Assignment - default parameters.ipynb

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    "# Assignment"
   ]
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    "# Import \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy.matlib\n",
    "import pandas as pd\n",
    "from degree_freedom_queen import *\n",
    "from degree_freedom_king1 import *\n",
    "from degree_freedom_king2 import *\n",
    "from generate_game import *\n",
    "from Chess_env import *\n",
    "import random\n",
    "\n",
    "\n",
    "## INITIALISE THE ENVIRONMENT\n",
    "size_board = 4\n",
    "env=Chess_Env(size_board)"
   ]
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    "## The Environment\n",
    "\n",
    "You can find the environment in the file Chess_env, which contains the class Chess_env. To define an object, you need to provide the board size considered as input. In our example, size_board=4. \n",
    "Chess_env is composed by the following methods:\n",
    "\n",
    "1. Initialise_game. The method initialises an episode by placing the three pieces considered (Agent's king and queen, enemy's king) in the chess board. The outputs of the method are described below in order.\n",
    "\n",
    "     S $\\;$ A matrix representing the board locations filled with 4 numbers: 0, no piece in that position; 1, location of the \n",
    "     agent's king; 2 location of the queen; 3 location of the enemy king.\n",
    "     \n",
    "     X $\\;$ The features, that is the input to the neural network. See the assignment for more information regarding the            definition of the features adopted. To personalise this, go into the Features method of the class Chess_env() and change        accordingly.\n",
    "     \n",
    "     allowed_a $\\;$ The allowed actions that the agent can make. The agent is moving a king, with a total number of 8                possible actions, and a queen, with a total number of $(board_{size}-1)\\times 8$ actions. The total number of possible actions correspond      to the sum of the two, but not all actions are allowed in a given position (movements to locations outside the borders or      against chess rules). Thus, the variable allowed_a is a vector that is one (zero) for an action that the agent can (can't)      make. Be careful, apply the policy considered on the actions that are allowed only.\n",
    "     \n",
    "\n",
    "2. OneStep. The method performs a one step update of the system. Given as input the action selected by the agent, it updates the chess board by performing that action and the response of the enemy king (which is a random allowed action in the settings considered). The first three outputs are the same as for the Initialise_game method, but the variables are computed for the position reached after the update of the system. The fourth and fifth outputs are:\n",
    "\n",
    "     R $\\;$ The reward. To change this, look at the OneStep method of the class where the rewards are set.\n",
    "     \n",
    "     Done $\\;$ A variable that is 1 if the episode has ended (checkmate or draw).\n",
    "     \n",
    "     \n",
    "3. Features. Given the chessboard position, the method computes the features.\n",
    "\n",
    "This information and a quick analysis of the class should be all you need to get going. The other functions that the class exploits are uncommented and constitute an example on how not to write a python code. You can take a look at them if you want, but it is not necessary.\n",
    "\n",
    "\n",
    "\n",
    "\n"
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    "##  Define functions\n",
    "\n",
    "def EpsilonGreedy_Policy(Qvalues, epsilon, allowed_a):\n",
    "    \n",
    "    N_a=np.shape(Qvalues)[0]\n",
    "    a = list(range(0, N_a))\n",
    "    a = [i for idx, i in enumerate(a) if allowed_a[idx]]\n",
    "    Qvalues = [i for idx, i in enumerate(Qvalues) if allowed_a[idx]]\n",
    "\n",
    "    rand_value=np.random.uniform(0,1)\n",
    " ## epsilon is probability that we go random\n",
    "    rand_a=rand_value<epsilon\n",
    "\n",
    "    if rand_a==True:\n",
    "        \n",
    "        a = random.choice(a)\n",
    "\n",
    "    else:\n",
    "        idx=np.argmax(Qvalues)\n",
    "     \n",
    "        a = a[idx]\n",
    "            \n",
    "    return a\n",
    "\n",
    "\n",
    "def ComputeQvalues(W1, W2, bias_W1, bias_W2, X, hiddenactivfunction , outeractivfunction):\n",
    "    ## Qvalues=np.matmul(W2, np.matmul(W1,X)) ## this is direct computation of hidden layer and then output layer, without applying any non linear activation function\n",
    "    ## below is a better solution:\n",
    "    # Neural activation: input layer -> hidden layer\n",
    "    H1 = np.matmul(W1,X)+bias_W1 ## make sure that bias_W1 does not need to be transposed\n",
    "    # if hidden activ function is given:\n",
    "    if (hiddenactivfunction == 1):\n",
    "        H1 = np.round(1/(1+np.exp(-H1)), 5) ## sigmoid\n",
    "    elif(hiddenactivfunction == 2):\n",
    "         H1 = (H1>0).astype(int)*H1  ## RELU\n",
    "        \n",
    "    Qvalues = np.matmul(W2,H1) + bias_W2\n",
    "    \n",
    "    #if outer activ function is given\n",
    "    if (outeractivfunction == 1):\n",
    "        Qvalues = np.round(1/(1+np.exp(- Qvalues)), 5)\n",
    "    elif (outeractivfunction == 2):\n",
    "        Qvalues = (Qvalues>0).astype(int)*Qvalues\n",
    "\n",
    "    return Qvalues\n"
   ]
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    "# set seed\n",
    "np.random.seed(2022)\n",
    "\n",
    "# INITIALISE THE PARAMETERS OF YOUR NEURAL NETWORK\n",
    "S,X,allowed_a=env.Initialise_game()\n",
    "\n",
    "N_a=np.shape(allowed_a)[0]   # TOTAL NUMBER OF POSSIBLE ACTIONS\n",
    "N_in=np.shape(X)[0]          ## INPUT SIZE\n",
    "N_h=200                      ## NUMBER OF HIDDEN NODES\n",
    "\n",
    "## INITALISE YOUR NEURAL NETWORK... Here weights from input to hidden layer and from the hidden layer to output layer are initialized\n",
    "W1 = np.random.randn(N_h, N_in) * np.sqrt(1 / (N_in)) \n",
    "W2 = np.random.randn(N_a, N_h) * np.sqrt(1 / (N_h))\n",
    "\n",
    "#W1 = np.random.uniform(0, 1,(N_h,N_in))/(N_h*N_in) won't converge\n",
    "#W2 = np.random.uniform(0, 1,(N_a,N_h))/(N_a*N_h) won't converge\n",
    "\n",
    "bias_W1 = np.zeros((N_h,))\n",
    "bias_W2 = np.zeros((N_a,))\n",
    "\n",
    "# HYPERPARAMETERS SUGGESTED (FOR A GRID SIZE OF 4)\n",
    "epsilon_0 = 0.2     # STARTING VALUE OF EPSILON FOR THE EPSILON-GREEDY POLICY 0.2\n",
    "beta = 0.00005      # THE PARAMETER SETS HOW QUICKLY THE VALUE OF EPSILON IS DECAYING (SEE epsilon_f BELOW) 0.00005\n",
    "gamma = 0.85        # THE DISCOUNT FACTOR 0.85\n",
    "eta = 0.0035        # THE LEARNING RATE 0.0035\n",
    "\n",
    "N_episodes = 100000 # THE NUMBER OF GAMES TO BE PLAYED 100000\n",
    "\n",
    "hiddenactivfunction = 0\n",
    "outeractivfunction = 1\n",
    "\n",
    "# SAVING VARIABLES\n",
    "R_save = np.zeros([N_episodes, 1])\n",
    "N_moves_save = np.zeros([N_episodes, 1])\n",
    "Delta_save = np.zeros([N_episodes, 1])"
   ]
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    "## Backpropagation Derivation for Sigmoid as the Activation Function\n",
    "\n",
    "Overall definitions:\n",
    "- Loss: E = $0.5(R-Q){^2}$\n",
    "- Q-Values: $Q = f(Y)$, where $Y = W_2*H + B_2$\n",
    "- Hidden Layer: $H = f(Z)$, where $Z = W_1*X + B_1$\n",
    "\n",
    "Backpropagation rules derived for Sigmoid activation function f (for weigths and biases):\n",
    "- $dE/dW_2 = dEdQ * dQdY * dYdW_2 = -(R-Q)*(Q)(1-Q)*H$\n",
    "- $dE/dB_2 = dEdQ * dQdY * dYdB_2 = -(R-Q)*(Q)(1-Q)$\n",
    "- $dE/dW_1 = dEdQ * dQdY * dYdH * dHdZ * dZdW_1 = -(R-Q)*(Q)(1-Q)*W_2*(H)(1-H)*X$\n",
    "- $dE/dB_1 = dEdQ * dQdY * dYdH * dHdZ * dZdB_1= -(R-Q)*(Q)(1-Q)*W_2*(H)(1-H)$"
   ]
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   "source": [
    "## SARSA"
   ]
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   "source": [
    "for n in range(N_episodes):\n",
    "    S,X,allowed_a=env.Initialise_game()\n",
    "   \n",
    "    epsilon_f = epsilon_0 / (1 + beta * n)   ## DECAYING EPSILON\n",
    "    Done=0                                   ## SET DONE TO ZERO (BEGINNING OF THE EPISODE)\n",
    "    i = 1                                    ## COUNTER FOR NUMBER OF ACTIONS\n",
    "                               \n",
    "    Qvalues = ComputeQvalues(W1, W2, bias_W1, bias_W2, X, hiddenactivfunction , outeractivfunction)\n",
    "\n",
    "    a=EpsilonGreedy_Policy(Qvalues,epsilon_f, allowed_a)\n",
    "    \n",
    "    while (Done==0 and i<50):                           ## START THE EPISODE\n",
    "       \n",
    "        Qvalues = ComputeQvalues(W1, W2, bias_W1, bias_W2, X, hiddenactivfunction , outeractivfunction)\n",
    "       \n",
    "        S_next, X_next,allowed_a_next,R,Done=env.OneStep(a)\n",
    "       \n",
    "        \n",
    "        ## THE EPISODE HAS ENDED, UPDATE...BE CAREFUL, THIS IS THE LAST STEP OF THE EPISODE\n",
    "        if Done==1:\n",
    "            \n",
    "            R_save[n,]=np.copy(R)\n",
    "            N_moves_save[n,]=i\n",
    "            \n",
    "            dEdQ=R-Qvalues[a]\n",
    "           \n",
    "            Delta_save[n,] = 0.5*(dEdQ)*(dEdQ)\n",
    "            \n",
    "            ## update W2 and B2   \n",
    "            dQdY = 1  \n",
    "            if outeractivfunction == 1:\n",
    "                    dYdQ = Qvalues[a]*(1-Qvalues[a])\n",
    "            elif outeractivfunction == 2:\n",
    "                    dYdQ = (Qvalues[a]>0).astype(int)\n",
    "                    \n",
    "            H = np.matmul(W1,X) + bias_W1\n",
    "            if hiddenactivfunction == 1:\n",
    "                     H = np.round(1/(1+np.exp(-H)), 5)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                     H = (H>0).astype(int)*H\n",
    "            dYdW = H\n",
    "    \n",
    "            W2[a,:]=W2[a,:]+eta*dEdQ*dQdY*dYdW\n",
    "            bias_W2[a]=bias_W2[a]+eta*dEdQ*dQdY\n",
    "            \n",
    "            ## update W1 and B1 after W2 and B2 were updated\n",
    "            if hiddenactivfunction == 1:\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * H*(1-H).reshape(1, 200)).reshape(200,1)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * (H>0).astype(int)).reshape(200,1)\n",
    "            else:\n",
    "                dYdZ =  W2[a,:].reshape(200, 1)\n",
    "        \n",
    "            dZDW = X.reshape(1, 58)        \n",
    "            W1[:,:]=W1[:,:]+ eta*dEdQ*dQdY*dYdZ*dZDW \n",
    "            bias_W1=bias_W1+ eta*dEdQ*dQdY*dYdZ.reshape(200,) \n",
    "            \n",
    "            break\n",
    "        \n",
    "        \n",
    "        # IF THE EPISODE IS NOT OVER...\n",
    "        else:\n",
    "            \n",
    "            Qvalues1=ComputeQvalues(W1, W2, bias_W1, bias_W2, X_next, hiddenactivfunction , outeractivfunction)\n",
    "\n",
    "            a1=EpsilonGreedy_Policy(Qvalues1,epsilon_f, allowed_a_next)\n",
    "\n",
    "            # Compute the delta\n",
    "            dEdQ=R+gamma*Qvalues1[a1]- Qvalues[a]\n",
    "         \n",
    "                  \n",
    "            ## update W2 and B2   \n",
    "            dQdY = 1  \n",
    "            if outeractivfunction == 1:\n",
    "                    dYdQ = Qvalues[a]*(1-Qvalues[a])\n",
    "            elif outeractivfunction == 2:\n",
    "                    dYdQ = (Qvalues[a]>0).astype(int)\n",
    "                    \n",
    "          \n",
    "            H = np.matmul(W1,X) + bias_W1\n",
    "            if hiddenactivfunction == 1:\n",
    "                     H = np.round(1/(1+np.exp(-H)), 5)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                     H = (H>0).astype(int)*H\n",
    "            dYdW = H\n",
    "          \n",
    "            W2[a,:]=   W2[a,:]+   eta*dEdQ*dQdY*dYdW\n",
    "            bias_W2[a]=bias_W2[a]+eta*dEdQ*dQdY\n",
    "            \n",
    "            ## update W1 and B1 after W2 and B2 were updated\n",
    "            if hiddenactivfunction == 1:\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * H*(1-H).reshape(1, 200)).reshape(200,1)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * (H>0).astype(int)).reshape(200,1)\n",
    "            else:\n",
    "                dYdZ =  W2[a,:].reshape(200, 1)\n",
    "        \n",
    "            dZDW = X.reshape(1, 58)   \n",
    "            \n",
    "            W1[:,:]=W1[:,:]+ eta*dEdQ*dQdY*dYdZ*dZDW \n",
    "            bias_W1=bias_W1+ eta*dEdQ*dQdY*dYdZ.reshape(200,) \n",
    "           \n",
    "            \n",
    "        # NEXT STATE AND CO. BECOME ACTUAL STATE...     \n",
    "        S=np.copy(S_next)\n",
    "        X=np.copy(X_next)\n",
    "        a = np.copy(a1)\n",
    "\n",
    "        i += 1  # UPDATE COUNTER FOR NUMBER OF ACTIONS"
   ]
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    "In case of the following reward schema, SARSA runs into overflow issues when trying to compute the Qvalues:\n",
    "- Reward if episode is not over: 1\n",
    "- Reward for checkmate: 0\n",
    "- Reward for draw: 1\n",
    "\n",
    "Hence, the szenario was adapted for lower reward if the episode is not over."
