLVPjf2uO+++3juuecICQnBz8+Phx9+GE9PT9LS0pwdWpPav38/06ZN46GHHmLw4ME212mKz4sUgovQarUYjcZay4xGIyqVCq1WW2t5YGCgzXX/vF5b4UhubAkNDeXMmTNNFF3r0L59e9Rqtc08dujQwTlBtVBubm506tSpTX9mdu3axYwZM/jHP/7BlClTbK7TVOcZKQQXERMTQ25uLnq93rosPT2d8PBwfH1966yr0+msv5vNZg4fPkzfvn2bLd7m5Ehu3nzzTfbu3VtrWWZmJl26dGmWWFsqLy8vevbsWetzU1hYSHZ2Nn369HFiZM6lKArPP/88GRkZ1mWVlZVkZ2e32c/Mjz/+yCOPPMKrr77K+PHj610vJiamTl9Jenp6g88zUgguouY+5pUrV1JcXExmZiYpKSkkJSUBkJCQYO3ZT0pKYvPmzRw4cICysjJWr16Np6cnN9xwgxOPoOk4khuj0ciSJUs4ceIEFRUVvPvuu2RnZ3Prrbc68xCcIi8vj4SEBOuzAklJSaxfv57MzEyKi4tZsWKF9ZkLV3JhXlQqFadOnWLJkiXk5eVRUlLCihUr8PDwYNSoUc4OtdGZTCYWLVrEwoULGTp0aJ3X7777bnbs2AHA7bffzjfffMOePXuoqKhg06ZNnDx5knHjxjUoBvcGbe0CVq1axRNPPMGQIUPw8/Nj0qRJTJ48GYCsrCzrcwLDhg1jwYIFzJs3j/z8fGJjY1m7di3e3t7ODL9J2Zubhx56CIDk5GSMRiPh4eG89957dOzY0WmxN6Wak7jJZAKwtmunp6dTVVVFVlYWlZWVAEyaNImzZ89y1113UVJSQlxcHK+//rpzAm9ijuTl2WefZdmyZUyYMIHi4mL69OnDunXraNeunXOCb0IHDhwgMzOTpUuXsnTp0lqvffrpp/z2228UFBQAEBERwYoVK3j++efJyckhPDyct956i+Dg4AbFIJPXCyGEi5OmISGEcHFSCIQQwsVJIRBCCBcnhUAIIVycFAIhhHBxUgiEEMLFSSEQQggXJ4VAuLTY2Fg++OADZ4fRYuIQrkkeKBPivJKSEv79738zbdq0Jn+vLVu2cPXVV8skLaJFkCsCIc777rvvePfdd5v8fWoGVfv111+b/L2EsIcUAuHSIiMj2bhxI++//z73338/586dq9VM88MPP3DXXXcxcOBArrnmGmbPnl1rcvkRI0bw2muv8be//Y24uDgASktLWbx4MYMGDaJPnz6MGjWK9957D4CioiJiY2MxGAzMmTOHO++8s1YcNVJTUxk7dixXX301Q4cOZcmSJZSVlQHVBSsyMpKff/6ZyZMn069fP0aMGMHmzZut2x85coS7776bAQMG0K9fPyZNmtSm5/wVDaQI4cIiIiKUf/3rX4qiKMqqVauUwYMHW187fvy4Ehsbq6SkpCgVFRWKXq9XFixYoIwcOVKpqKhQFEVR4uPjlWHDhinffPONYjabFUVRlKeffloZOXKkkpubq1gsFmX37t1KRESE8uWXXyqKoii//fabEhERoXzxxRc24/joo4+UPn36KF988YVSVVWlZGRkKPHx8cqjjz6qKIqifPvtt0pERIQydepUJSsrS6mqqlKee+45JSYmRjEYDIqiKEpCQoLy0ksvKRUVFUp5ebmyZs0aZfjw4YrJZGrahIpWSa4IhKhHamoq4eHhJCcn4+npSWBgII8//ji//fYb+/fvt64XFRXFoEGDUKur/zs98sgjfPTRR3Ts2BGVSsUNN9xAcHAwBw4csOt9/+///o+xY8cybNgw3N3diYyM5O6772b79u3W0TkB7rjjDsLCwnB3d+eWW26hsrLS2txUWFiIp6cnnp6eeHl5MXPmTPbs2YObm1vjJUi0GTIMtRD1OHHiBEeOHKkzN4C7uzunTp2y/t61a9dar+fl5bF8+XL27dtHUVERUD2xSkVFhV3vm52dXWdykvDwcCorK8nLy7Muu7CjuWZ45vLycgD+/ve/8/TTT7Np0yYGDRrEiBEjiI+Pl0IgbJJCIEQ9vL29uf7661m7du1F1/Pw8LD+bLFYmD59OkFBQWzcuJGuXbuiUqkYPny43e9rq2BYLBYAVCqVddmFP/9ZYmIio0aNYu/evXz11Vc8/vjj9OzZk3Xr1kkxEHVI05AQ9ejevTsZGRmYzWbrMrPZXOtq4M/y8/M5efIkd9xxB926dUOlUpGbm1vrm/ylhIWFcfTo0VrLfvnlF3x8fOyezEev1+Pr68uoUaNYvHgxH3zwAT/88EOt6R+FqCGFQIjzfHx8KCoq4vTp05SUlJCUlITRaOTFF1+ksLDQOpXkbbfdRnFxsc19aLVa/P39+fHHHzGZTBw9epQlS5bQpUsXcnNzgT+acU6cOEFhYWGdfSQlJbFt2za++uorzGYzOp2OdevWcdttt+HufumL+N9//51hw4axbds2KisrMZlM7N+/Hy8vLzp37tyADIm2SgqBEOfdeOONdOzYkVGjRrFhwwY6d+7M2rVrOXjwINdffz3XX389x44dY926dfj5+dnch5ubGy+88AJ79uzh2muv5YknnuD+++8nOTmZzz//nIcffhitVsu4ceNYsWIFd9xxR519JCUl8cADD/Dcc89x7bXXsmDBAiZOnMgjjzxi13F07tyZl19+mXfeeYeBAwdy3XXXkZqayurVqwkMDGxQjkTbJE8WCyGEi5MrAiGEcHFSCIQQwsVJIRBCCBcnhUAIIVycFAIhhHBxUgiEEMLFSSEQQggXJ4VACCFcnBQCIYRwcVIIhBDCxUkhEEIIFyeFQAghXNz/B08eL4AKmdMKAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x300 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "visible_env.play()\n",
        "\n",
        "visualize(MPI_planner.V_logs, (1, 1, 1), 6)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IA8AkX2Feuwt"
      },
      "source": [
        "### Value Iteration (VI) Recap\n",
        "\n",
        "**Idea**\n",
        "\n",
        "Gradually advance to $\\pi^{*}$ with combined **truncated policy evaluation** and **policy improvement** steps.\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "**Truncated Policy Evaluation and Improvement step**\n",
        "\n",
        "No arbitrary starting policy needed. Estimate $V^{\\pi^*}$ as follows:\n",
        "\n",
        "  * For $k = 0,1,2,\\cdots, K$\n",
        "\n",
