n-step TD Learning.ipynb

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     "start_time": "2020-06-22T09:46:23.444137Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-22T09:46:24.716404Z",
     "start_time": "2020-06-22T09:46:24.712508Z"
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   "outputs": [],
   "source": [
    "def get_label(x):\n",
    "    if x==0:\n",
    "        return 'Left'\n",
    "    elif x==1:\n",
    "        return 'Right'\n",
    "    elif x==2:\n",
    "        return 'Up'\n",
    "    elif x==3:\n",
    "        return 'Down'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
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     "start_time": "2020-06-22T09:46:24.718861Z"
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   "source": [
    "class WindyGridWorld:\n",
    "    \n",
    "    def __init__(self, n, terminal_state, windy_blocks, steps, on_policy = 'on-policy', verbose=False):\n",
    "        \n",
    "        self.grid_size = n\n",
    "        self.terminal_state = terminal_state\n",
    "        self.windy_blocks = windy_blocks\n",
    "        self.on_policy = on_policy\n",
    "        self.steps = steps\n",
    "        self.verbose = verbose\n",
    "        self.gamma = 0.1\n",
    "        \n",
    "        self.Q = np.zeros((self.grid_size, self.grid_size, 4)) + 0.25\n",
    "        \n",
    "        self.actions = [(0,-1), (0, 1), (-1,0), (1, 0)]# Left, Right, Up, Down\n",
    "\n",
    "        #Equi-probable action selection at each state for all actions\n",
    "        self.policy = np.random.randint(1,4,size = (self.grid_size, self.grid_size))\n",
    "                \n",
    "        if self.verbose:\n",
    "            print(\"Shape of Q\", self.Q.shape)\n",
    "            print(\"Shape of Policy\", self.policy.shape)\n",
    "            print(\"Initial State-Action/Q Function\", *self.Q, sep='\\n',end='\\n\\n')\n",
    "            print(\"Initial Policy\", *self.policy, sep='\\n',end='\\n\\n')\n",
    "        \n",
    "    def _get_reward(self, x, y):\n",
    "        if x==self.terminal_state[0] and y==self.terminal_state[1]:\n",
    "            return 300\n",
    "        return -1\n",
    "    \n",
    "    def _get_next_state(self, x, y, a):\n",
    "        \n",
    "        if x+a[0]!=-1 and x+a[0]!=self.grid_size:\n",
    "            x = x + a[0]\n",
    "        if y+a[1]!=-1 and y+a[1]!=self.grid_size:\n",
    "            y = y + a[1]\n",
    "        if x in self.windy_blocks[0] and y in self.windy_blocks[1]:\n",
    "            if x-1!=-1:\n",
    "                x-=1\n",
    "        return x,y\n",
    "        \n",
    "    def play(self, epochs = 100, threshold = 1e-8):\n",
    "        \n",
    "        if self.on_policy == 'on-policy':\n",
    "            res = self._play_n_step_on_policy(epochs, threshold)\n",
    "            \n",
    "            fig, ax = plt.subplots(figsize=(self.grid_size*2, self.grid_size*2))\n",
    "            anotations = np.array(list(map(get_label, self.policy.reshape(-1,1)))).reshape(self.policy.shape)\n",
    "            anotations[self.terminal_state[0], self.terminal_state[1]] = 'Terminal'\n",
    "            sns.heatmap(self.policy, annot=anotations, fmt='', cmap='Blues', ax = ax)\n",
    "            plt.show()\n",
    "            \n",
    "            if self.verbose:\n",
    "                print(\"Final Policy:\")\n",
    "                print(*self.policy, sep = '\\n', end = '\\n\\n')\n",
    "                print(\"Final State-Action/Q Function:\")\n",
    "                print(*self.Q, sep = '\\n', end = '\\n\\n')\n",
    "                \n",
    "            return res\n",
    "        \n",
    "        elif self.on_policy == 'off-policy':\n",
    "            res = self._play_n_step_off_policy(epochs, threshold)\n",
    "            \n",
    "            fig, ax = plt.subplots(figsize=(self.grid_size*2, self.grid_size*2))\n",
    "            anotations = np.array(list(map(get_label, self.policy.reshape(-1,1)))).reshape(self.policy.shape)\n",
