reinforcement-learning-chess-3-q-networks.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reinforcement Learning Chess\n",
    "Reinforcement Learning Chess is a series of notebooks where I implement Reinforcement Learning algorithms to develop a chess AI. I start of with simpler versions (environments) that can be tackled with simple methods and gradually expand on those concepts untill I have a full-flegded chess AI."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Notebook 1: Policy Iteration](https://www.kaggle.com/arjanso/reinforcement-learning-chess-1-policy-iteration)  \n",
    "[Notebook 2: Model-free learning](https://www.kaggle.com/arjanso/reinforcement-learning-chess-2-model-free-methods)  \n",
    "[Notebook 4: Policy Gradients](https://www.kaggle.com/arjanso/reinforcement-learning-chess-4-policy-gradients)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Notebook III: Q-networks\n",
    "In this notebook I implement an simplified version of chess named capture chess. In this environment the agent (playing white) is rewarded for capturing pieces (not for checkmate).  After running this notebook, you end up with an agent that can capture pieces against a random oponnent as demonstrated in the gif below. The main difference between this notebook and the previous one is that I use Q-networks as an alternative to Q-tables. Q-tables are nice and straightforward, but can only contain a limited amount of action values. Chess has state space complexity of 10<sup>47</sup>. Needless to say, this is too much information to put in a Q-table. This is where supervised learning comes in. A Q-network can represent a generalized mapping from state to action values.\n",
    "\n",
    "![](https://images.chesscomfiles.com/uploads/game-gifs/90px/green/neo/0/cc/0/0/aXFZUWpyN1Brc1BPbHQwS211WEhudkh6cXohMGFPMExPUTJNUTY4MDY1OTI1NFpSND8yOT85M1Y5MTA3MUxLQ3RDUkpDSjcwTE0wN293V0d6Rzc2cHhWTXJ6NlhzQVg0dUM0WGNNWDU,.gif)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import and Install"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "_cell_guid": "b1076dfc-b9ad-4769-8c92-a6c4dae69d19",
    "_uuid": "8f2839f25d086af736a60e9eeb907d3b93b6e0e5"
   },
   "outputs": [],
   "source": [
    "import numpy as np # linear algebra\n",
    "import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)\n",
    "import os\n",
    "import inspect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "_cell_guid": "79c7e3d0-c299-4dcb-8224-4455121ee9b0",
    "_uuid": "d629ff2d2480ee46fbb7e2d37f6b5fab8052498a"
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting python-chess\r\n",
      "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/74/f3/b0caa4307443926d9f9ba8752270a8fc159e3ac6c9859c4615244c5ba74c/python_chess-0.30.0-py3-none-any.whl (127kB)\r\n",
      "\u001b[K     |████████████████████████████████| 133kB 3.4MB/s \r\n",
      "\u001b[?25hInstalling collected packages: python-chess\r\n",
      "Successfully installed python-chess-0.30.0\r\n",
      "Collecting git+https://github.com/arjangroen/RLC.git\r\n",
      "  Cloning https://github.com/arjangroen/RLC.git to /tmp/pip-req-build-wsbm6wem\r\n",
      "  Running command git clone -q https://github.com/arjangroen/RLC.git /tmp/pip-req-build-wsbm6wem\r\n",
      "Building wheels for collected packages: RLC\r\n",
      "  Building wheel for RLC (setup.py) ... \u001b[?25l-\b \b\\\b \bdone\r\n",
      "\u001b[?25h  Stored in directory: /tmp/pip-ephem-wheel-cache-2_uuic69/wheels/04/68/a5/cb835cd3d76a49de696a942739c71a56bfe66d0d8ea7b4b446\r\n",
      "Successfully built RLC\r\n",
      "Installing collected packages: RLC\r\n",
      "Successfully installed RLC-0.3\r\n"
     ]
    }
   ],
   "source": [
    "!pip install python-chess  # Python-Chess is the Python Chess Package that handles the chess environment\n",
    "!pip install --upgrade git+https://github.com/arjangroen/RLC.git  # RLC is the Reinforcement Learning package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import chess\n",
    "from chess.pgn import Game\n",
    "import RLC\n",
    "from RLC.capture_chess.environment import Board\n",
    "from RLC.capture_chess.learn import Q_learning\n",
    "from RLC.capture_chess.agent import Agent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The environment: Capture Chess\n",
    "In this notebook we'll upgrade our environment to one that behaves more like real chess. It is mostly based on the Board object from python-chess.\n",