        "    * Set $V = \\mathbf{0}$ when $k = 0$ and $V_{k-1}$ otherwise\n",
        "      <div>\n",
        "      <img src=\"https://drive.google.com/uc?export=view&id=1fsi3ZZgqZ-p061AxvSdeluWZTlwSjnGj\" alt=\"policy evaluation and improvement\" width=\"400\"/>\n",
        "      </div>\n",
        "\n",
        "      return $V$ as $V_{k}$.\n",
        "\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "#### Putting everything together\n",
        "\n",
        "* Estimate $V^{\\pi^*}$ with $V_{K} = (T^*)^{K}\\mathbf{0}$\n",
        "* Return $\\hat{\\pi}^{*}$ as the greedy policy w.r.t $V_{K}$. That is,\n",
        "\n",
        "  $$ \\hat{\\pi}^{*}(s) \\in \\underset{a\\in\\mathcal{A}}{\\arg\\max} \\bigg\\{r(s,a) + \\gamma\\sum_{s'\\in\\mathcal{X}}p(s'|s,a)V_{K}(s')\\bigg\\},\\quad s\\in\\mathcal{S}$$\n",
        "\n",
        "\n",
        "\n",
        "&nbsp;\n",
        "\n",
        "#### Theoretical guarantee [[2]](#scrollTo=XqJPFe6f6gFV&line=5&uniqifier=1)\n",
        "\n",
        "VI finds an **$\\mathbf{\\varepsilon}$-optimal policy** ($\\pi^{\\varepsilon}$) satisfying\n",
        "\n",
        "$\\qquad V^* - V^{\\pi^{\\varepsilon}}\\leq \\varepsilon\\,\\mathbf{1}$\n",
        "\n",
        "after $K = \\mathcal{O}(\\ln(2\\gamma/\\varepsilon(1-\\gamma)^2)/(1-\\gamma))$ iterations.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "id": "cWtqSTiD9Kko"
      },
      "outputs": [],
      "source": [
        "class ValueIteration:\n",
        "  \"\"\"\n",
        "  Implements value iteration\n",
        "  \"\"\"\n",
        "  def __init__(self,\n",
        "              env: Env,\n",
        "              gamma: float,\n",
        "              epsilon: float,\n",
        "              num_iterations = None,\n",
        "  ):\n",
        "    self.env = env\n",
        "    self.states = self.env.states\n",
        "    self.n_states = len(self.states)\n",
        "    self.actions = self.env.actions\n",
        "    self.n_actions = len(self.actions)\n",
        "    self.gamma = gamma\n",
        "    self.K = num_iterations\n",
        "    self.V_logs = []\n",
        "\n",
        "    if self.K is None:\n",
        "      self.K = math.ceil(np.log((2*self.gamma)/(epsilon*(1-self.gamma)**2))/(1-self.gamma))\n",
        "\n",
        "    self.policy = {state: 0 for state in self.env.states}\n",
        "    self.V = {state: 0 for state in self.env.states}\n",
        "\n",
        "\n",
        "  def estimate_vstar(self):\n",
        "    \"\"\"\n",
        "    Starting from an initial guess 'V',\n",
        "    iteratively estimate V^{π*} as T*V\n",
        "\n",
        "    Assign new values to self.V\n",
        "    \"\"\"\n",
        "    # Task: Complete this and delete line *\n",
        "\n",
        "    # Main loop for iterative value update\n",
        "    for k in range(self.K):\n",
        "      for state in self.states:\n",
        "        a_s = []\n",
        "        for a in self.actions:\n",
        "          sum_ = 0\n",
        "          for s_next in self.states:\n",
        "            sum_ += self.env.T[state][a][s_next] * (self.env.R[state][a] + self.gamma * self.V[s_next])\n",
        "          a_s.append(sum_)\n",
        "        self.V[state] = max(a_s)\n",
        "\n",
        "\n",
        "    self.V_logs.append(self.V.copy())\n",
        "\n",
        "\n",
        "  def get_policy(self):\n",
        "    \"\"\"\n",
        "    Get the greedy policy:\n",
        "      π(s) = argmax_{a\\in A} Q(s,a)\n",
        "    where\n",
        "      Q(s,a) = r(s,a) + gamma*<P(.|s,a),v>\n",