    "            anotations[self.terminal_state[0], self.terminal_state[1]] = 'Terminal'\n",
    "            sns.heatmap(self.policy, annot=anotations, fmt='', cmap='Blues', ax = ax)\n",
    "            plt.show()\n",
    "            \n",
    "            if self.verbose:\n",
    "                print(\"Final Policy:\")\n",
    "                print(*self.policy, sep = '\\n', end = '\\n\\n')\n",
    "                print(\"Final State-Action/Q Function:\")\n",
    "                print(*self.Q, sep = '\\n', end = '\\n\\n')\n",
    "                \n",
    "            return res\n",
    "        \n",
    "    def _get_action(self, x,y):\n",
    "        \n",
    "        m = np.round(np.min(self.Q[x][y])-1, 3)\n",
    "        probs = (np.round(self.Q[x][y], 5)-m) / np.sum(np.round(self.Q[x][y], 5) - m)\n",
    "        try:\n",
    "            \n",
    "            return np.random.choice([0,1,2,3],p=probs)\n",
    "        except:\n",
    "            print(m,probs)\n",
    "    \n",
    "    def _get_unform_action(self):\n",
    "        return np.random.choice([0,1,2,3], p = [0.25, 0.25, 0.25, 0.25])\n",
    "    \n",
    "    def _get_policy_ratio(self, x, y, action):\n",
    "        m = np.round(np.min(self.Q[x][y])-1, 3)\n",
    "        probs = (np.round(self.Q[x][y], 5)-m) / np.sum(np.round(self.Q[x][y], 5) - m)\n",
    "        return probs[action]/0.25\n",
    "    \n",
    "    def _play_n_step_on_policy(self, epochs, threshold):\n",
    "        \n",
    "        iters = 0\n",
    "        while True:\n",
    "            \n",
    "            iters+=1\n",
    "            x=0\n",
    "            y=0\n",
    "            diff = 0\n",
    "            rewards = []\n",
    "            next_action = 0\n",
    "            action = self._get_action(x,y)\n",
    "            old_Q = np.array(self.Q)\n",
    "            length = 0\n",
    "            avg_length = []\n",
    "            \n",
    "            while True:\n",
    "                \n",
    "                    length+=1\n",
    "                    new_x, new_y = self._get_next_state(x,y,self.actions[action])\n",
    "                    reward = self._get_reward(new_x, new_y)\n",
    "                    rewards.append(reward)\n",
    "                    \n",
    "                    if self.verbose:\n",
    "                        print(\"X, Y, Action, Rewards:\", [x,y,action,rewards])\n",
    "                    \n",
    "                    if reward<0:\n",
    "                        next_action = self._get_action(x,y)                        \n",
    "                    \n",
    "                    if self.steps < len(rewards):\n",
    "                        \n",
    "                        G = 0\n",
    "                        if self.verbose:\n",
    "                            print(\"rewards taken:\", rewards[-1*self.steps:])\n",
    "                        for i, g in enumerate(rewards[-1*self.steps:]):\n",
    "                            G += ((self.gamma ** i) * g)\n",
    "                    \n",
    "                        G += ((self.gamma ** self.steps) * self.Q[new_x, new_y, next_action])\n",
    "                        \n",
    "                        self.Q[x,y,action] = self.Q[x,y,action] + 0.1*(G - self.Q[x,y,action])\n",
    "\n",
    "                        self.policy[x,y] = np.argmax(self.Q[x][y])\n",
    "                    \n",
    "                    x, y, action = new_x, new_y, next_action\n",
    "                    \n",
    "                    if reward>0:\n",
    "                        break\n",
    "\n",
    "            avg_length.append(length)\n",
    "            diff = np.mean(np.square(old_Q-self.Q))\n",
    "            \n",
    "            if self.verbose:\n",
    "                print('IDs & Difference(MSE):', id(old_Q), id(self.Q), diff)\n",
    "                \n",
    "                        \n",
    "            if self.verbose:\n",
    "                print(\"Q function at iter:\", iters)\n",
    "                print(*self.Q, sep = '\\n', end = '\\n\\n')\n",
    "            \n",
    "            if self.verbose:\n",