   ]
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2OYE0Q9I8SfPWr19fStGCGmszbGnxZLuZWb5yBpIVwJic/dHAqh4ou1bSSID0e12hE0TEjRExOSImNzU1lVTxQvrVVrO5pbXb5zEz623KGUjmAuMljZNUC0wHZvdA2dnApen2pcAve7DOHXp2/SaaW1qJKKljZGbW61WX68QR0SppJnA3kAFuioiFki5Lj98g6WBgHjAQaJd0BTAxIjYWKpue+hrgDkkfAp4H3lmuNuTauC3pjWze3kb/urL92MzMDjhl/Y0YEXOAOXlpN+RsryEZtiqqbJr+InBWz9a0axedNIrHlm9gqwOJmdlufBtSkfrVJsFjy3bPk5iZ5eoykEiqkvSafVGZ/Vn/uuSdJJt955aZ2W66DCQR0Q58bR/UZb+W7ZFsdo/EzGw3xQ5t3SPpIkmFnu/oExrTeRHfAmxmtrtiZ43/GWgE2iRtJXlgMCJiYNlqtp9p9NCWmVlBRQWSiBhQ7ors7xo9tGVmVlDR97FKeitwerr7h4j4VXmqtH/q76EtM7OCipojkXQN8HHgyfTz8TStz+iXDm1t8VsSzcx2U2yP5DxgUnoHF5JuBh6lD70LpK46Q01GbHKPxMxsN6U8kDg4Z3tQD9fjgNCvtpotDiRmZrsptkfyJeBRSb8nuWPrdOCqstVqP9W/rppNvmvLzGw3XQYSSVVAO3AacApJIPl0uk5Wn9KvNuMlUszM8nQZSCKiXdLMiLiD4peB75Ua66o9R2JmlqfYOZJ7JV0paYykodlPWWu2H2qsy/iuLTOzPMXOkXww/f5YTloAh/dsdfZvjbXVvLhpS6WrYWa2Xyl2jmRWRPxkH9Rnv9ZYV+0n283M8hS7+u/HusrXFzTWZbzWlplZHs+RlKCxrtpLpJiZ5fEcSQkaa6tpaW2nta2d6oxfLmlmBsWv/juu3BU5EOx8J8n2NgY1OJCYmUEXQ1uSPpWz/c68Y1/q6uSSpkpaJGmJpD3W5VLiW+nxxyWdlKYfLWl+zmejpCvSY1dLWplz7Lwi29ptjbXZd5J4eMvMLKurP6un52znL4kytbOCkjLAd4BpwETgYkkT87JNA8annxnA9QARsSgiJkXEJOBkYAtwV06567LHI2JOF23oMdkeiZ9uNzPbpatAog62C+3nmwIsiYilEbEduB24IC/PBcCPIvEgMFjSyLw8ZwHPRsRzXVyv7LJvSfR6W2Zmu3QVSKKD7UL7+UYBy3P2V6RppeaZDtyWlzYzHQq7SdKQLurRY3a+JdFDW2ZmO3UVSE5I5yeagePT7ez+cV2ULdRjyQ8+neaRVAu8FfhpzvHrgSOAScBq4GsFLy7NkDRP0rz169d3UdXiNPotiWZme+g0kEREJiIGRsSAiKhOt7P7NV2cewUwJmd/NLCqxDzTgEciYm1OndZGRFv6oOT3SIbQCtX9xoiYHBGTm5qauqhqcXbdteVAYmaWVc57WOcC4yWNS3sW09lz9eDZwCXp3VunAa9ExOqc4xeTN6yVN4fyNmBBz1e9sF13bXmOxMwsq9gHEksWEa2SZgJ3AxngpohYKOmy9PgNwByS1/guIbkz6wPZ8pL6AecAH8k79bWSJpEMgS0rcLxsPLRlZransgUSgPTW3Dl5aTfkbAcdrOMVEVuAgwqkv7+Hq1m0hpq0R+Kl5M3MdvLj2SWoqhKNtRn3SMzMcjiQlKixrtoPJJqZ5XAgKVHyul0PbZmZZTmQlKhfbYYtHtoyM9uprJPtvdHCVRtZuGpjpathZrbfcI+kRE0D6ipdBTOz/YoDSYnOOKqJQwbVV7oaZmb7DQeSEg2sr2HjNs+RmJllOZCUaFBDDZtaWmlta690VczM9gsOJCVatWErAC9s2l7hmpiZ7R8cSEo0oD650e2VrTsqXBMzs/2DA0mJTjs8Wf6rpdUPJZqZgQNJybI9kmZPuJuZAQ4kJRvYkLzPa6OHtszMAAeSkrlHYma2OweSEu3skWxzj8TMDBxISta/NumR/OAvf69wTczM9g8OJCWqqhIAq1/ZVuGamJntHxxIzMysWxxIzMysW8oaSCRNlbRI0hJJswocl6Rvpccfl3RSzrFlkp6QNF/SvJz0oZLulbQ4/R5SzjZ0JiIqdWkzs/1G2QKJpAzwHWAaMBG4WNLEvGzTgPHpZwZwfd7xN0bEpIiYnJM2C7gvIsYD96X7+9SV5x4FQLPflGhmVtYeyRRgSUQsjYjtwO3ABXl5LgB+FIkHgcGSRnZx3guAm9Ptm4ELe7DORTlkcAMALzS37OtLm5ntd8oZSEYBy3P2V6RpxeYJ4B5JD0uakZNnRESsBki/h/dorYuQfUuiVwA2MytvIFGBtPxJhc7yvDYiTiIZ/vqYpNNLurg0Q9I8SfPWr19fStEuHdSYBJJHn3+5R89rZnYgKmcgWQGMydkfDawqNk9EZL/XAXeRDJUBrM0Of6Xf6wpdPCJujIjJETG5qampm03ZXXaZlLseXdmj5zUzOxCVM5DMBcZLGiepFpgOzM7LMxu4JL176zTglYhYLalR0gAASY3AucCCnDKXptuXAr8sYxsKGpXOkQzuV7OvL21mtt+pLteJI6JV0kzgbiAD3BQRCyVdlh6/AZgDnAcsAbYAH0iLjwDukpSt460R8dv02DXAHZI+BDwPvLNcbehI9un21jbf/mtmVrZAAhARc0iCRW7aDTnbAXysQLmlwAkdnPNF4Kyerenemfec50jMzMoaSHqzNx7dxLIXt1S6GmZmFeclUvbSIYMb/N52MzMcSPbasP51vLxlO61t7ZWuiplZRTmQ7KVlL24mAp5a3VzpqpiZVZQDyV4a0q8WgKdWb6xwTczMKsuBZC9ddNJoAGqqCz2cb2bWdziQ7KVDD+oHwHov3GhmfZwDyV4amC6T8qU5T1e4JmZmleVAspfSp+7NzPo8BxIzM+sWB5IesMlvSjSzPsyBpBvecXJy59Z9T62tcE3MzCrHgaQbZpx+OABVni8xsz7MgaQbRgyoB+CWh56rcE3MzCrHgaQbBjYktwA/uPSlCtfEzKxyHEi6QRIHNdaSqfLQlpn1XQ4k3TRuWCNt7UF7u9+WaGZ9kwNJNx03ehAAazZuq3BNzMwqw4Gkm84+ZgQAy17YXOGamJlVhgNJN40b1gjAzNserXBNzMwqo6yBRNJUSYskLZE0q8BxSfpWevxxSSel6WMk/V7SU5IWSvp4TpmrJa2UND/9nFfONnTl4IHJLcAvbd5eyWqYmVVMdblOLCkDfAc4B1gBzJU0OyKezMk2DRiffk4Frk+/W4FPRsQjkgYAD0u6N6fsdRHx1XLVvRRVvmPLzPq4cvZIpgBLImJpRGwHbgcuyMtzAfCjSDwIDJY0MiJWR8QjABHRDDwFjCpjXbsl2ytZ6wl3M+uDyhlIRgHLc/ZXsGcw6DKPpLHAicBDOckz06GwmyQN6bEa76XXjx8GwAPPvljhmpiZ7XvlDCSFxnzyH7boNI+k/sDPgSsiIvty9OuBI4BJwGrgawUvLs2QNE/SvPXr15dY9dL836lHA54nMbO+qZyBZAUwJmd/NLCq2DySakiCyC0RcWc2Q0SsjYi2iGgHvkcyhLaHiLgxIiZHxOSmpqZuN6YzTf3rAPi3Xz3ZRU4zs96nnIFkLjBe0jhJtcB0YHZentnAJendW6cBr0TEaiWvH/wB8FREfD23gKSRObtvAxaUrwnFyX1b4sZtOypYEzOzfa9sgSQiWoGZwN0kk+V3RMRCSZdJuizNNgdYCiwh6V18NE1/LfB+4MwCt/leK+kJSY8DbwQ+Ua42lOL845P49vTq5grXxMxs3yrb7b8AETGHJFjkpt2Qsx3AxwqU+wuF50+IiPf3cDV7xKypE/j146tZsm4TU8YNrXR1zMz2GT/Z3kNGD2kA4DN3PVHhmpiZ7VsOJD0kd57Ez5OYWV/iQNKD/v3CYwE49Uv3VbgmZmb7jgNJD5p+ypiuM5mZ9TIOJD2oJrPrx/nt+xZXsCZmZvuOA0kPO+nQwQB87d5nuGfhmspWxsxsH3Ag6WF3fvS1O7dn/PfDrHnFE+9m1rs5kJTB0/8+def2aV/2xLuZ9W4OJGVQX5PhynOP2rn/4FKvCmxmvZcDSZnMPHM8d370NQBMv/FBXnvN/bS1B69s3cFn7nqCFS9vqXANzcx6RlmXSOnrTjp016tSVm7YyhGf2bVazK0PPQ/AsmvO3+f1MjPrSe6RlNnfv3wex48e1OHxsbN+TVt7/mtazMwOHA4kZSaJ2TNfxzNfmLYz7Yqzx3Pk8P4794/4zBx+u2B1JapnZtZtShbg7d0mT54c8+bNq3Q1aGsPMlW71uS67t5n+GaBBxdHDW7gL59+I8te3EJ1lRgztN++rKaZGQCSHo6IyV3mcyCpvDP+4/c892Lnk++vOmQgH379OM6ZeDCNtRk2bm1lUL+afVRDM+uLHEhy7O+BJCIYd1UyEX94UyNL128uuuziL07bbWmWfM3bdvDZuxYwZmgD//dNE7pdVzPrOxxIcuzvgSRfa1s7tzz0PGcc1cQ3fvcMv5if/6r7XRprM0wYOZDLzxpPe3vQHsGQxlo+c+cT/NcHTuHVX75/t/yfmno07z31MAY1uDdjZp1zIMlxoAWSQjZu28GAuuqdPRcJuvNPt+gLU6mrzvDs+k18/d5n+Pq7TuDGPy5lXFMji9Y0M6x/HRMOHsCphx/U4Tl+OX8lH799/h7pv/jYa5k0ZjCrNmzlK799mg++dhzHjBxIbXXhntP21vYOj+Wa9fPHWbNxGz/8wJQu80bEbu+IKUVEsHFbKwPrq/f6HGa9gQNJjt4QSLK27Whj8dpNHDd6EC2tbRz9ud92WebMCcP5twtexTuuf4A1Jb506yOnH85H33Akqzdu5f6n1zFmSD/OP24kt/ztef7lFws6LHfYQf32mPf56jtP4B0nj2Z9cwunfPF3Bcs984VpBYPKrQ89v/PtkxdMOoRr33E8ddWZPfL9+vHVfOzWRwD4j3ccz9nHjKB/fTUZiaqqzoPC1G/8iafXNO+W9puPv55jRg7stFxvFxHMfmwVZ04YzoB692T7EgeSHL0pkOTL/uWd/X5hUwvzn9/A2RNH8NyLm6nJVHHI4Ibdylx15+Pc9rflPVaHUYMbOGHMIE46dAjPvbiF/37wuR47N8C0Yw/mNwv2XEn5tMOHMqihhrb24HdPrSvqXB9+3Tg+9+aJe6Sv27iNKR28kOxf3jyRD71uHAA/+MvfueXB51j6wmaOGtGfq9/yKt7z/YcYPqCOfzrzSN5z6mH8+MHnGNa/jjOObqKxNlNyr2bbjja+fu8zrG9u4a5HV+5Mf++ph/Kvb3lVUb23e59cy5RxQwsOYW5qaS2pXlfd+QS3/S15gPb2GacxZezQLoPy/iIi2LK9jca64p+9LtSbbW1rB6A6Zz6y2J70gWy/CCSSpgLfBDLA9yPimrzjSo+fB2wB/iEiHumsrKShwE+AscAy4F0R8XJn9ejNgWRvPbO2mT8vfoF/eM1YMlWipbWNNa9sY2B9DVt3tDFyUD3rN7Vw+rW/Z9uO9g7PU+jJ/OZtOzj+8/cQAXMufz3HjBzAI8+/zEXXP7BbvrefOIrTj2qiOiPOPmYEX5rzFD96oPMgNP//ncOkf7u3y/ZdfuaRfOv+JV3mAzhhzGAeW75h5/6ghhouP2s8DTWZnb2gnnDxlDH805nj+fPi9bxxwnCat7UyYmA9VYJ+tckvuhc3tXDyFwr31rKOHTWQw4f1Z/qUMdwxdzltActf2sL85RuY+cYjufmBZTRvawXgM+dNYPiAehava+b7f/47/WozvLxlB0cO78+M0w/nhj8+y9L1m6nNVPHjD5/KyYcNYfqNDzCooZZ/fctEqjPaY54N4EtvO443HN3EIYMbaG8PzvvWn3l6TTMNNRn+5c0TmX7KGH4ybzmvHz+Mvyx+gcOb+jNyUD2jBjfsFoS2bm+jtb19Z0/njnnLuWfhGt59yqH844/mMeP0w9M/UDZTnali6/ZWPnLGETtvMPnG757hG7/b/Rb6oY21fOLs8Zx2+EGcc92fALj2ouN5x8mj+fb9S7jud89w1bQJnHF0E1O/8eed5QbWV/Oz//Mazk3L/J83HMEnzj6K2uoqxs76NQDfvvhEJo0ZzGd/sYA/PbOey844gk+eexRPrtrIlT99jMXrNnHMyIH8+wWvYkdbMH5Ef4b1r9t5jYhgXXMLIwbWs765hUyVGNpYW8R/PYVt2d5KBFQp+X94cL+9P1chFQ8kkjLAM8A5wApgLnBxRDyZk+c84J9IAsmpwDcj4tTOykq6FngpIq6RNAsYEhGf7qwuDiQ9a+6yl1i8dhPvOfXQksrtaGvn6dXNDO1fy6i8XlLWK1t30LKjjQH1NTz30mZ+u2AN65tbuOWh57nm7ccxfUpyzadWb+R7f17KlpY2MlViwapXeMvxh3DsqEFMPfbgndfbsGUHP37wOd59yhjmLnuJH/51GY8+v6HDOv7vrDN3q9uSdc3M+vkTzHtu979V3nvqoRwyuIH/uHsRAKOHNLDi5a0l/TyKMXJQPV9827E8tbqZnz+yoqQ7+nra7/75DC78zv+yqaV1Z1qVoJSFGYYPqOPkw4YU7GGWYvJhQ/b4NymXUtuY76KTRvPzR1bsljZ8QB3rmlsAeNfk0bz6iIMYUFfD0QcPQILFazfxgR/OBeA9px5Kv5oMtdVVPLt+E6tf2cb5x43ky795usNrnjVhOMP613Hc6EFceOIo+pfQI8u1PwSSVwNXR8Sb0v2rACLiyzl5vgv8ISJuS/cXAW8g6W0ULJvNExGrJY1Myx/dWV0cSCxXS2sbL27azpbtbYwe0sBP5y2nqkqMG9bIa44YVrDMth1t1KXDGJ0NCbW1B4vXNTPh4GReZeWGrVQJajNVPLj0Ja7/4xIWrNzIqMENrNywteBcEsBPZpxW8EaHtvbg4ede5pHnX+YPi9bx4qbtnHzYEMYNa6SltZ3Gumpmz1/JP55+OOcfN5K7F67lsh8/zFtPOISaTBUTDh7AwIZqThgzmCt/+hh11RnGDWvk/ONH8tjyDTv/un/35DEsXP0KC1ZupGlAHXM/ezaQ/EXd0trOzx5ewed+sYDG2gybt7cBcMdHXk2mCh5c+tLOAHv0iAEsWtvMa444iL8++2JRAffggfUcOrQfCD76hiP40M3zOGbkABas3MjbTxrFb55Yw9YdbTvzX3vR8YwZ2o/a6ipOHDOYZ9Y1c+OflvKXxS+wrrmFn172alZt2MqnfvY4La3t3PC+k3hi5Ss8+vwG/vrsi/zog1MY1FDD9rZ2vnXfYv68+AXmfe5s7n96HV+/55md84o/+uAUfvHoSmY/torW9uArFx3HkH61fOrnj7Nhyw4APv/WV3HK2KFcctPfqFLSO8qfd8s3sL6ajdtaOzxem6lie1vHowJd+d4lkzln4oi9Krs/BJJ3AFMj4sPp/vuBUyNiZk6eXwHXRMRf0v37gE+TBJKCZSVtiIjBOed4OSJ2rY5YgAOJHQhe3ryd6owqOqG9N3e7vbJlR3JDQxHzJhHBwlUbqclUMX54/72ea2lrDx5bsYExQ/rRNKCu6wLdkP0dubd38L20eTvLXtzMiWMGs72tnbrqDK1t7by8ZQdDG2sR8OTqjdz75Fpqq6tYtKaZAI4a3p+ZZx5JS2s7f332BQbW17Byw1aOHz2YltY2nl7dzJtedTANtZmd/27bdrRRk6liR1s7v396Hc3bWrngxEMK3phSjGIDSTlX/y30U8+PWh3lKaZs5xeXZgAzAA49tLQhGLNKGNKNsfKesje/LEtZYUESx47qeBHTYmWqtNvq2uXU3VvAhzbW7pwHyf5Cr85U7RYAjx01qMOfS31NhjMnJD2K3N/o2V5vbh3ra5LzZ6oyTDtuZLfqXYpy3nKwAhiTsz8ayH+yrqM8nZVdmw5pkX4XvF0nIm6MiMkRMbmpqWmvG2FmZp0rZyCZC4yXNE5SLTAdmJ2XZzZwiRKnAa9ExOouys4GLk23LwV+WcY2mJlZF8o2tBURrZJmAneT3MJ7U0QslHRZevwGYA7JHVtLSG7//UBnZdNTXwPcIelDwPPAO8vVBjMz65ofSDQzs4KKnWzv3Y9lmplZ2TmQmJlZtziQmJlZtziQmJlZt/SJyXZJ64G9XZJ2GPBCD1bnQOA29w1uc9/QnTYfFhFdPojXJwJJd0iaV8xdC72J29w3uM19w75os4e2zMysWxxIzMysWxxIunZjpStQAW5z3+A29w1lb7PnSMzMrFvcIzEzs25xIDEzs25xIOmEpKmSFklakr4f/oAhaYyk30t6StJCSR9P04dKulfS4vR7SE6Zq9K2LpL0ppz0kyU9kR77ltK36Eiqk/STNP0hSWP3eUPzSMpIejR9+2avby+ApMGSfibp6fTf+9W9ud2SPpH+N71A0m2S6ntjeyXdJGmdpAU5afuknZIuTa+xWFL2tR0diwh/CnxIlq9/FjgcqAUeAyZWul4l1H8kcFK6PQB4BpgIXAvMStNnAV9JtyembawDxqVtz6TH/ga8muTNlb8BpqXpHwVuSLenAz/ZD9r9z8CtwK/S/V7d3rQuNwMfTrdrgcG9td3AKODvQEO6fwfwD72xvcDpwEnAgpy0srcTGAosTb+HpNtDOq1rpf8n2F8/6Q/+7pz9q4CrKl2vbrTnl8A5wCJgZJo2ElhUqH0k74J5dZrn6Zz0i4Hv5uZJt6tJnp5VBds4GrgPOJNdgaTXtjetx0CSX6zKS++V7SYJJMvTX3LVwK+Ac3txe8eyeyApeztz86THvgtc3Fk9PbTVsex/sFkr0rQDTtplPRF4CBgRyVsoSb+Hp9k6au+odDs/fbcyEdEKvAIcVJZGFOcbwKeA9py03txeSHrM64H/Sof0vi+pkV7a7ohYCXyV5KV2q0neqnoPvbS9BeyLdpb8u8+BpGMqkHbA3SstqT/wc+CKiNjYWdYCadFJemdl9jlJbwbWRcTDxRYpkHbAtDdHNcnwx/URcSKwmWTIoyMHdLvTOYELSIZvDgEaJb2vsyIF0g6Y9pagJ9tZcvsdSDq2AhiTsz8aWFWhuuwVSTUkQeSWiLgzTV4raWR6fCSwLk3vqL0r0u389N3KSKoGBgEv9XxLivJa4K2SlgG3A2dK+jG9t71ZK4AVEfFQuv8zksDSW9t9NvD3iFgfETuAO4HX0Hvbm29ftLPk330OJB2bC4yXNE5SLclk1OwK16lo6Z0ZPwCeioiv5xyaDWTvwriUZO4kmz49vZNjHDAe+FvafW6WdFp6zkvyymTP9Q7g/kgHVfe1iLgqIkZHxFiSf6v7I+J99NL2ZkXEGmC5pKPTpLOAJ+m97X4eOE1Sv7SeZwFP0Xvbm29ftPNu4FxJQ9Ie4LlpWscqMYF0oHyA80judnoW+Gyl61Ni3V9H0h19HJiffs4jGQO9D1icfg/NKfPZtK2LSO/sSNMnAwvSY//JrhUR6oGfAktI7gw5vNLtTuv1BnZNtveF9k4C5qX/1r8gudOm17Yb+DzwdFrX/ya5U6nXtRe4jWQeaAdJL+FD+6qdwAfT9CXAB7qqq5dIMTOzbvHQlpmZdYsDiZmZdYsDiZmZdYsDiZmZdYsDiZmZdYsDiVmRJLVJmp/z6XRFaEmXSbqkB667TNKw7p7HrFx8+69ZkSRtioj+FbjuMmByRLywr69tVgz3SMy6Ke0xfEXS39LPkWn61ZKuTLcvl/SkpMcl3Z6mDZX0izTtQUnHp+kHSbonXYTxu+SsfSTpfek15kv6rpL3r2Qk/VDJ+zmekPSJCvwYrA9zIDErXkPe0Na7c45tjIgpJE8Of6NA2VnAiRFxPHBZmvZ54NE07TPAj9L0fwX+EskijLOBQwEkHQO8G3htREwC2oD3kjzZPioijo2I44D/6qkGmxWjutIVMDuAbE1/gRdyW873dQWOPw7cIukXJMuYQLKMzUUAEXF/2hMZRPJCo7en6b+W9HKa/yzgZGBu+pK7BpJF+/4HOFzSt4FfA/fsZfvM9op7JGY9IzrYzjof+A5JIHg4XW21s+W6C51DwM0RMSn9HB0RV0fEy8AJwB+AjwHf38s2mO0VBxKznvHunO8Hcg9IqgLGRMTvSV68NRjoD/yJZGgKSW8AXojknTG56dNIFmGEZJG+d0ganh4bKumw9I6uqoj4OfAvJMvIm+0zHtoyK16DpPk5+7+NiOwtwHWSHiL54+zivHIZ4MfpsJWA6yJig6SrSd5s+DiwhV1Len8euE3SI8AfSZZOJyKelPQ54J40OO0g6YFsTc+T/cPwqh5rsVkRfPuvWTf59lzr6zy0ZWZm3eIeiZmZdYt7JGZm1i0OJGZm1i0OJGZm1i0OJGZm1i0OJGZm1i3/H8FIEel5FikdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the performance\n",