    "Some modifications are made to make it easier for the algorithm to converge:\n",
    "* There is a maximum of 25 moves, after that the environment resets\n",
    "* Our Agent only plays white\n",
    "* The Black player is part of the environment and returns random moves\n",
    "* The reward structure is not based on winning/losing/drawing but on capturing black pieces:\n",
    "    - pawn capture: +1\n",
    "    - knight capture: +3\n",
    "    - bishop capture: +3\n",
    "    - rook capture: +5\n",
    "    - queen capture: +9\n",
    "* Our state is represent by an 8x8x8 array\n",
    "    - Plane 0 represents pawns\n",
    "    - Plane 1 represents rooks\n",
    "    - Plane 2 represents knights\n",
    "    - Plane 3 represents bishops\n",
    "    - Plane 4 represents queens\n",
    "    - Plane 5 represents kings\n",
    "    - Plane 6 represents 1/fullmove number (needed for markov property)\n",
    "    - Plane 7 represents can-claim-draw\n",
    "* White pieces have the value 1, black pieces are minus 1\n",
    "       \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Board representation of python-chess:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "Board('rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "board = Board()\n",
    "board.board"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Numerical representation of the pawns (layer 0)\n",
    "Change the index of the first dimension to see the other pieces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  0,  0,  0,  0,  0,  0,  0],\n",
       "       [-1, -1, -1, -1, -1, -1, -1, -1],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0],\n",
       "       [ 1,  1,  1,  1,  1,  1,  1,  1],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "board.layer_board[0,::-1,:].astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Agent\n",
    "* The agent is no longer a single piece, it's a chess player\n",
    "* Its action space consist of 64x64=4096 actions:\n",
    "    * There are 8x8 = 64 piece from where a piece can be picked up\n",
    "    * And another 64 pieces from where a piece can be dropped. \n",
    "* Of course, only certain actions are legal. Which actions are legal in a certain state is part of the environment (in RL, anything outside the control of the agent is considered part of the environment). We can use the python-chess package to select legal moves. (It seems that AlphaZero uses a similar approach https://ai.stackexchange.com/questions/7979/why-does-the-policy-network-in-alphazero-work)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "board_layer (InputLayer)        (None, 8, 8, 8)      0                                            \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_1 (Conv2D)               (None, 1, 8, 8)      9           board_layer[0][0]                \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_2 (Conv2D)               (None, 1, 8, 8)      9           board_layer[0][0]                \n",
      "__________________________________________________________________________________________________\n",
      "reshape_1 (Reshape)             (None, 1, 64)        0           conv2d_1[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "reshape_2 (Reshape)             (None, 1, 64)        0           conv2d_2[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "dot_1 (Dot)                     (None, 64, 64)       0           reshape_1[0][0]                  \n",
      "                                                                 reshape_2[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "reshape_3 (Reshape)             (None, 4096)         0           dot_1[0][0]                      \n",
      "==================================================================================================\n",
      "Total params: 18\n",
      "Trainable params: 18\n",
      "Non-trainable params: 0\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "board = Board()\n",
    "agent = Agent(network='conv',gamma=0.1,lr=0.07)\n",
    "R = Q_learning(agent,board)\n",
    "R.agent.fix_model()\n",
    "R.agent.model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    def network_update(self, minibatch):\n",
      "        \"\"\"\n",
      "        Update the Q-network using samples from the minibatch\n",
      "        Args:\n",
      "            minibatch: list\n",
      "                The minibatch contains the states, moves, rewards and new states.\n",