    "                print(\"Policy at iter:\", iters)\n",
    "                print(*self.policy, sep = '\\n', end = '\\n\\n')\n",
    "            \n",
    "            if epochs==iters or diff < threshold:\n",
    "                return diff, iters, np.mean(avg_length)\n",
    "            \n",
    "    def _play_n_step_off_policy(self, epochs, threshold):\n",
    "        \n",
    "        iters = 0\n",
    "        while True:\n",
    "            \n",
    "            iters+=1\n",
    "            x=0\n",
    "            y=0\n",
    "            diff = 0\n",
    "            rewards = []\n",
    "            prob_ratios = []\n",
    "            next_action = 0\n",
    "            action = self._get_unform_action()\n",
    "            old_Q = np.array(self.Q)\n",
    "            length = 0\n",
    "            avg_length = []\n",
    "            \n",
    "            while True:\n",
    "                \n",
    "                    length += 1\n",
    "                    prob_ratios.append(self._get_policy_ratio(x,y,action))\n",
    "                    \n",
    "                    new_x, new_y = self._get_next_state(x,y,self.actions[action])\n",
    "                    \n",
    "                    reward = self._get_reward(new_x, new_y)\n",
    "                    rewards.append(reward)\n",
    "                    \n",
    "                    if self.verbose:\n",
    "                        print(\"X, Y, Action, Rewards:\", [x,y,action,rewards])\n",
    "                    \n",
    "                    if reward<0:\n",
    "                        next_action = self._get_unform_action()                        \n",
    "                    \n",
    "                    if self.steps < len(rewards):\n",
    "                        \n",
    "                        P = 1\n",
    "                        for p in prob_ratios[-1*self.steps:]:\n",
    "                            P = P * p\n",
    "                        \n",
    "                        G = 0\n",
    "                        if self.verbose:\n",
    "                            print(\"rewards taken:\", rewards[-1*self.steps:])\n",
    "                        for i, g in enumerate(rewards[-1*self.steps:]):\n",
    "                            G += ((self.gamma ** i) * g)\n",
    "                    \n",
    "                        G += ((self.gamma ** self.steps) * self.Q[new_x, new_y, next_action])\n",
    "                        \n",
    "                        self.Q[x,y,action] = self.Q[x,y,action] + 0.1 * P * (G - self.Q[x,y,action])\n",
    "\n",
    "                        self.policy[x,y] = np.argmax(self.Q[x][y])\n",
    "                    \n",
    "                    x, y, action = new_x, new_y, next_action\n",
    "                    \n",
    "                    if reward>0:\n",
    "                        break\n",
    "\n",
    "            avg_length.append(length)\n",
    "            diff = np.mean(np.square(old_Q-self.Q))\n",
    "            \n",
    "            if self.verbose:\n",
    "                print('IDs & Difference(MSE):', id(old_Q), id(self.Q), diff)\n",
    "                \n",
    "                        \n",
    "            if self.verbose:\n",
    "                print(\"Q function at iter:\", iters)\n",
    "                print(*self.Q, sep = '\\n', end = '\\n\\n')\n",
    "            \n",
    "            if self.verbose:\n",
    "                print(\"Policy at iter:\", iters)\n",
    "                print(*self.policy, sep = '\\n', end = '\\n\\n')\n",
    "            \n",
    "            if epochs==iters or diff < threshold:\n",
    "                return diff, iters, np.mean(avg_length)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# On Policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-22T09:47:09.323252Z",
     "start_time": "2020-06-22T09:46:24.962466Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TD with step size: 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Length of Episode: 26.0\n",
      "TD with step size: 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Length of Episode: 125.0\n",