    "N_moves_save = pd.DataFrame(N_moves_save, columns = ['N_moves'])\n",
    "N_moves_save.to_csv('N_moves_SARSA.csv')\n",
    "N_moves_save['N_moves'] = N_moves_save['N_moves'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "plt.plot(N_moves_save['N_moves'])\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Number of Steps until \"Done\"')\n",
    "plt.title('Average Number of Steps until \"Done\" per Episode')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "R_save = pd.DataFrame(R_save, columns = ['R_save'])\n",
    "R_save.to_csv('R_save_SARSA.csv')\n",
    "R_save['R_save'] = R_save['R_save'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "\n",
    "plt.plot(R_save)\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Reward')\n",
    "plt.title('Average Rewards per Episode')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "Delta_save = pd.DataFrame(Delta_save, columns = ['Delta_save'])\n",
    "Delta_save.to_csv('Delta_save_SARSA.csv')\n",
    "Delta_save['Delta_save'] = Delta_save['Delta_save'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "\n",
    "plt.plot(Delta_save)\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Error')\n",
    "plt.title('Average Loss')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q-Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-28T14:06:32.254129Z",
     "start_time": "2022-03-28T14:06:32.226124Z"
    }
   },
   "outputs": [],
   "source": [
    "# set environment\n",
    "size_board = 4\n",
    "env=Chess_Env(size_board)\n",
    "\n",
    "# set seed\n",
    "np.random.seed(2022)\n",
    "\n",
    "# INITIALISE THE PARAMETERS OF YOUR NEURAL NETWORK\n",
    "S,X,allowed_a=env.Initialise_game()\n",
    "\n",
    "N_a=np.shape(allowed_a)[0]   # TOTAL NUMBER OF POSSIBLE ACTIONS\n",
    "N_in=np.shape(X)[0]          ## INPUT SIZE\n",
    "N_h=200                      ## NUMBER OF HIDDEN NODES\n",
    "\n",
    "## INITALISE YOUR NEURAL NETWORK... Here weights from input to hidden layer and from the hidden layer to output layer are initialized\n",
    "W1 = np.random.randn(N_h, N_in) * np.sqrt(1 / (N_in)) \n",
    "W2 = np.random.randn(N_a, N_h) * np.sqrt(1 / (N_h))\n",
    "\n",
    "bias_W1 = np.zeros((N_h,))\n",
    "bias_W2 = np.zeros((N_a,))\n",
    "\n",
    "# HYPERPARAMETERS SUGGESTED (FOR A GRID SIZE OF 4)\n",
    "epsilon_0 = 0.2     # STARTING VALUE OF EPSILON FOR THE EPSILON-GREEDY POLICY 0.2\n",
    "beta = 0.00005      # THE PARAMETER SETS HOW QUICKLY THE VALUE OF EPSILON IS DECAYING (SEE epsilon_f BELOW) 0.00005\n",
    "gamma = 0.85        # THE DISCOUNT FACTOR 0.85\n",
    "eta = 0.0035        # THE LEARNING RATE 0.0035\n",
    "\n",
    "# REWARD SCHEME DEFAULT\n",
    "# Reward if episode is not ended: 0\n",
    "# Reward if checkmate: 1\n",
    "# Reward if draw: 0\n",
    "\n",
    "N_episodes = 100000 # THE NUMBER OF GAMES TO BE PLAYED 100000\n",
    "\n",
    "hiddenactivfunction = 0\n",
    "outeractivfunction = 1\n",
    "\n",
    "# SAVING VARIABLES\n",
    "R_save = np.zeros([N_episodes, 1])\n",
    "N_moves_save = np.zeros([N_episodes, 1])\n",
    "Delta_save = np.zeros([N_episodes, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-28T14:22:56.346566Z",
     "start_time": "2022-03-28T14:06:32.260125Z"
    }
   },
   "outputs": [],
   "source": [
    "for n in range(N_episodes):\n",
    "    S,X,allowed_a=env.Initialise_game()\n",
    "    epsilon_f = epsilon_0 / (1 + beta * n)   ## DECAYING EPSILON\n",
    "    Done=0                                   ## SET DONE TO ZERO (BEGINNING OF THE EPISODE)\n",
    "    i = 1                                    ## COUNTER FOR NUMBER OF ACTIONS\n",
    "    \n",
    "    while (Done==0 and i<50):                           ## START THE EPISODE\n",
    "       \n",
    "        Qvalues = ComputeQvalues(W1, W2, bias_W1, bias_W2, X, hiddenactivfunction , outeractivfunction)\n",
    "        a=EpsilonGreedy_Policy(Qvalues,epsilon_f, allowed_a)\n",
    "        S_next, X_next,allowed_a_next,R,Done=env.OneStep(a)\n",
    "        \n",
    "        ## THE EPISODE HAS ENDED, UPDATE...BE CAREFUL, THIS IS THE LAST STEP OF THE EPISODE\n",
    "        if Done==1:\n",
    "            \n",
    "            R_save[n,]=np.copy(R)\n",
    "            N_moves_save[n,]=i\n",
    "            \n",
    "            dEdQ=R-Qvalues[a]\n",
    "           \n",
    "            Delta_save[n,] = 0.5*(dEdQ)*(dEdQ)\n",
    "            \n",
    "            ## update W2 and B2\n",
    "            dQdY = 1  \n",
    "            if outeractivfunction == 1:\n",
    "                    dYdQ = Qvalues[a]*(1-Qvalues[a])\n",
    "            elif outeractivfunction == 2:\n",
    "                    dYdQ = (Qvalues[a]>0).astype(int)\n",
    "                    \n",
    "            H = np.matmul(W1,X) + bias_W1\n",
    "            if hiddenactivfunction == 1:\n",
    "                     H = np.round(1/(1+np.exp(-H)), 5)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                     H = (H>0).astype(int)*H\n",
    "            dYdW = H\n",
    "    \n",
    "            W2[a,:]=W2[a,:]+eta*dEdQ*dQdY*dYdW\n",
    "            bias_W2[a]=bias_W2[a]+eta*dEdQ*dQdY\n",
    "            \n",
    "            ## update W1 and B1 after W2 and B2 were updated\n",
    "            if hiddenactivfunction == 1:\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * H*(1-H).reshape(1, 200)).reshape(200,1)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * (H>0).astype(int)).reshape(200,1)\n",
    "            else:\n",
    "                dYdZ =  W2[a,:].reshape(200, 1)\n",
    "        \n",
    "            dZDW = X.reshape(1, 58)        \n",
    "            W1[:,:]=W1[:,:]+ eta*dEdQ*dQdY*dYdZ*dZDW \n",
    "            bias_W1=bias_W1+ eta*dEdQ*dQdY*dYdZ.reshape(200,) \n",
    "            \n",
    "            break\n",
    "        \n",
    "        # IF THE EPISODE IS NOT OVER...\n",
    "        else:\n",
    "            \n",
    "            Qvalues1=ComputeQvalues(W1, W2, bias_W1, bias_W2, X_next, hiddenactivfunction , outeractivfunction)\n",
    "            a1=EpsilonGreedy_Policy(Qvalues1,0, allowed_a_next)\n",
    "\n",
    "            # Compute the delta\n",
    "            dEdQ=R+gamma*Qvalues1[a1]- Qvalues[a]\n",
    "                    \n",
    "            ## update W2 and B2   \n",
    "            dQdY = 1  \n",
    "            if outeractivfunction == 1:\n",
    "                    dYdQ = Qvalues[a]*(1-Qvalues[a])\n",
    "            elif outeractivfunction == 2:\n",
    "                    dYdQ = (Qvalues[a]>0).astype(int)\n",
    "                    \n",
    "            H = np.matmul(W1,X) + bias_W1\n",
    "            if hiddenactivfunction == 1:\n",
    "                     H = np.round(1/(1+np.exp(-H)), 5)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                     H = (H>0).astype(int)*H\n",
    "            dYdW = H\n",
    "          \n",
    "            W2[a,:]=   W2[a,:]+   eta*dEdQ*dQdY*dYdW\n",
    "            bias_W2[a]=bias_W2[a]+eta*dEdQ*dQdY\n",
    "            \n",
    "            ## update W1 and B1 after W2 and B2 were updated\n",
    "            if hiddenactivfunction == 1:\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * H*(1-H).reshape(1, 200)).reshape(200,1)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * (H>0).astype(int)).reshape(200,1)\n",
    "            else:\n",
    "                dYdZ =  W2[a,:].reshape(200, 1)\n",
    "        \n",
    "            dZDW = X.reshape(1, 58)   \n",
    "            \n",
    "            W1[:,:]=W1[:,:]+ eta*dEdQ*dQdY*dYdZ*dZDW \n",
    "            bias_W1=bias_W1+ eta*dEdQ*dQdY*dYdZ.reshape(200,) \n",
    "            \n",
    "        # NEXT STATE AND CO. BECOME ACTUAL STATE...     \n",
    "        S=np.copy(S_next)\n",
    "        X=np.copy(X_next)\n",
    "        allowed_a = np.copy(allowed_a_next)\n",
    "       \n",
    "\n",
    "        i += 1  # UPDATE COUNTER FOR NUMBER OF ACTIONS\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-28T14:22:58.886025Z",
     "start_time": "2022-03-28T14:22:56.346566Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "# Plot the performance\n",
    "N_moves_save = pd.DataFrame(N_moves_save, columns = ['N_moves'])\n",
    "N_moves_save.to_csv('N_moves_QLearning.csv')\n",