      "\n",
      "        Returns:\n",
      "            td_errors: np.array\n",
      "                array of temporal difference errors\n",
      "\n",
      "        \"\"\"\n",
      "\n",
      "        # Prepare separate lists\n",
      "        states, moves, rewards, new_states = [], [], [], []\n",
      "        td_errors = []\n",
      "        episode_ends = []\n",
      "        for sample in minibatch:\n",
      "            states.append(sample[0])\n",
      "            moves.append(sample[1])\n",
      "            rewards.append(sample[2])\n",
      "            new_states.append(sample[3])\n",
      "\n",
      "            # Episode end detection\n",
      "            if np.array_equal(sample[3], sample[3] * 0):\n",
      "                episode_ends.append(0)\n",
      "            else:\n",
      "                episode_ends.append(1)\n",
      "\n",
      "        # The Q target\n",
      "        q_target = np.array(rewards) + np.array(episode_ends) * self.gamma * np.max(\n",
      "            self.fixed_model.predict(np.stack(new_states, axis=0)), axis=1)\n",
      "\n",
      "        # The Q value for the remaining actions\n",
      "        q_state = self.model.predict(np.stack(states, axis=0))  # batch x 64 x 64\n",
      "\n",
      "        # Combine the Q target with the other Q values.\n",
      "        q_state = np.reshape(q_state, (len(minibatch), 64, 64))\n",
      "        for idx, move in enumerate(moves):\n",
      "            td_errors.append(q_state[idx, move[0], move[1]] - q_target[idx])\n",
      "            q_state[idx, move[0], move[1]] = q_target[idx]\n",
      "        q_state = np.reshape(q_state, (len(minibatch), 4096))\n",
      "\n",
      "        # Perform a step of minibatch Gradient Descent.\n",
      "        self.model.fit(x=np.stack(states, axis=0), y=q_state, epochs=1, verbose=0)\n",
      "\n",
      "        return td_errors\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(inspect.getsource(agent.network_update))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Q learning with a Q-network\n",
    "**Theory**\n",
    "- The Q-network is usually either a linear regression or a (deep) neural network. \n",
    "- The input of the network is the state (S) and the output is the predicted action value of each Action (in our case, 4096 values). \n",
    "- The idea is similar to learning with Q-tables. We update our Q value in the direction of the discounted reward + the max successor state action value\n",
    "- I used prioritized experience replay to de-correlate the updates. If you want to now more about it, check the link in the references\n",
    "> - I used fixed-Q targets to stabilize the learning process. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Implementation\n",
    "- I built two networks, A linear one and a convolutional one\n",
    "- The linear model maps the state (8,8,8) to the actions (64,64), resulting in over 32k trainable weights! This is highly inefficient because there is no parameter sharing, but it will work.\n",
    "- The convolutional model uses 2 1x1 convulutions and takes the outer product of the resulting arrays. This results in only 18 trainable weights! \n",
    "    - Advantage: More parameter sharing -> faster convergence\n",
    "    - Disadvantage: Information gets lost -> lower performance\n",
    "- For a real chess AI we need bigger neural networks. But now the neural network only has to learn to capture valuable pieces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    def play_game(self, k, greedy=False, maxiter=25):\n",
      "        \"\"\"\n",
      "        Play a game of capture chess\n",
      "        Args:\n",
      "            k: int\n",
      "                game count, determines epsilon (exploration rate)\n",
      "            greedy: Boolean\n",
      "                if greedy, no exploration is done\n",
      "            maxiter: int\n",
      "                Maximum amount of steps per game\n",
      "\n",
      "        Returns:\n",
      "\n",
      "        \"\"\"\n",
      "        episode_end = False\n",
      "        turncount = 0\n",
      "\n",
      "        # Here we determine the exploration rate. k is divided by 250 to slow down the exploration rate decay.\n",
      "        eps = max(0.05, 1 / (1 + (k / 250))) if not greedy else 0.\n",
      "\n",
      "        # Play a game of chess\n",