      "TD with step size: 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Length of Episode: 60.0\n",
      "TD with step size: 4\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Length of Episode: 192.0\n",
      "TD with step size: 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Length of Episode: 12.0\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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epochs Count [1000, 1000, 1000, 550, 142]\n",
      "Difference(MSE) Value [0.0303809530218535, 4.192387179896136e-06, 2.3058218092312479e-10, 4.893137146753936e-17, 2.637108915841276e-17]\n"
     ]
    }
   ],
   "source": [
    "blocks = [[1,2,3,4],[2,3,4]]\n",
    "\n",
    "epochs_count = []\n",
    "diff_count = []\n",
    "\n",
    "for i in range(1,6):\n",
    "    print(\"TD with step size:\", i)\n",
    "    game = WindyGridWorld(6, (2,5), windy_blocks = blocks, steps=i, on_policy = 'on-policy', verbose=False)\n",
    "    diff, epochs, avg_episode_length = game.play(epochs=1000, threshold=1e-16)\n",
    "    print(\"Average Length of Episode:\", avg_episode_length)\n",
    "    epochs_count.append(epochs)\n",
    "    diff_count.append(diff)\n",
    "\n",
    "plt.plot(epochs_count)\n",
    "plt.xlabel('Step Size')\n",
    "plt.ylabel('Epochs taken for Converging')\n",
    "plt.show()\n",
    "plt.plot(diff_count)\n",
    "plt.xlabel('Step Size')\n",
    "plt.ylabel('Change in Q function(MSE)')\n",
    "plt.show()\n",
    "\n",
    "print('Epochs Count', epochs_count)\n",
    "print('Difference(MSE) Value', diff_count)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Off-Policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-22T09:48:10.621467Z",
     "start_time": "2020-06-22T09:47:09.325859Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TD with step size: 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Length of Episode: 292.0\n",
      "TD with step size: 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Length of Episode: 99.0\n",
      "TD with step size: 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Length of Episode: 79.0\n",
      "TD with step size: 4\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Length of Episode: 41.0\n",
      "TD with step size: 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Length of Episode: 116.0\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"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epochs Count [1000, 1000, 1000, 797, 138]\n",
      "Difference(MSE) Value [0.9057833289626599, 3.098847482510231e-07, 3.611783031012206e-10, 5.980695904092187e-17, 6.353259963110444e-17]\n"
     ]
    }
   ],
   "source": [
    "blocks = [[1,2,3,4],[2,3,4]]\n",
    "\n",
    "epochs_count = []\n",
    "diff_count = []\n",
    "\n",
    "for i in range(1,6):\n",
    "    print(\"TD with step size:\", i)\n",
    "    game = WindyGridWorld(6, (2,5), windy_blocks = blocks, steps=i, on_policy = 'off-policy', verbose=False)\n",
    "    diff, epochs, avg_episode_length = game.play(epochs=1000, threshold=1e-16)\n",
    "    print(\"Average Length of Episode:\", avg_episode_length)\n",
    "    epochs_count.append(epochs)\n",
    "    diff_count.append(diff)\n",
    "\n",
    "plt.plot(epochs_count)\n",
    "plt.show()\n",
    "plt.plot(diff_count)\n",
    "plt.show()\n",
    "\n",
    "print('Epochs Count', epochs_count)\n",
    "print('Difference(MSE) Value', diff_count)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Deductions/Observations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li>Terminal state & the bottom most state of windy region(3,2 for 4x4 matrix) will never be explored/updated and hence the Q function and policy is never changed.</li>\n",
    "    <li>Due to simple problem and less number of states there is no significant improvement in On-policy methods and Off-policy methods.</li>\n",
    "    <li>Epochs: Convergence is achieved faster when the step size is greater than 3.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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