    "N_moves_save['N_moves'] = N_moves_save['N_moves'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "\n",
    "plt.plot(N_moves_save['N_moves'])\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Number of Steps until \"Done\"')\n",
    "plt.title('Average Number of Steps until \"Done\" per Episode')\n",
    "plt.show()\n",
    "\n",
    "R_save = pd.DataFrame(R_save, columns = ['R_save'])\n",
    "R_save.to_csv('R_save_QLearning.csv')\n",
    "R_save['R_save'] = R_save['R_save'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "plt.plot(R_save)\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Reward')\n",
    "plt.title('Average Rewards per Episode')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "Delta_save = pd.DataFrame(Delta_save, columns = ['Delta_save'])\n",
    "Delta_save.to_csv('Delta_save_QLearning.csv')\n",
    "Delta_save['Delta_save'] = Delta_save['Delta_save'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "plt.plot(Delta_save)\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Error')\n",
    "plt.title('Average Loss')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experience Replay"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T19:20:44.058417Z",
     "start_time": "2022-03-29T19:20:44.040844Z"
    }
   },
   "outputs": [],
   "source": [
    "# set environment\n",
    "size_board = 4\n",
    "env=Chess_Env(size_board)\n",
    "\n",
    "# set seed\n",
    "np.random.seed(2022)\n",
    "\n",
    "# INITIALISE THE PARAMETERS OF YOUR NEURAL NETWORK\n",
    "S,X,allowed_a=env.Initialise_game()\n",
    "\n",
    "N_a=np.shape(allowed_a)[0]   # TOTAL NUMBER OF POSSIBLE ACTIONS\n",
    "N_in=np.shape(X)[0]          ## INPUT SIZE\n",
    "N_h=200                      ## NUMBER OF HIDDEN NODES\n",
    "\n",
    "## INITALISE YOUR NEURAL NETWORK... Here weights from input to hidden layer and from the hidden layer to output layer are initialized\n",
    "W1 = np.random.randn(N_h, N_in) * np.sqrt(1 / (N_in)) \n",
    "W2 = np.random.randn(N_a, N_h) * np.sqrt(1 / (N_h))\n",
    "\n",
    "bias_W1 = np.zeros((N_h,))\n",
    "bias_W2 = np.zeros((N_a,))\n",
    "\n",
    "# HYPERPARAMETERS SUGGESTED (FOR A GRID SIZE OF 4)\n",
    "epsilon_0 = 0.2     # STARTING VALUE OF EPSILON FOR THE EPSILON-GREEDY POLICY 0.2\n",
    "beta = 0.00005      # THE PARAMETER SETS HOW QUICKLY THE VALUE OF EPSILON IS DECAYING (SEE epsilon_f BELOW) 0.00005\n",
    "gamma = 0.85        # THE DISCOUNT FACTOR 0.85\n",
    "eta = 0.0035        # THE LEARNING RATE 0.0035\n",
    "\n",
    "# REWARD SCHEME DEFAULT\n",
    "# Reward if episode is not ended: 0\n",
    "# Reward if checkmate: 1\n",
    "# Reward if draw: 0\n",
    "\n",
    "N_episodes = 100000 # THE NUMBER OF GAMES TO BE PLAYED 100000\n",
    "\n",
    "hiddenactivfunction = 0\n",
    "outeractivfunction = 1\n",
    "\n",
    "# SAVING VARIABLES\n",
    "R_save = np.zeros([N_episodes, 1])\n",
    "N_moves_save = np.zeros([N_episodes, 1])\n",
    "Delta_save = np.zeros([N_episodes, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T19:21:41.978494Z",
     "start_time": "2022-03-29T19:20:45.286734Z"
    }
   },
   "outputs": [],
   "source": [
    "for n in range(N_episodes):\n",
    "    S,X,allowed_a=env.Initialise_game()\n",
    "    epsilon_f = epsilon_0 / (1 + beta * n)   ## DECAYING EPSILON\n",
    "    Done=0                                   ## SET DONE TO ZERO (BEGINNING OF THE EPISODE)\n",
    "    i = 1  ## COUNTER FOR NUMBER OF ACTIONS\n",
    "    if (n%20)==0:  #reinitialize dictionary every 20 steps\n",
    "        k = 0\n",
    "        superd = {}\n",
    "        \n",
    "    superd[k] = {} #k corresponds to n and reinitialized each 20 steps\n",
    "    \n",
    "       \n",
    "    \n",
    "    \n",
    "    while (Done==0 and i<50):                           ## START THE EPISODE\n",
    "       # create tuple of state, actiona, reward, next state, Done, allowed a next and store it in the corresponding dictionary\n",
    "        Qvalues = ComputeQvalues(W1, W2, bias_W1, bias_W2, X, hiddenactivfunction , outeractivfunction)\n",
    "        a=EpsilonGreedy_Policy(Qvalues,epsilon_f, allowed_a)\n",
    "        S_next, X_next,allowed_a_next,R,Done=env.OneStep(a)\n",
    "        \n",
    "        dataToStore = (X,a,R,X_next,Done, allowed_a_next)\n",
    "        \n",
    "        superd[k][i] = dataToStore\n",
    "        superd[k][0] = i\n",
    "     \n",
    "        \n",
    "        if Done==1: # \n",
    "            #store data for plotting\n",
    "            R_save[n,]=np.copy(R)\n",
    "            N_moves_save[n,]=i\n",
    "            Delta_save[n,]=0.5*(r-Qvalues[a])*(r-Qvalues[a])\n",
    "            \n",
    "          \n",
    "            \n",
    "            # randomly pick an apisode number x and retrive the corresponding dictionary\n",
    "            x = random.randint(0,k) #if you also want to randomize across episodes, use this and x below instea dof k\n",
    "            d = superd[x]\n",
    "            nmbr = d[0] # check how many steps were in that episode\n",
    "            y = random.randint(1,nmbr )\n",
    "        \n",
    "            \n",
    "            x = d[y][0]\n",
    "            a = d[y][1]\n",
    "            r = d[y][2] \n",
    "            next_x = d[y][3]\n",
    "            done = d[y][4]\n",
    "            allowed = d[y][5]\n",
    "            Qvalues=ComputeQvalues(W1, W2, bias_W1, bias_W2, x, hiddenactivfunction , outeractivfunction)\n",
    "            \n",
    "            if done:\n",
    "                    dEdQ=r-Qvalues[a]\n",
    "                    \n",
    "            else:\n",
    "                    Qvalues1=ComputeQvalues(W1, W2, bias_W1, bias_W2, next_x, hiddenactivfunction , outeractivfunction)\n",
    "                    a1=EpsilonGreedy_Policy(Qvalues1,0, allowed) # make sure to go off policy\n",
    "                    dEdQ=R+gamma*Qvalues1[a1]- Qvalues[a]\n",
    "\n",
    "          \n",
    "                \n",
    "            ## update W2 and B2\n",
    "            dQdY = 1  \n",
    "            if outeractivfunction == 1:\n",
    "                        dYdQ = Qvalues[a]*(1-Qvalues[a])\n",
    "            elif outeractivfunction == 2:\n",
    "                        dYdQ = (Qvalues[a]>0).astype(int)\n",
    "\n",
    "            H = np.matmul(W1,X) + bias_W1\n",
    "            if hiddenactivfunction == 1:\n",
    "                         H = np.round(1/(1+np.exp(-H)), 5)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                         H = (H>0).astype(int)*H\n",
    "            dYdW = H\n",
    "\n",
    "            W2[a,:]=W2[a,:]+eta*dEdQ*dQdY*dYdW\n",
    "            bias_W2[a]=bias_W2[a]+eta*dEdQ*dQdY\n",
    "\n",
    "            ## update W1 and B1 after W2 and B2 were updated\n",
    "            if hiddenactivfunction == 1:\n",
    "                    dYdZ =  (W2[a,:].reshape(1, 200) * H*(1-H).reshape(1, 200)).reshape(200,1)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                    dYdZ =  (W2[a,:].reshape(1, 200) * (H>0).astype(int)).reshape(200,1)\n",
    "            else:\n",
    "                    dYdZ =  W2[a,:].reshape(200, 1)\n",
    "\n",
    "            dZDW = X.reshape(1, 58)        \n",
    "            W1[:,:]=W1[:,:]+ eta*dEdQ*dQdY*dYdZ*dZDW \n",
    "            bias_W1=bias_W1+ eta*dEdQ*dQdY*dYdZ.reshape(200,) \n",
    "               \n",
    "            break\n",
    "        \n",
    "        else:\n",
    "            # transition to the next step in the episode\n",
    "            S=np.copy(S_next)\n",
    "            X=np.copy(X_next)\n",
    "            allowed_a = np.copy(allowed_a_next)\n",
    "            \n",
    "            # same replay thing as in the case of done\n",
    "            x = random.randint(0,k) # if you want to randomize across episodes use x below instead of k \n",
    "            d = superd[x]\n",
    "            nmbr = d[0]\n",
    "        \n",
    "            y = random.randint(1,nmbr )\n",
    "        \n",
    "            \n",
    "            x = d[y][0]\n",
    "            a = d[y][1]\n",
    "            r = d[y][2] \n",
    "            next_x = d[y][3]\n",
    "            done = d[y][4]\n",
    "            allowed = d[y][5]\n",
    "            Qvalues=ComputeQvalues(W1, W2, bias_W1, bias_W2, x, hiddenactivfunction , outeractivfunction)\n",
    "            \n",
    "            if done:\n",
    "                    dEdQ=r-Qvalues[a]\n",
    "                    \n",
    "            else:\n",
    "                    Qvalues1=ComputeQvalues(W1, W2, bias_W1, bias_W2, next_x, hiddenactivfunction , outeractivfunction)\n",
    "                    a1=EpsilonGreedy_Policy(Qvalues1,0, allowed) # make sure to go off policy\n",
    "                    dEdQ=R+gamma*Qvalues1[a1]- Qvalues[a]\n",
    "\n",
    "        \n",
    "                \n",
    "            ## update W2 and B2\n",
    "            dQdY = 1  \n",
    "            if outeractivfunction == 1:\n",
    "                        dYdQ = Qvalues[a]*(1-Qvalues[a])\n",
    "            elif outeractivfunction == 2:\n",
    "                        dYdQ = (Qvalues[a]>0).astype(int)\n",
    "\n",
    "            H = np.matmul(W1,X) + bias_W1\n",
    "            if hiddenactivfunction == 1:\n",
    "                         H = np.round(1/(1+np.exp(-H)), 5)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                         H = (H>0).astype(int)*H\n",