      "        while not episode_end:\n",
      "            state = self.env.layer_board\n",
      "            explore = np.random.uniform(0, 1) < eps  # determine whether to explore\n",
      "            if explore:\n",
      "                move = self.env.get_random_action()\n",
      "                move_from = move.from_square\n",
      "                move_to = move.to_square\n",
      "            else:\n",
      "                action_values = self.agent.get_action_values(np.expand_dims(state, axis=0))\n",
      "                action_values = np.reshape(np.squeeze(action_values), (64, 64))\n",
      "                action_space = self.env.project_legal_moves()  # The environment determines which moves are legal\n",
      "                action_values = np.multiply(action_values, action_space)\n",
      "                move_from = np.argmax(action_values, axis=None) // 64\n",
      "                move_to = np.argmax(action_values, axis=None) % 64\n",
      "                moves = [x for x in self.env.board.generate_legal_moves() if \\\n",
      "                         x.from_square == move_from and x.to_square == move_to]\n",
      "                if len(moves) == 0:  # If all legal moves have negative action value, explore.\n",
      "                    move = self.env.get_random_action()\n",
      "                    move_from = move.from_square\n",
      "                    move_to = move.to_square\n",
      "                else:\n",
      "                    move = np.random.choice(moves)  # If there are multiple max-moves, pick a random one.\n",
      "\n",
      "            episode_end, reward = self.env.step(move)\n",
      "            new_state = self.env.layer_board\n",
      "            if len(self.memory) > self.memsize:\n",
      "                self.memory.pop(0)\n",
      "                self.sampling_probs.pop(0)\n",
      "            turncount += 1\n",
      "            if turncount > maxiter:\n",
      "                episode_end = True\n",
      "                reward = 0\n",
      "            if episode_end:\n",
      "                new_state = new_state * 0\n",
      "            self.memory.append([state, (move_from, move_to), reward, new_state])\n",
      "            self.sampling_probs.append(1)\n",
      "\n",
      "            self.reward_trace.append(reward)\n",
      "\n",
      "            self.update_agent(turncount)\n",
      "\n",
      "        return self.env.board\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(inspect.getsource(R.play_game))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Demo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "iter 330\n",
      "iter 340\n",
      "iter 350\n",
      "iter 360\n",
      "iter 370\n",
      "iter 380\n",
      "iter 390\n",
      "iter 400\n",
      "iter 410\n",
      "iter 420\n",
      "iter 430\n",
      "iter 440\n",
      "iter 450\n",
      "iter 460\n",
      "iter 470\n",
      "iter 480\n",
      "iter 490\n",
      "iter 500\n",
      "iter 510\n",
      "iter 520\n",
      "iter 530\n",
      "iter 540\n",
      "iter 550\n",
      "iter 560\n",
      "iter 570\n",
      "iter 580\n",
      "iter 590\n",
      "iter 600\n",
      "iter 610\n",
      "iter 620\n",
      "iter 630\n",
      "iter 640\n",
      "iter 650\n",
      "iter 660\n",
      "iter 670\n",
      "iter 680\n",
      "iter 690\n",
      "iter 700\n",
      "iter 710\n",
      "iter 720\n",
      "iter 730\n",
      "iter 740\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pgn = R.learn(iters=750)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7ef77121d390>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "reward_smooth = pd.DataFrame(R.reward_trace)\n",
    "reward_smooth.rolling(window=125,min_periods=0).mean().plot(figsize=(16,9),title='average performance over the last 125 steps')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The PGN file is exported to the output folder. You can analyse is by pasting it on the [chess.com analysis board](https://www.chess.com/analysis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"final_game.pgn\",\"w\") as log:\n",
    "    log.write(str(pgn))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learned action values analysis\n",
    "So what has the network learned? The code below checks the action values of capturing every black piece for every white piece. \n",