        "\n",
        "    assign new policy to self.policy\n",
        "    \"\"\"\n",
        "    return PolicyIteration.get_policy(self)\n",
        "\n",
        "\n",
        "  def get_expected_update(self, state, action):\n",
        "    \"\"\"\n",
        "    Compute:\n",
        "\n",
        "      Q(s,a) = r(s,a) + gamma <p(.|s,a),V>\n",
        "\n",
        "    :param state\n",
        "    :param action\n",
        "\n",
        "    :return Q(s,a): float\n",
        "    \"\"\"\n",
        "    return PolicyIteration.get_expected_update(self, state, action)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M7DXuWm3v82W"
      },
      "source": [
        "Finally, we also plan with Value Iteration."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "id": "BFFnzxCfaS-E"
      },
      "outputs": [],
      "source": [
        "VI_planner = ValueIteration(env,\n",
        "                            gamma = 0.9, #same as PI\n",
        "                            epsilon = 0.01,\n",
        "                            num_iterations = None) # You can set the number of iterations\n",
        "\n",
        "VI_planner.estimate_vstar()\n",
        "VI_planner.get_policy()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "id": "dgj9qrYohLWm",
        "outputId": "3eb1a628-9713-49ca-a967-1fb97759c7f5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.3476792496898552\n"
          ]
        }
      ],
      "source": [
        "avg_return = rollouts(env=visible_env,\n",
        "                      policy=make_policy(VI_planner.policy),\n",
        "                      n_trajectories=80,\n",
        "                      gamma=0.9)\n",
        "\n",
        "print(avg_return)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "id": "QY-Vrp5J0gDC",
        "outputId": "7a8c1ffc-2465-4e64-9a39-4cde33d94d17",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 778
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
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          "metadata": {}
        },
        {
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          "data": {
            "text/plain": [
              "<Figure size 400x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "visible_env.play()\n",
        "\n",
        "visualize(VI_planner.V_logs, (1, 1, 0), 6)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8fS7zGk2tas0"
      },
      "source": [
        "### Bonus Task ⭐\n",
        "\n",
        "Implement Optimistic Policy Iteration. See slide 33 of [[1]](#scrollTo=XqJPFe6f6gFV&line=5&uniqifier=1).\n",
        "\n",
        "Improve the efficiency of the implementations above with Numpy/Pytorch/Tensorflow."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XqJPFe6f6gFV"
      },
      "source": [
        "# Credit:\n",
        "\n",
        "1.   Bruno Scherrer, \"a lecture on Markov Decision Processes and Dynamic Programming\", June 2023, [Slides](https://drive.google.com/file/d/1sFh0TyU_nq60R7kouPg6MCI4IMYicSII/view?usp=sharing)\n",
        "2.   Csaba Szepesvári \"a lecture series on Theoretical Foundations of Reinforcement Learning\", 2020, [RL Theory course](https://rltheory.github.io/)\n",
        "3.   Richard S. Sutton, Andrew G. Barto \"Reinforcement Learning: An Introduction\", second edition, 2020, [Book](http://incompleteideas.net/book/RLbook2020.pdf)\n",
        "\n",
        "\n",
        "\n"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "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": "3.9.2"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}