    "            dYdW = H\n",
    "\n",
    "            W2[a,:]=W2[a,:]+eta*dEdQ*dQdY*dYdW\n",
    "            bias_W2[a]=bias_W2[a]+eta*dEdQ*dQdY\n",
    "\n",
    "            ## update W1 and B1 after W2 and B2 were updated\n",
    "            if hiddenactivfunction == 1:\n",
    "                    dYdZ =  (W2[a,:].reshape(1, 200) * H*(1-H).reshape(1, 200)).reshape(200,1)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                    dYdZ =  (W2[a,:].reshape(1, 200) * (H>0).astype(int)).reshape(200,1)\n",
    "            else:\n",
    "                    dYdZ =  W2[a,:].reshape(200, 1)\n",
    "\n",
    "            dZDW = X.reshape(1, 58)        \n",
    "            W1[:,:]=W1[:,:]+ eta*dEdQ*dQdY*dYdZ*dZDW \n",
    "            bias_W1=bias_W1+ eta*dEdQ*dQdY*dYdZ.reshape(200,) \n",
    "            \n",
    "            \n",
    "            \n",
    "            \n",
    "            \n",
    "       \n",
    "            i = i+1 # this takes care of step in episode\n",
    "    k +=1    # this is for keeping track of experiences \n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T19:21:42.562588Z",
     "start_time": "2022-03-29T19:21:41.981427Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "# Plot the performance\n",
    "N_moves_save = pd.DataFrame(N_moves_save, columns = ['N_moves'])\n",
    "N_moves_save.to_csv('N_moves_ER.csv')\n",
    "N_moves_save['N_moves'] = N_moves_save['N_moves'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "\n",
    "plt.plot(N_moves_save['N_moves'])\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Number of Steps until \"Done\"')\n",
    "plt.title('Average Number of Steps until \"Done\" per Episode')\n",
    "plt.show()\n",
    "\n",
    "R_save = pd.DataFrame(R_save, columns = ['R_save'])\n",
    "R_save.to_csv('R_save_ER.csv')\n",
    "R_save['R_save'] = R_save['R_save'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "plt.plot(R_save)\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Reward')\n",
    "plt.title('Average Rewards per Episode')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "Delta_save = pd.DataFrame(Delta_save, columns = ['Delta_save'])\n",
    "Delta_save.to_csv('Delta_save_ER.csv')\n",
    "Delta_save['Delta_save'] = Delta_save['Delta_save'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "plt.plot(Delta_save)\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Error')\n",
    "plt.title('Average Loss')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adagrad SARSA\n",
    "\n",
    "First we will use a reasonable weight initialization method. Then, in the second run we will use a naive weight initialization method, which would lead to exploding gradients.\n",
    "\n",
    "With the reversed reward scheme (0 for checkmate, 0 steps, 1 draw) there is an overflow for naive weight initialization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-28T15:30:59.756232Z",
     "start_time": "2022-03-28T15:30:59.665231Z"
    }
   },
   "outputs": [],
   "source": [
    "# set environment\n",
    "size_board = 4\n",
    "env=Chess_Env(size_board)\n",
    "\n",
    "# set seed\n",
    "np.random.seed(2022)\n",
    "\n",
    "# INITIALISE THE PARAMETERS OF YOUR NEURAL NETWORK\n",
    "S,X,allowed_a=env.Initialise_game()\n",
    "\n",
    "N_a=np.shape(allowed_a)[0]   # TOTAL NUMBER OF POSSIBLE ACTIONS\n",
    "N_in=np.shape(X)[0]          ## INPUT SIZE\n",
    "N_h=200                      ## NUMBER OF HIDDEN NODES\n",
    "\n",
    "## INITALISE YOUR NEURAL NETWORK... Here weights from input to hidden layer and from the hidden layer to output layer are initialized\n",
    "W1 = np.random.randn(N_h, N_in) * np.sqrt(1 / (N_in)) \n",
    "W2 = np.random.randn(N_a, N_h) * np.sqrt(1 / (N_h))\n",
    "\n",
    "bias_W1 = np.zeros((N_h,))\n",
    "bias_W2 = np.zeros((N_a,))\n",
    "\n",
    "# HYPERPARAMETERS SUGGESTED (FOR A GRID SIZE OF 4)\n",
    "epsilon_0 = 0.2     # STARTING VALUE OF EPSILON FOR THE EPSILON-GREEDY POLICY 0.2\n",
    "beta = 0.00005      # THE PARAMETER SETS HOW QUICKLY THE VALUE OF EPSILON IS DECAYING (SEE epsilon_f BELOW) 0.00005\n",
    "gamma = 0.85        # THE DISCOUNT FACTOR 0.85\n",
    "eta = 0.0035        # THE LEARNING RATE 0.0035\n",
    "eps = 0.000001      # EPSILON FOR NUMERICAL STABILITY\n",
    "\n",
    "# REWARD SCHEME DEFAULT\n",
    "# Reward if episode is not ended: 0\n",
    "# Reward if checkmate: 1\n",
    "# Reward if draw: 0\n",
    "\n",
    "N_episodes = 100000 # THE NUMBER OF GAMES TO BE PLAYED 100000\n",
    "\n",
    "hiddenactivfunction = 0\n",
    "outeractivfunction = 1\n",
    "\n",
    "# SAVING VARIABLES\n",
    "R_save = np.zeros([N_episodes, 1])\n",
    "N_moves_save = np.zeros([N_episodes, 1])\n",
    "Delta_save = np.zeros([N_episodes, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-28T15:50:43.647765Z",
     "start_time": "2022-03-28T15:30:59.769233Z"
    }
   },
   "outputs": [],
   "source": [
    "for n in range(N_episodes):\n",
    "    \n",
    "    S,X,allowed_a=env.Initialise_game()\n",
    "   \n",
    "    epsilon_f = epsilon_0 / (1 + beta * n)   ## DECAYING EPSILON\n",
    "    Done=0                                   ## SET DONE TO ZERO (BEGINNING OF THE EPISODE)\n",
    "    i =  1                                        ## COUNTER FOR NUMBER OF ACTIONS\n",
    "    if (n%10 ==0):\n",
    "\n",
    "        diagonal2 = np.zeros((N_h+1,N_a))\n",
    "        diagonal1 = np.zeros((N_in*N_h + N_h, ))\n",
    "                               \n",
    "    Qvalues = ComputeQvalues(W1, W2, bias_W1, bias_W2, X, hiddenactivfunction , outeractivfunction)\n",
    "\n",
    "    a=EpsilonGreedy_Policy(Qvalues,epsilon_f, allowed_a)\n",
    "    \n",
    "    while (Done==0 and i<50):                           ## START THE EPISODE\n",
    "       \n",
    "        Qvalues = ComputeQvalues(W1, W2, bias_W1, bias_W2, X, hiddenactivfunction , outeractivfunction)\n",
    "       \n",
    "        S_next, X_next,allowed_a_next,R,Done=env.OneStep(a)\n",
    "       \n",
    "        ## THE EPISODE HAS ENDED, UPDATE...BE CAREFUL, THIS IS THE LAST STEP OF THE EPISODE\n",
    "        if Done==1:\n",
    "            \n",
    "            R_save[n,]=np.copy(R)\n",
    "            N_moves_save[n,]=i\n",
    "            \n",
    "            dEdQ=R-Qvalues[a]\n",
    "           \n",
    "            Delta_save[n,] = 0.5*(dEdQ)*(dEdQ)\n",
    "            \n",
    "            ## update W2 and B2   \n",
    "            dQdY = 1  \n",
    "            if outeractivfunction == 1:\n",
    "                    dYdQ = Qvalues[a]*(1-Qvalues[a])\n",
    "            elif outeractivfunction == 2:\n",
    "                    dYdQ = (Qvalues[a]>0).astype(int)\n",
    "                    \n",
    "            H = np.matmul(W1,X) + bias_W1\n",
    "            if hiddenactivfunction == 1:\n",
    "                     H = np.round(1/(1+np.exp(-H)), 5)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                     H = (H>0).astype(int)*H\n",
    "            dYdW = H\n",
    "    \n",
    "            gradient2 =dEdQ*dQdY*dYdW\n",
    "            grandientBias2 = dEdQ*dQdY\n",
    "            G = np.round(np.append(gradient2, grandientBias2), 4)\n",
    "            diagonal2[:,a] = diagonal2[:,a] + G**2\n",
    "            diagonal_to_use2 = (eps + diagonal2[:,a])**(-1/2)\n",
    "    \n",
    "            W2[a,:]=W2[a,:]+eta*diagonal_to_use2[0:-1]*gradient2\n",
    "            bias_W2[a]=bias_W2[a]+eta*diagonal_to_use2[-1]*grandientBias2\n",
    "            \n",
    "            ## update W1 and B1 after W2 and B2 were updated\n",
    "            if hiddenactivfunction == 1:\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * H*(1-H).reshape(1, 200)).reshape(200,1)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * (H>0).astype(int)).reshape(200,1)\n",
    "            else:\n",
    "                dYdZ =  W2[a,:].reshape(200, 1)\n",
    "        \n",
    "            dZDW = X.reshape(1, 58)        \n",
    "            \n",
    "            gradient1 =dEdQ*dQdY*dYdZ*dZDW\n",
    "            grandientBias1 = dEdQ*dQdY*dYdZ.reshape(200,1) \n",
    "            G = np.ravel(np.concatenate((gradient1, grandientBias1), axis=1))\n",
    "\n",
    "            diagonal1 = diagonal1 + G**2\n",
    "            diagonal_to_use1 = ((eps+diagonal1).reshape(200, -1))**(-1/2)\n",
    "            \n",
    "            W1[:,:]=W1[:,:]+ eta*diagonal_to_use1[:, 0:-1]*gradient1\n",
    "            bias_W1=bias_W1+ eta*diagonal_to_use1[:, -1]*grandientBias1.reshape(200,)\n",
    "            \n",
    "            break\n",
    "        \n",
    "        \n",
    "        # IF THE EPISODE IS NOT OVER...\n",
    "        else:\n",
    "            \n",
    "            Qvalues1=ComputeQvalues(W1, W2, bias_W1, bias_W2, X_next, hiddenactivfunction , outeractivfunction)\n",
    "\n",
    "            a1=EpsilonGreedy_Policy(Qvalues1,epsilon_f, allowed_a_next)\n",
    "\n",
    "            # Compute the delta\n",
    "            dEdQ=R+gamma*Qvalues1[a1] - Qvalues[a]\n",
    "         \n",
    "                  \n",
    "            ## update W2 and B2   \n",
    "            dQdY = 1  \n",
    "            if outeractivfunction == 1:\n",
    "                    dYdQ = Qvalues[a]*(1-Qvalues[a])\n",