    "- We expect that the action values for capturing black pieces is similar to the (Reinfeld) rewards we put in our environment. \n",
    "- Of course the action values also depend on the risk of re-capture by black and the opportunity for consecutive capture. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "board.reset()\n",
    "bl = board.layer_board\n",
    "bl[6,:,:] = 1/10  # Assume we are in move 10\n",
    "av = R.agent.get_action_values(np.expand_dims(bl,axis=0))\n",
    "\n",
    "av = av.reshape((64,64))\n",
    "\n",
    "p = board.board.piece_at(20)#.symbol()\n",
    "\n",
    "\n",
    "white_pieces = ['P','N','B','R','Q','K']\n",
    "black_piece = ['_','p','n','b','r','q','k']\n",
    "\n",
    "df = pd.DataFrame(np.zeros((6,7)))\n",
    "\n",
    "df.index = white_pieces\n",
    "df.columns = black_piece\n",
    "\n",
    "for from_square in range(16):\n",
    "    for to_square in range(30,64):\n",
    "        from_piece = board.board.piece_at(from_square).symbol()\n",
    "        to_piece = board.board.piece_at(to_square)\n",
    "        if to_piece:\n",
    "            to_piece = to_piece.symbol()\n",
    "        else:\n",
    "            to_piece = '_'\n",
    "        df.loc[from_piece,to_piece] = av[from_square,to_square]\n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ### Learned action values for capturing black (lower case) with white (upper case) pieces.\n",
    "Underscore represents capturing an empty square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>_</th>\n",
       "      <th>p</th>\n",
       "      <th>n</th>\n",
       "      <th>b</th>\n",
       "      <th>r</th>\n",
       "      <th>q</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>P</th>\n",
       "      <td>0.896254</td>\n",
       "      <td>1.711901</td>\n",
       "      <td>3.692928</td>\n",
       "      <td>4.038760</td>\n",
       "      <td>6.876412</td>\n",
       "      <td>10.946907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>N</th>\n",
       "      <td>0.742323</td>\n",
       "      <td>1.417884</td>\n",
       "      <td>3.058672</td>\n",
       "      <td>3.345108</td>\n",
       "      <td>5.695396</td>\n",
       "      <td>9.066788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.748629</td>\n",
       "      <td>1.429929</td>\n",
       "      <td>3.084656</td>\n",
       "      <td>3.373525</td>\n",
       "      <td>5.743780</td>\n",
       "      <td>9.143813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R</th>\n",
       "      <td>0.719952</td>\n",
       "      <td>1.375154</td>\n",
       "      <td>2.966494</td>\n",
       "      <td>3.244298</td>\n",
       "      <td>5.523756</td>\n",
       "      <td>8.793546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Q</th>\n",
       "      <td>0.702950</td>\n",
       "      <td>1.342680</td>\n",
       "      <td>2.896441</td>\n",
       "      <td>3.167684</td>\n",
       "      <td>5.393314</td>\n",
       "      <td>8.585888</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>K</th>\n",
       "      <td>0.670431</td>\n",
       "      <td>1.280565</td>\n",
       "      <td>2.762446</td>\n",
       "      <td>3.021141</td>\n",
       "      <td>5.143809</td>\n",
       "      <td>8.188688</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          _         p         n         b         r          q\n",
       "P  0.896254  1.711901  3.692928  4.038760  6.876412  10.946907\n",
       "N  0.742323  1.417884  3.058672  3.345108  5.695396   9.066788\n",
       "B  0.748629  1.429929  3.084656  3.373525  5.743780   9.143813\n",
       "R  0.719952  1.375154  2.966494  3.244298  5.523756   8.793546\n",
       "Q  0.702950  1.342680  2.896441  3.167684  5.393314   8.585888\n",
       "K  0.670431  1.280565  2.762446  3.021141  5.143809   8.188688"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['_','p','n','b','r','q']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "Reinforcement Learning: An Introduction  \n",
    "> Richard S. Sutton and Andrew G. Barto  \n",
    "> 1st Edition  \n",
    "> MIT Press, march 1998  \n",
    "\n",
    "RL Course by David Silver: Lecture playlist  \n",
    "> https://www.youtube.com/watch?v=2pWv7GOvuf0&list=PLqYmG7hTraZDM-OYHWgPebj2MfCFzFObQ  \n",
    "\n",
    "Experience Replay  \n",
    "> https://datascience.stackexchange.com/questions/20535/what-is-experience-replay-and-what-are-its-benefits"
   ]
  }
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