    "            elif outeractivfunction == 2:\n",
    "                    dYdQ = (Qvalues[a]>0).astype(int)\n",
    "                    \n",
    "            H = np.matmul(W1,X) + bias_W1\n",
    "            if hiddenactivfunction == 1:\n",
    "                     H = np.round(1/(1+np.exp(-H)), 5)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                     H = (H>0).astype(int)*H\n",
    "            dYdW = H\n",
    "          \n",
    "            gradient2 =dEdQ*dQdY*dYdW\n",
    "            grandientBias2 = dEdQ*dQdY\n",
    "            G = np.round(np.append(gradient2, grandientBias2), 4)\n",
    "            \n",
    "            diagonal2[:,a] = diagonal2[:,a] + G**2\n",
    "            diagonal_to_use2 = (eps + diagonal2[:,a])**(-1/2)\n",
    "    \n",
    "            W2[a,:]=W2[a,:]+eta*diagonal_to_use2[0:-1]*gradient2\n",
    "            bias_W2[a]=bias_W2[a]+eta*diagonal_to_use2[-1]*grandientBias2\n",
    "            \n",
    "            ## update W1 and B1 after W2 and B2 were updated\n",
    "            if hiddenactivfunction == 1:\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * H*(1-H).reshape(1, 200)).reshape(200,1)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * (H>0).astype(int)).reshape(200,1)\n",
    "            else:\n",
    "                dYdZ =  W2[a,:].reshape(200, 1)\n",
    "        \n",
    "            dZDW = X.reshape(1, 58)    \n",
    "            \n",
    "            gradient1 =dEdQ*dQdY*dYdZ*dZDW\n",
    "            grandientBias1 = dEdQ*dQdY*dYdZ.reshape(200,1) \n",
    "            G = np.ravel(np.concatenate((gradient1, grandientBias1), axis=1))\n",
    "\n",
    "            diagonal1 = diagonal1 + G**2\n",
    "            diagonal_to_use1 = ((eps+diagonal1).reshape(200, -1))**(-1/2)\n",
    "                    \n",
    "            W1[:,:]=W1[:,:]+ eta*diagonal_to_use1[:, 0:-1]*gradient1\n",
    "            bias_W1=bias_W1+ eta*diagonal_to_use1[:, -1]*grandientBias1.reshape(200,)\n",
    "           \n",
    "            \n",
    "        # NEXT STATE AND CO. BECOME ACTUAL STATE...     \n",
    "        S=np.copy(S_next)\n",
    "        X=np.copy(X_next)\n",
    "        a = np.copy(a1)\n",
    "\n",
    "        i += 1  # UPDATE COUNTER FOR NUMBER OF ACTIONS   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-28T15:50:47.022772Z",
     "start_time": "2022-03-28T15:50:43.651769Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "# Plot the performance\n",
    "N_moves_save = pd.DataFrame(N_moves_save, columns = ['N_moves'])\n",
    "N_moves_save.to_csv('N_moves_Adagrad_good.csv')\n",
    "N_moves_save['N_moves'] = N_moves_save['N_moves'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "\n",
    "plt.plot(N_moves_save['N_moves'])\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Number of Steps until \"Done\"')\n",
    "plt.title('Average Number of Steps until \"Done\" per Episode')\n",
    "plt.show()\n",
    "\n",
    "R_save = pd.DataFrame(R_save, columns = ['R_save'])\n",
    "R_save.to_csv('R_save_Adagrad_good.csv')\n",
    "R_save['R_save'] = R_save['R_save'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "plt.plot(R_save)\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Reward')\n",
    "plt.title('Average Rewards per Episode')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "Delta_save = pd.DataFrame(Delta_save, columns = ['Delta_save'])\n",
    "Delta_save.to_csv('Delta_save_Adagrad_good.csv')\n",
    "Delta_save['Delta_save'] = Delta_save['Delta_save'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "plt.plot(Delta_save)\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Error')\n",
    "plt.title('Average Loss')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-28T15:50:47.060956Z",
     "start_time": "2022-03-28T15:50:47.028768Z"
    }
   },
   "outputs": [],
   "source": [
    "# set environment\n",
    "size_board = 4\n",
    "env=Chess_Env(size_board)\n",
    "\n",
    "# set seed\n",
    "np.random.seed(2022)\n",
    "\n",
    "# INITIALISE THE PARAMETERS OF YOUR NEURAL NETWORK\n",
    "S,X,allowed_a=env.Initialise_game()\n",
    "\n",
    "N_a=np.shape(allowed_a)[0]   # TOTAL NUMBER OF POSSIBLE ACTIONS\n",
    "N_in=np.shape(X)[0]          ## INPUT SIZE\n",
    "N_h=200                      ## NUMBER OF HIDDEN NODES\n",
    "\n",
    "## INITALISE YOUR NEURAL NETWORK... Here weights from input to hidden layer and from the hidden layer to output layer are initialized\n",
    "W1 = np.random.randn(N_h,N_in)/1000\n",
    "W1 = np.divide(W1,np.matlib.repmat(np.sum(W1,1)[:,None],1,N_in))\n",
    "W2 = W2=np.random.randn(N_a,N_h)/1000\n",
    "W2 = np.divide(W2,np.matlib.repmat(np.sum(W2,1)[:,None],1,N_h))\n",
    "\n",
    "bias_W1 = np.zeros((N_h,))\n",
    "bias_W2 = np.zeros((N_a,))\n",
    "\n",
    "# HYPERPARAMETERS SUGGESTED (FOR A GRID SIZE OF 4)\n",
    "epsilon_0 = 0.2     # STARTING VALUE OF EPSILON FOR THE EPSILON-GREEDY POLICY 0.2\n",
    "beta = 0.00005      # THE PARAMETER SETS HOW QUICKLY THE VALUE OF EPSILON IS DECAYING (SEE epsilon_f BELOW) 0.00005\n",
    "gamma = 0.85        # THE DISCOUNT FACTOR 0.85\n",
    "eta = 0.0035        # THE LEARNING RATE 0.0035\n",
    "eps = 0.000001      # EPSILON FOR NUMERICAL STABILITY\n",
    "\n",
    "# REWARD SCHEME DEFAULT\n",
    "# Reward if episode is not ended: 0\n",
    "# Reward if checkmate: 1\n",
    "# Reward if draw: 0\n",
    "\n",
    "N_episodes = 100000 # THE NUMBER OF GAMES TO BE PLAYED 100000\n",
    "\n",
    "hiddenactivfunction = 0\n",
    "outeractivfunction = 1\n",
    "\n",
    "# SAVING VARIABLES\n",
    "R_save = np.zeros([N_episodes, 1])\n",
    "N_moves_save = np.zeros([N_episodes, 1])\n",
    "Delta_save = np.zeros([N_episodes, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-28T16:06:52.630254Z",
     "start_time": "2022-03-28T15:50:47.064956Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\adria\\AppData\\Local\\Temp/ipykernel_53532/4067716023.py:41: RuntimeWarning: overflow encountered in exp\n",
      "  Qvalues = np.round(1/(1+np.exp(- Qvalues)), 5)\n"
     ]
    }
   ],
   "source": [
    "for n in range(N_episodes):\n",
    "    \n",
    "    S,X,allowed_a=env.Initialise_game()\n",
    "   \n",
    "    epsilon_f = epsilon_0 / (1 + beta * n)   ## DECAYING EPSILON\n",
    "    Done=0                                   ## SET DONE TO ZERO (BEGINNING OF THE EPISODE)\n",
    "    i =  1                                        ## COUNTER FOR NUMBER OF ACTIONS\n",
    "    if (n%10 ==0):\n",
    "\n",
    "        diagonal2 = np.zeros((N_h+1,N_a))\n",
    "        diagonal1 = np.zeros((N_in*N_h + N_h, ))\n",
    "                               \n",
    "    Qvalues = ComputeQvalues(W1, W2, bias_W1, bias_W2, X, hiddenactivfunction , outeractivfunction)\n",
    "\n",
    "    a=EpsilonGreedy_Policy(Qvalues,epsilon_f, allowed_a)\n",
    "    \n",
    "    while (Done==0 and i<50):                           ## START THE EPISODE\n",
    "       \n",
    "        Qvalues = ComputeQvalues(W1, W2, bias_W1, bias_W2, X, hiddenactivfunction , outeractivfunction)\n",
    "       \n",
    "        S_next, X_next,allowed_a_next,R,Done=env.OneStep(a)\n",
    "       \n",
    "        ## THE EPISODE HAS ENDED, UPDATE...BE CAREFUL, THIS IS THE LAST STEP OF THE EPISODE\n",
    "        if Done==1:\n",
    "            \n",
    "            R_save[n,]=np.copy(R)\n",
    "            N_moves_save[n,]=i\n",
    "            \n",
    "            dEdQ=R-Qvalues[a]\n",
    "           \n",
    "            Delta_save[n,] = 0.5*(dEdQ)*(dEdQ)\n",
    "            \n",
    "            ## update W2 and B2   \n",
    "            dQdY = 1  \n",
    "            if outeractivfunction == 1:\n",
    "                    dYdQ = Qvalues[a]*(1-Qvalues[a])\n",
    "            elif outeractivfunction == 2:\n",
    "                    dYdQ = (Qvalues[a]>0).astype(int)\n",
    "                    \n",
    "            H = np.matmul(W1,X) + bias_W1\n",
    "            if hiddenactivfunction == 1:\n",
    "                     H = np.round(1/(1+np.exp(-H)), 5)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                     H = (H>0).astype(int)*H\n",
    "            dYdW = H\n",
    "    \n",
    "            gradient2 =dEdQ*dQdY*dYdW\n",
    "            grandientBias2 = dEdQ*dQdY\n",
    "            G = np.round(np.append(gradient2, grandientBias2), 4)\n",
    "            diagonal2[:,a] = diagonal2[:,a] + G**2\n",
    "            diagonal_to_use2 = (eps + diagonal2[:,a])**(-1/2)\n",
    "    \n",
    "            W2[a,:]=W2[a,:]+eta*diagonal_to_use2[0:-1]*gradient2\n",
    "            bias_W2[a]=bias_W2[a]+eta*diagonal_to_use2[-1]*grandientBias2\n",
    "            \n",
    "            ## update W1 and B1 after W2 and B2 were updated\n",
    "            if hiddenactivfunction == 1:\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * H*(1-H).reshape(1, 200)).reshape(200,1)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * (H>0).astype(int)).reshape(200,1)\n",
    "            else:\n",
    "                dYdZ =  W2[a,:].reshape(200, 1)\n",
    "        \n",
    "            dZDW = X.reshape(1, 58)        \n",
    "            \n",
    "            gradient1 =dEdQ*dQdY*dYdZ*dZDW\n",
    "            grandientBias1 = dEdQ*dQdY*dYdZ.reshape(200,1) \n",
    "            G = np.ravel(np.concatenate((gradient1, grandientBias1), axis=1))\n",
    "\n",
    "            diagonal1 = diagonal1 + G**2\n",
    "            diagonal_to_use1 = ((eps+diagonal1).reshape(200, -1))**(-1/2)\n",
    "            \n",
    "            W1[:,:]=W1[:,:]+ eta*diagonal_to_use1[:, 0:-1]*gradient1\n",
    "            bias_W1=bias_W1+ eta*diagonal_to_use1[:, -1]*grandientBias1.reshape(200,)\n",
    "            \n",
    "            break\n",
    "        \n",
    "        \n",
    "        # IF THE EPISODE IS NOT OVER...\n",
    "        else:\n",
    "            \n",
    "            Qvalues1=ComputeQvalues(W1, W2, bias_W1, bias_W2, X_next, hiddenactivfunction , outeractivfunction)\n",
    "\n",
    "            a1=EpsilonGreedy_Policy(Qvalues1,epsilon_f, allowed_a_next)\n",
    "\n",
    "            # Compute the delta\n",
    "            dEdQ=R+gamma*Qvalues1[a1] - Qvalues[a]\n",
    "         \n",
    "                  \n",
    "            ## update W2 and B2   \n",
    "            dQdY = 1  \n",
    "            if outeractivfunction == 1:\n",
    "                    dYdQ = Qvalues[a]*(1-Qvalues[a])\n",
    "            elif outeractivfunction == 2:\n",
    "                    dYdQ = (Qvalues[a]>0).astype(int)\n",
    "                    \n",
    "            H = np.matmul(W1,X) + bias_W1\n",
    "            if hiddenactivfunction == 1:\n",
    "                     H = np.round(1/(1+np.exp(-H)), 5)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                     H = (H>0).astype(int)*H\n",
    "            dYdW = H\n",
    "          \n",
    "            gradient2 =dEdQ*dQdY*dYdW\n",
    "            grandientBias2 = dEdQ*dQdY\n",
    "            G = np.round(np.append(gradient2, grandientBias2), 4)\n",
    "            \n",
    "            diagonal2[:,a] = diagonal2[:,a] + G**2\n",
    "            diagonal_to_use2 = (eps + diagonal2[:,a])**(-1/2)\n",
    "    \n",
    "            W2[a,:]=W2[a,:]+eta*diagonal_to_use2[0:-1]*gradient2\n",
    "            bias_W2[a]=bias_W2[a]+eta*diagonal_to_use2[-1]*grandientBias2\n",
    "            \n",
    "            ## update W1 and B1 after W2 and B2 were updated\n",
    "            if hiddenactivfunction == 1:\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * H*(1-H).reshape(1, 200)).reshape(200,1)\n",
    "            elif(hiddenactivfunction == 2):\n",
    "                dYdZ =  (W2[a,:].reshape(1, 200) * (H>0).astype(int)).reshape(200,1)\n",
    "            else:\n",
    "                dYdZ =  W2[a,:].reshape(200, 1)\n",
    "        \n",
    "            dZDW = X.reshape(1, 58)    \n",
    "            \n",
    "            gradient1 =dEdQ*dQdY*dYdZ*dZDW\n",
    "            grandientBias1 = dEdQ*dQdY*dYdZ.reshape(200,1) \n",
    "            G = np.ravel(np.concatenate((gradient1, grandientBias1), axis=1))\n",
    "\n",
    "            diagonal1 = diagonal1 + G**2\n",
    "            diagonal_to_use1 = ((eps+diagonal1).reshape(200, -1))**(-1/2)\n",
    "                    \n",
    "            W1[:,:]=W1[:,:]+ eta*diagonal_to_use1[:, 0:-1]*gradient1\n",
    "            bias_W1=bias_W1+ eta*diagonal_to_use1[:, -1]*grandientBias1.reshape(200,)\n",
    "           \n",
    "            \n",
    "        # NEXT STATE AND CO. BECOME ACTUAL STATE...     \n",
    "        S=np.copy(S_next)\n",
    "        X=np.copy(X_next)\n",
    "        a = np.copy(a1)\n",
    "\n",
    "        i += 1  # UPDATE COUNTER FOR NUMBER OF ACTIONS   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-28T16:06:55.146645Z",
     "start_time": "2022-03-28T16:06:52.634258Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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z1dIt2wFw/tDt8xmOc841WZmuGIYAQ4Ef5yaU7IrVMRQXBZcKd705M5/hOOdck5X2igG4n+CKYSlwfE6iyaJp88sB+Da889k551xqaRODmQ1tjBVIKgLGAXPN7KikaQL+ChwJrAFON7NPGmO9yWKd6K0L+0jqWJIpJzrnXOGqs/JZUltJV0j6V/i+v6Sj6vpcnAuAz9JMOwLoH76GA/+ox3LrZWBpFwB27NGBHbt34Ds9O2ZrVc45t1mL0irpPqACGBS+nwNcH2XhknoDw4B/p5nlWOBBC3wIdJLUM8qy6yvWBcaXi1fTuV1xTad6zjnnEkVJDNuZ2S1AJYCZrQWiNva8A/gDkO42417A7Lj3c8JxCSQNlzRO0rjFixdHXHWi4/fuDcCefTpRUlzkdz4751waURLDekltCCqikbQdwRVERmFx0yIzG59pthTjap3Km9k9ZjbQzAZ269YtQsi1HbBDN8puHkafLm0paVlERZU/j8E551KJUgN7FfAK0EfSI8Bg4PQInxsMHCPpSKAE6CjpYTM7OW6eOUCfuPe9gXlRAt8UJcUt/IrBOefSqPOKwcxeB44jSAaPAQPN7O0In7vUzHqbWSlwEvBmUlIAeAE4VYH9gBVmlvX+sIOiJL9icM65VKK22SwBloXz7ywJM3unISuUdA6AmY0EXiJoqjqToLnqGQ1ZZn21atmC8nWVuViVc85tdupMDJL+BJwITGVjJbIBkRNDeIXxdjg8Mm68AedHjraRPPjB10BwN3SRd5rknHMJolwx/BDY0cya3ZNtKqs3UNSiKN9hOOdckxKlVdJXQHG2A8ml3x+2IxAkBuecc4miXDGsASZKGk1cM1Uz+03Wosqy9q2Dza6s9pvcnHMuWZTE8EL4ajaKi4ILpfVVfsXgnHPJ6kwMZvaApFbADuGoGWa2WTfpadMqSAzeZNU552qL0ippCPAAUEZwp3IfSac1tLlqU9CmOKhwXrPeE4NzziWLUvl8K3ComR1oZgcAhwG3Zzes7Cr7dg0A970/K8+ROOdc0xMlMRSb2YzYGzP7nM28lVLsaW5fLFqV50icc67piZIYxkm6V9KQ8PUvIFPHeE1erKfVH4d/nXPObRSlVdK5BHcn/4agjuEd4O/ZDCrbWrcM8mGlt0pyzrlaorRKqpD0EPCQmTXsYQhNTKswMaz3G9ycc66WtEVJYY+nV0taAkwHZkhaLOnK3IWXHa3C+xgqvOtt55yrJVMdw4UEz1T4rpltaWZdgH2BwZIuykVw2dKyqAVFLcT6am+u6pxzyTIlhlOBn5pZTZtOM/sKODmctlmr3mCM+bxZlIw551yjypQYis1sSfLIsJ5hs26uGjNlbnm+Q3DOuSYnU2JY38BpzjnnNmOZWiXtISnVKbUInujmnHOuGUqbGMysWT/BpnvH1iwsb3bPHnLOuU0W5c7nZsmTgnPOpZb2ikHSLIJnOy82s31zF5Jzzrl8ylTHMCT826wb+1dWb6h5cI9zzrnMieF+giuGpcDxOYkmD75cvIqdenTMdxjOOddkpD1VNrOhZnaQmTUoKUgqkfSxpEmSpkq6JsU8QyStkDQxfOW8u40vFnrX2845Fy9K76oNVQEcZGarJBUD70l62cw+TJrvXTM7KotxZHTf+7M4eo+t87V655xrcrJWuG6B2Ol4cfiybK2vvgZvvyUAa70jPeecS5DVWldJRZImAouA183soxSzDQqLm16WtEs244k3/IDtADhq9565WqVzzm0WMjVX3SvTB83sk7oWbmbVwABJnYD/StrVzKbEzfIJ0C8sbjoSeA7onyKW4cBwgL59+9a12ki236o9AN3at26U5TnnXHORqY7h1gzTDDgo6krMbLmkt4HDgSlx48vjhl+S9HdJXZM77zOze4B7AAYOHNgoxVEl4cN61lU169a4zjlXb5m6xBi6KQuW1A2oDJNCG+AQ4E9J8/QAFpqZSdqHoGjr201Zb1Sti4MeP75c5K2SnHMuXqaipIPM7E1Jx6WabmbP1rHsnsADkooIDvhPmtmLks4JPz+S4P6IcyVVAWuBk8wsJxXUsSuGBz74mmuO3TUXq3TOuc1CpqKkA4E3gaNTTDMgY2Iws8nAninGj4wbvhu4O1Kkjayl3+3snHMpZSpKuiocvDb+KW4AkrbJalTOOefyJspp8zMpxj3d2IE455xrGjLVMewE7AJskVTP0BF/UI9zzjVbmeoYdgSOAjqRWM+wEvhlFmNyzjmXR5nqGJ4Hnpc0yMw+yGFMOXPC3r1594sldc/onHMFJEonejMlXQaUxs9vZmdmK6hcaV/SktUVVfkOwznnmpQoieF54F3gDZrZQ3vKlqxmZUUVGzYYLVoo3+E451yTECUxtDWzS7IeSR68NWMxAEtWV7BVB69Pd845iNZc9cWwg7tm59pjw85cm0xn4M45l39REsMFBMlhraRySSslldf5qc1Au1bBBdM6fyaDc87VqLMoycw65CKQfGhd7D2sOudcsjoTg6QDUo03s3caP5zcKmkZ9LBa4VcMzjlXI0rl8+/jhkuAfYDx1ON5DE1VSdj1tl8xOOfcRlGKkhJ6V5XUB7glaxHlUE1RUqUnBueci2lI39NzgGbxAAMvSnLOudqi1DHcxcYGnS2AAcCkLMaUM1757JxztUWpYxgXN1wFPGZm72cpnpyKXTF4c1XnnNsoSh3DA7kIJB9iVwwVfsXgnHM1Cvr5lrFWSWvXe2JwzrmYgk4M7VoFiWGV97DqnHM16pUYJLWQ1DFbweRay6IWlBS38K63nXMuTp2JQdKjkjpKagdMA2ZI+n1dn9tcrKvcwDuf+8N6nHMuJsoVw85mVg78EHgJ6Aucks2gcm3GwpX5DsE555qMKImhWFIxQWJ43swqidBRtaQSSR9LmiRpqqRrUswjSXdKmilpsqS96r0FzjnnGlWUxPBPoAxoB7wjqR8QpdvtCuAgM9uD4Ka4wyXtlzTPEUD/8DUc+Ee0sJ1zzmVLnYnBzO40s15mdqQFvgaGRvicmdmq8G1x+Eq+0jgWeDCc90Ogk6Se9dwG55xzjShK5fOWYXHPJ5LGS/orsEWUhUsqkjQRWAS8bmYfJc3SC5gd935OOC55OcMljZM0bvHixVFWXW+V1X73s3POQbSipMeBxcCPgePD4SeiLNzMqs1sANAb2EdScud7SvWxFMu5x8wGmtnAbt26RVl1vT3y4ddZWa5zzm1uoiSGLmZ2nZnNCl/XA53qsxIzWw68DRyeNGkO0CfufW9gXn2WvanOH7odAKVd2+Vytc4512RFSQxvSTopvLmthaSfAKPq+pCkbpI6hcNtgEOA6UmzvQCcGrZO2g9YYWbz67cJm2bPPp0BGFu2NJerdc65JitK76pnA78FHiYo5ikCVkv6LUEdc7o7oXsCD0gqIkhAT5rZi5LOIfjgSIL7Io4EZgJrgDM2ZWMaYqeewSOtu7ZvnetVO+dckxSld9UODVmwmU0G9kwxfmTcsAHnN2T5jaVjm2IAqqrrvDXDOecKQpRWSZJ0sqQrwvd9JO2T/dByo12rIDf+692v8hyJc841DVHqGP4ODAJ+Fr5fBfwtaxHlWFGLoGHUopUVeY7EOeeahih1DPua2V6SJgCY2TJJrbIcl3POuTyJkhgqwwpkg6C1EdCs7gbbZ5su+Q7BOeeajChFSXcC/wW2knQD8B5wU1ajyrEOrVuyap0/k8E55yBaq6RHJI0HDia4U/mHZvZZ1iPLofJ1lUybH6VfQOeca/7qTAySHjKzU4i7OS1uXLMwtmxZvkNwzrkmI0pR0i7xb8L6hr2zE05+7Ng9uFXDn/3snHMZEoOkSyWtBHaXVC5pZfh+EfB8ziLMgVjPqovK1+U5Euecy7+0icHMbgrvev6zmXU0sw7ha0szuzSHMWbdSfsE/fitWV+d50iccy7/0tYxhE9qWx5LApKGEjzeswz4m5mtz0WAuRDrJ6miyhODc85lqmN4kuBxnkgaADwFfEPwmM6/ZzuwXOrVqQ0A6yqb1e0ZzjnXIJkSQxsziz0b4WTgP2Z2K0EPqM2mrySA4pbBbvholne97ZxzmRJD/NPVDgJGA5hZszutjt3cdufoL/IciXPO5V+m+xjelPQkMB/oDLwJIKkn0GzqF8C7xHDOuXiZrhguBJ4lqGz+vplVhuN7AH/Mbli5VVJcVDO8YYM/l8E5V9jSXjGED9F5PMX4CVmNKM/mLFtL3y3b5jsM55zLmyh3PheUyXOX5zsE55zLK08MofOHbgfA1mHTVeecK1SZusQYHf79U+7CyZ8hO24FwGrvL8k5V+AytUrqKelA4BhJj5PYfBUz+ySrkeVYh5JgV5Sv9cTgnCtsmRLDlcAIoDdwW9I0I7i3odlo3zrYFW/PWMSw3XvmORrnnMufTJ3oPW1mRwC3mNnQpFezSgqwMTE8NX5OniNxzrn8qrPy2cyuk3SMpL+Er6OiLFhSH0lvSfpM0lRJF6SYZ4ikFZImhq8rG7IRjaFT21YAlHpTVedcgYvyBLebCPpGeiQcdYGkwRG63q4CLjazTyR1AMZLet3MpiXN966ZRUo22bZ3v860bukNtZxzha3OxAAMAwbE+kiS9AAwAciYGMxsPkF3GpjZSkmfAb2A5MTQZHRt34pZS1bnOwznnMurqKfHneKGt6jvSiSVAnsCH6WYPEjSJEkvS9olxXQkDZc0TtK4xYsX13f1kc1ZtpbPF66iqrrZ9RPonHORRUkMNwETJN0fXi2MB26MugJJ7YFngAvNrDxp8idAPzPbA7gLeC7VMszsHjMbaGYDu3XrFnXV9TZ1XhDe014B7ZwrYFEqnx8D9iPoUO9ZYJCZ1epDKRVJxQRJ4REzezbFssvNbFU4/BJQLKlrPeJvVMVFwa0ai1ZW5CsE55zLu0hFSWY238xeMLPnzWxBlM9IEnAv8JmZJd8HEZunRzgfkvYJ4/k2WuiN79lzBwOwU48O+QrBOefyLkrlc0MNBk4BPpU0MRx3GdAXwMxGAscD50qqAtYCJ4W9uuZFxzbB7li5zu9+ds4VrqwlBjN7j6RuNFLMczdwd7ZiqK8OJcUAlK+rrGNO55xrvjIWJUlqIWlKroLJt1h/SX7F4JwrZBkTQ3jvwiRJfXMUT14VF7Wgbasiytf6FYNzrnBFqXzuCUyVNFrSC7FXtgPLlzXrq3lrxqJ8h+Gcc3kTpY7hmqxH0cR8udjvfnbOFa46E4OZjZHUD+hvZm9IagsUZT+0/Ni7X2fWV/mdz865whWlE71fAsOBLsB2BP0djQQOzm5o+TH+62X5DsE55/IqSh3D+QT3JJQDmNkXwFbZDKop8KsG51yhipIYKsxsfeyNpJYET3Brlq48amcAlq5eX8eczjnXPEVJDGMkXQa0kfQD4Cng/7IbVv588FXQI8fvn56U50iccy4/oiSGEcBi4FPgbOAl4PJsBpVPB+wQ9N46Ze6KPEfinHP5EaV31Q3AA8B1BE1XH8hnf0bZdsweWwOwbI3f5OacK0xRWiUNI2iF9CVB30fbSDrbzF7OdnD50LEkm/0KOudc0xflKHgrMNTMZgJI2g4YBTTLxBD2Au6ccwUrSh3DolhSCH0FNOs+I7bfqj0AzbjEzDnn0kqbGCQdJ+k4gn6SXpJ0uqTTCFokjc1ZhHlw4sA+AKys8F5WnXOFJ9MVw9HhqwRYCBwIDCFoodQ565Hl0aMffwPAVc9PzXMkzjmXe2nrGMzsjFwG0pQc0L8rs5as5r8T5nL7iQPyHY5zzuVUlFZJ2wC/Bkrj5zezY7IXVn5dftTOPPDB1/kOwznn8iJKq6TngHsJ6hYKogOh4qIodfLOOdc8RUkM68zszqxH0kStq6ympLjZ9jLunHO1RDk1/qukqyQNkrRX7JX1yJqIna54Jd8hOOdcTkW5YtgNOAU4iI1FSRa+d84518xESQw/AraN73q7ELzx2wM45LZ38h2Gc87lXJSipElAp/ouWFIfSW9J+kzSVEkXpJhHku6UNFPS5KZURLX9Vh3yHYJzzuVFlCuG7sB0SWOBitjICM1Vq4CLzewTSR2A8ZJeN7NpcfMcAfQPX/sC/wj/Ouecy5MoieGqhizYzOYD88PhlZI+I3hedHxiOBZ4MOzG+0NJnST1DD/bZMxctKqm/yTnnGvu6kwMZjZmU1ciqRTYE/goaVIvYHbc+znhuITEIGk4MBygb9++mxpOZNf/cFcuf24Ky9YUVPWKc67A1VnHIGmlpPLwtU5StaTyqCuQ1B54BrjQzJI/l6qP61pdmprZPWY20MwGduvWLeqqN9mAPp0AOGHkBzlbp3PO5VuUJ7h1MLOO4asE+DFwd5SFSyomSAqPmNmzKWaZA/SJe98bmBdl2bnQq1ObmuHSEaPyGIlzzuVOvft+MLPniHAPg4In3twLfGZmt6WZ7QXg1LB10n7AiqZUv9C5XauE9598syxPkTjnXO5E6UTvuLi3LYCBpCjuSWEwwY1xn0qaGI67DOgLYGYjgZeAI4GZwBqgSffoetzf/0fZzcPyHYZzzmVVlFZJR8cNVwFlBK2JMjKz90hdhxA/jwHnR4ghb8puHsa7XyzmlHs/zncozjmXE1FaJTXps/hc2L9/7iq8nXMu39ImBklXZvicmdl1WYinSetYEuUCyznnNm+ZjnSrU4xrB/wC2BIouMRQvs6fAe2ca/7Stkoys1tjL+AeoA1B5fDjwLY5iq/JueTpyfkOwTnnsipjc1VJXSRdD0wmuLrYy8wuMbNFOYmuCXpi3GwqqwviQXbOuQKVNjFI+jMwFlgJ7GZmV5tZwTbkn3nDETXD/f/4Musqq5m3fC1/e2smqyu8iMk513woaDGaYoK0gaA31SoS71sQQeVzx+yHV9vAgQNt3Lhx+Vh1xruf/f4G51xTJmm8mQ2MMm+mOoYWZtYmqUuMjrH3jRfu5uOIXXuknVY6YhTrqzatiOnN6Qv5YuHKTVqGc85tqnp3iVHI/nHy3hmn73D5y5SOGMWvHv2kQcs/8/5x/OB2f2qccy6/PDHU05sXH5jw/oS9e9ea58XJ8+vd6V58hfbilRUZ5nTOuexKW8fQVOWzjiFmfdUGnps4lxP27o0kJs5ezg//9n6t+fp0acO7f8jc3+DilRWcef9Yfr5vX0Y8+2mt6Tt278D+/bvy7/dmMenKQ9mibXGjbYdzrnDUp47BE0MjOfT2MXy+cFWt8b07t+G9S4Lk8NyEuVz4xMSaaU8M348T7/kw8jp+fdD2XHzojpscq3Ou8HhiyJNY8dH4yw9h7+vfyMo6vrjhCAQsKF9H1/atKSkuysp6Mrnjjc95bepCXvz192nRQnw6ZwXL1qzngB28Tynnmqr6JAbv/KcRvfW7IXRuW0yntq3o1LaY5WsqG30df3/rS25/4/Oa98nNZF+YNI+Zi1bxq6Hb06pl41chTV9Qzh1vfAHAtpe9xKdXH8rRd78HwEeXHUz3jiWNvk7nXG555XMj2qZrOzq1DR7uM/HKQzn7wNo9h+zfvyuzbjoyYdyY3w9hz76dANi558aWwOcN2Y5ZNx3Jx5cdXDMuPimk8pvHJnDn6C/Y4fKX2eeG9Fct6yqrOfT2McxfsZaPvvqWH9w2hm9Xpa/0NjPue38Wh9/xbsL43a5+rWZ43xtHM3f52lqfrarewH3vz2LN+ipue20Ga9b7DYHONWVelJRlh9/xDtMXrGTQtlvywVffctxevbjtJwP45ts1HPDnt3j+/MHsET5bOmbU5Pl8d5vObNVh49n3hg3Gtpe9VGv5s246kuBheannKbt5GIvK19GxTTFm0KZVUPR03iPjeenTBbWW9+hZ+7LPNl1oWbTxnGHe8rXc+94s7n1vVp3b26GkJZ9efVjCuFQttPyGQOdyy4uSmpBXLjwACA7aD3xQxnF7Bc1b+27ZNu3BcdjuPWuNa9Ei9TOPtrn0pZrl/ObxCbWmJx+UY4kpVVIA+Nm/P+KEvXtz8493pyhc5/dufrPWfNOvO5ydrnil1viVEXugfW3qAoY/NJ5nz/see/XtHOkzzrnc8MSQIy1aiDMGb7NJy/jqxiO5971ZnLxfPwZc+xoV4Z3WsYNsFM9+Mpc1FdUZ53lq/ByeGj8HgJ16dKg1ffut2mes9F66ej1LV1ew/VYdWLRyXcp5YvEe9/f/8eCZ+7BHn05s0cab4jrXFHhR0mYs3U10M64/nNYtiyLdZNerUxvmLl/LtGsPY+crX61z/inXHEb71sH5xGMff8OlKe69SOWvJw3ggscnsmW7Vny7en3Keb644Qje+2IJQ3faqta0t6YvoluH1uzaa4tI63POJWqUvpJc0/ff875Xa9yefTvRumX0JqzvjziIspuH0bZVS/p2aZtx3tcvOqAmKQD8dJ++CdPPH7pd2s9KouzmYYy/4gdp5+n/x5c54/6xHH7Hxm5BxpYtZdid73LG/WM56q736toc51wj8MSwGdszqWz+qqN35r/nDa55P/nqQ2uGy24eRtnNw7jk8J1qxj19zqCEz7/zh6E8d/5gUim7eRj9u9cuVhrz+yEAPHf+YH6X4ea7o3bbWG8Si+W4vXqlnHf6gpX8J6zoPmHkB0ydV14zbcOG+l3hfv3takpHjKp3FyXJPp2zggUrUheLZZL87I76xt8UTJtXzriypTXvr39xGqUjRm2W2+Ki8aKkzdy6yuqaSuD6tPRZuno9Xdq1SjntgscncPTuW3PWg8F+fvcPQ+lTx9VEsmVhcdGe173OxT/YgV8f3D/tvFXVG9j+jy9HXvbjw/djYL/OCS2nXp+2kF8+OC6hqAvgquen8MAHXwPw6oUHsGOKOpNMvl1VwXH/+B9ff7sGyLyPzYwF5et49pO5nD90e/a7cTQLytcx/vJD2LJ9axaWr2PfG0dz2C7deXXqQl676AAOTeo0Mb6VWVMRS6ofX3YwHdsUJzQ6ePt3Qyjt2i5fobl68DufC0zsf5iNA4qZ5eRA1ZAz+thB+tWpCzg7rvJ9whU/YM/rXq/zcxBcCTzy0decO2Q7+m2ZeIA78/6xvDm99sMKUyWH0Z8t5BcPpP9elt08LPI2XvfDXTllv36R5s22KXNXJBThnTl4G/7zfu1my43d/NjMmL5gJd/pWZA9/GdFk6hjkPQfSYskTUkzfYikFZImhq8rsxVLcycpawfvXJ29zrzhCD679nAmXXUoe/ROrGAef/khTL/u8FqfKR0xim9XVSQkBSBjUgBYuz5olTVl7gqOvvs9Hh87mwP//DalI0bVTAPo3Db1FVVV9QZueWU6pSNGsXhlBaUjRmVMCjFR70S/4rkp/OHpSfzvyyUA/HfCHEpHjKJ8XSXzlq/NyqNlK6qqa4rcDrltTM34GQsSnw/Sp0ublJ//PO45IusqqzMW361YW8nlz31KRVX61nGvTl3AEX99l9IRozjpng8SYvy8Ac8sWbyygkNvH0PpiFE1yz3z/rH1Xk5d1lVWs7qiim0vDbb/0mcb9oz4LxevYtLs5Y0bXD1k7YpB0gHAKuBBM9s1xfQhwO/M7Kj6LNevGArb+zOXcP2oz/hsfnndM4c6lLSsdX9Fuvsw0plyzWHselXdrbYa6rc/2IEfDujFAX9+K+083y3tzNiyxKfr/vqg7fn1Qf0pLhJfLVnNwbcGB/V0Z/BmxjaXvlRrnrMeGMsbn0V/lPvMG46oVfwXW158Qjhsl+7885SBtdYd7/YT9+DLRau5+NAdqN5gVG0w9rnhDcoz3BPz6C/35Wf/+ohnzh3E3v26ZIw13Xpj2xFfJBlz95tf8JfXPufNiw9k227ta8YvX7Oe/5s8v9YV3fAHx9G/e3v+9taXtZb11Y1Hpr0PKZXqDcZ24Y2qt/1kD75b2oWOJcW0aAEdShrepLvJFCVJKgVe9MTgGlu6u6mfHDebPzw9mSE7duPQnXvws32DllPrqzYwe9mamgNnfcTK/UeO+ZKbX56edr6Hf7Ev3+/fFYDydZW0a9Wy5gee7Gf79uXGH+3GusrqhHtCrn5hKvf/r6zeMabStX1rDtqpG9ceuyslxUWsWV/Fve/O4tbXN3ar8p2eHXngjO+yz42jMy7r0bP25Wf//qjmfdnNwxjz+WJO+8/HNeN+uk8fbjpu902u6K+vf/x8L47YrfZNobE4Yk2lM3n2vO9RVW385J8f1Jo2/brDa/5HsWXu2L0Dr150QK11RfHBpQfRc4vUV16zl65h/1vSnxzEx1Jfm1NieAaYA8wjSBJT0yxnODAcoG/fvnt//fXXWYrYbU7if4wv/Gowu/fuVOdnDrv9HWYkFUWkOtNNNR3g5//+kPdnfltrnkwV9Efd9S5T5m68wslUHr++agM7XB69Ij6qJ88elPKgl+zpcwbRY4sSvv+nxINTfI/Bxw7Ymr+etGfNtIYkgpO+24fHx86u9+fSOW1QP9q2bsmLk+fx6Fn78ZfXZvD8xHm15rvu2F24ftRnNTeHRlV28zDmLl/L4BS9AByzx9a8MKn2uupaXlX1BlZXVNc8YyX+SiGd647dhVMGldZrXTGbS2LoCGwws1WSjgT+ambpm66E/IrBxZgZk+esoGuH1vTqlPoMLJX4A9mfj9+dEwb2qVlerE5l2er1nPvIeG79yYBay35q3Gz+MeZL7vrpnqyuqOaiJyby/ojMD2Sat3wtPbcoqVedzeqKKmYtWc0uW3fktWkLOfuh8Uy79jCKi1pQXNSippVTY4olrVhZ+X8nzKV1cRGn7NevZr+lSmypksP/RhyUsjuVcZcfQtf2rfl41tI6k9Wsm45k0cqKmu2MmuBSmXbtYbRttbHFWjavbOo62bjtJ3vw2ycnAdChdUtaFxexJEMnlqmWXV+bRWJIMW8ZMNDMlmSazxOD21SxIqEf7dmL208ckO9wNsm/3vmKDiUta57+l3wgTeXsA7fl1wf1Z1zZUk6/b2MF7OsXHZDyXpUoxpYt5YSRGw/YA/t15ulzN96AGTtAvvSb/dl568SWRre//jnzlq+t6Ybljd8eyCG3jeHqo3fm9BTdyJxx38fssvUWnPq9fuxzQ7TE+JcT9uD4pMfwbthg/O6pSTw7YW6t+Z8593vs1bdT2rqJdHbs3oEXfj245ibTCd8s40d//1+9lgFBVzQvX7A/T4+fQ8c2xRy2Sw9KR4yqs+l3JptFYpDUA1hoZiZpH+BpoJ/VEZAnBtcYVqypLIjHpD4zfg4XPzWp5n02e7V9cuxsilqI7bdqX6vH4DnL1vDFwlUpuzvZVOc/+gmjJs9nYL/OjPs6sXK+7OZhrKqoSri3JZUNGyxlBfG6ymr2vPZ11lZubEE166YjaxLG2QdsS88tSpg6r5w/n7BHnbFGuWfn0iN24uwD0/ci0FBNIjFIegwYAnQFFgJXAcUAZjZS0q+Ac4EqYC3wWzOrM7V6YnCufi54fAJmwZ3xW7Zvne9wsir+wPvKhfuzU4/GuQ8ivkhoU5Nr/LJ+c3B/7hz9BUfs2oOXpyxo0E2YUTWJxJAtnhicc7lWvcH4eNZS9tu2yybf27OofB373Dia9y4ZSu/O9etRYFP48xicc64RFbUQg7bbslGWtVXHkib/oCrvRM8551wCTwzOOecSeGJwzjmXwBODc865BJ4YnHPOJfDE4JxzLoEnBueccwk8MTjnnEuw2d35LGkx0NB+t7sCGTvpa4Z8mwuDb3Nh2JRt7mdm3aLMuNklhk0haVzUW8KbC9/mwuDbXBhytc1elOSccy6BJwbnnHMJCi0x3JPvAPLAt7kw+DYXhpxsc0HVMTjnnKtboV0xOOecq4MnBueccwkKJjFIOlzSDEkzJY3Idzz1IamPpLckfSZpqqQLwvFdJL0u6Yvwb+e4z1wabusMSYfFjd9b0qfhtDsVPo5KUmtJT4TjPwqf1513kookTZD0Yvi+WW+zpE6SnpY0Pfx/DyqAbb4o/F5PkfSYpJLmts2S/iNpkaQpceNyso2STgvX8YWk0yIFbGbN/gUUAV8C2wKtgEnAzvmOqx7x9wT2Coc7AJ8DOwO3ACPC8SOAP4XDO4fb2BrYJtz2onDax8AgQMDLwBHh+POAkeHwScAT+d7uMJbfAo8CL4bvm/U2Aw8AZ4XDrYBOzXmbgV7ALKBN+P5J4PTmts3AAcBewJS4cVnfRqAL8FX4t3M43LnOePP9Q8jRP2UQ8Grc+0uBS/Md1yZsz/PAD4AZQM9wXE9gRqrtA14N90FPYHrc+J8C/4yfJxxuSXB3pfK8nb2B0cBBbEwMzXabgY4EB0kljW/O29wLmB0euFoCLwKHNsdtBkpJTAxZ38b4ecJp/wR+WleshVKUFPvyxcwJx212wkvEPYGPgO5mNh8g/LtVOFu67e0VDiePT/iMmVUBK4DGechtw90B/AHYEDeuOW/ztsBi4L6w+OzfktrRjLfZzOYCfwG+AeYDK8zsNZrxNsfJxTY26NhXKIlBKcZtdu10JbUHngEuNLPyTLOmGGcZxmf6TF5IOgpYZGbjo34kxbjNapsJzvT2Av5hZnsCqwmKGNLZ7Lc5LFc/lqDIZGugnaSTM30kxbjNapsjaMxtbNC2F0pimAP0iXvfG5iXp1gaRFIxQVJ4xMyeDUcvlNQznN4TWBSOT7e9c8Lh5PEJn5HUEtgCWNr4WxLZYOAYSWXA48BBkh6meW/zHGCOmX0Uvn+aIFE0520+BJhlZovNrBJ4FvgezXubY3KxjQ069hVKYhgL9Je0jaRWBJUzL+Q5psjClgf3Ap+Z2W1xk14AYq0MTiOoe4iNPylsqbAN0B/4OLxcXSlpv3CZpyZ9Jras44E3LSyUzAczu9TMeptZKcH/600zO5nmvc0LgNmSdgxHHQxMoxlvM0ER0n6S2oaxHgx8RvPe5phcbOOrwKGSOodXZ4eG4zLLdQVMvl7AkQSteb4E/pjveOoZ+/cJLv8mAxPD15EEZYijgS/Cv13iPvPHcFtnELZcCMcPBKaE0+5m493vJcBTwEyClg/b5nu742IewsbK52a9zcAAYFz4v36OoCVJc9/ma4DpYbwPEbTGaVbbDDxGUIdSSXAW/4tcbSNwZjh+JnBGlHi9SwznnHMJCqUoyTnnXESeGJxzziXwxOCccy6BJwbnnHMJPDE455xL4InBFSRJ1ZImxr0y9rgr6RxJpzbCesskdd3U5TiXTd5c1RUkSavMrH0e1lsGDDSzJblet3NR+RWDc3HCM/o/Sfo4fG0fjr9a0u/C4d9ImiZpsqTHw3FdJD0XjvtQ0u7h+C0lvRZ2ivdP4vqukXRyuI6Jkv6p4NkTRZLuV/Bsgk8lXZSH3eAKnCcGV6jaJBUlnRg3rdzM9iG4s/SOFJ8dAexpZrsD54TjrgEmhOMuAx4Mx18FvGdBp3gvAH0BJH0HOBEYbGYDgGrg5wR3Pvcys13NbDfgvsbaYOeiapnvAJzLk7XhATmVx+L+3p5i+mTgEUnPEXRbAUG3JT8GMLM3wyuFLQge0HJcOH6UpGXh/AcDewNjw4dwtSHoRO3/gG0l3QWMAl5r4PY512B+xeBcbZZmOGYY8DeCA/v4sDfLTN0bp1qGgAfMbED42tHMrjazZcAewNvA+cC/G7gNzjWYJwbnajsx7u8H8RMktQD6mNlbBA8R6gS0B94hKApC0hBgiQXPzIgffwRBp3gQdJp2vKStwmldJPULWyy1MLNngCsIut12Lqe8KMkVqjaSJsa9f8XMYk1WW0v6iODE6adJnysCHg6LiQTcbmbLJV1N8OS1ycAaNnaBfA3wmKRPgDEE3UxjZtMkXQ68FiabSoIrhLXhcmInbZc22hY7F5E3V3Uujjcndc6LkpxzziXxKwbnnHMJ/IrBOedcAk8MzjnnEnhicM45l8ATg3POuQSeGJxzziX4f2B+Ae3m5+69AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "# Plot the performance\n",
    "N_moves_save = pd.DataFrame(N_moves_save, columns = ['N_moves'])\n",
    "N_moves_save.to_csv('N_moves_Adagrad_poor.csv')\n",
    "N_moves_save['N_moves'] = N_moves_save['N_moves'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "\n",
    "plt.plot(N_moves_save['N_moves'])\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Number of Steps until \"Done\"')\n",
    "plt.title('Average Number of Steps until \"Done\" per Episode')\n",
    "plt.show()\n",
    "\n",
    "R_save = pd.DataFrame(R_save, columns = ['R_save'])\n",
    "R_save.to_csv('R_save_Adagrad_poor.csv')\n",
    "R_save['R_save'] = R_save['R_save'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "plt.plot(R_save)\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Reward')\n",
    "plt.title('Average Rewards per Episode')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "Delta_save = pd.DataFrame(Delta_save, columns = ['Delta_save'])\n",
    "Delta_save.to_csv('Delta_save_Adagrad_poor.csv')\n",
    "Delta_save['Delta_save'] = Delta_save['Delta_save'].ewm(span=2000, adjust=False).mean()\n",
    "\n",
    "plt.plot(Delta_save)\n",
    "plt.xlabel('Episodes')\n",
    "plt.ylabel('Error')\n",
    "plt.title('Average Loss')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}