assignment_report_track2.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Assignment 6: Track 2 Project Report\n",
    "\n",
    "## Team: dayan-hunt\n",
    "* Nikhil Kakodkar: 260578689 | nikhil.kakodkar@mail.mcgill.ca\n",
    "* Karim Koreitem: 260460964 | karim.koreitem@mail.mcgill.ca"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: Successor Representation in GVF Framework\n",
    "\n",
    "Bellman's equations written in matrix form we get:\n",
    "\n",
    "$V_\\pi = R_\\pi + \\gamma P_\\pi V_\\pi$\n",
    "\n",
    "this represents a fixed point for the value function for a given policy. With a little matrix manipulation we can find the solution to this fixed ppoint as:\n",
    "\n",
    "$V_\\pi = (I - \\gamma P_\\pi)^{-1} R_\\pi$\n",
    "\n",
    "This can then be represented as:\n",
    "\n",
    "$V_\\pi = \\Phi_\\pi R_\\pi\\ \\ $ where $\\ \\ \\Phi_\\pi = (I - \\gamma P_\\pi)^{-1}$\n",
    "\n",
    "The main concept of Successor Representation[1] is to have an encoding for the state of the environment such that it represents the future transitions under the given policy. In the above equation $\\Phi_\\pi$ can be thought of representing such an encoding. We now think of i'th row of $\\Phi_\\pi$ as represnting an encoding for the corresponding state, where the j'th element of the row represents the future occupancy of the j'th state.\n",
    "\n",
    "Now with such a representation we can directly learn the temporal transition behaviour of a policy encoded in $\\Phi_\\pi$. Hence we can now directly calculate the value function by simple taking an inner product of $\\Phi_\\pi$ and the reward $R_\\pi$.\n",
    "\n",
    "This type of reformulation of the problem fits very naturally into the framework of the idea of General Value Function (GVF). In GVF framework the idea of the reward function is abstracted away. This can now be replaced by any property of the environment that might be of interest to us. Or also any combination of multiple properties of the environment. This is termed as the 'Cummulant'. \n",
    "\n",
    "$V_{\\pi, \\gamma, C} (s) = E[\\sum_{k=t}^{\\infty} C_{k+1} \\Pi_{i=t+1}^{k} \\gamma(S_i) | S_{t} = s, A_{t:\\infty} \\sim \\pi]$\n",
    "\n",
    "or in matric notation:\n",
    "\n",
    "$V_{\\pi, \\gamma, C} = C_\\pi + \\gamma P_\\pi V_{\\pi, \\gamma, C}$\n",
    "\n",
    "where $C$ represents the cummulant and  $\\gamma(s)$ represents the discounting or in general a termination condition. Incorporating the idea of successor representations, we get:\n",
    "\n",
    "$V_{\\pi, \\gamma, C} = \\Phi_{\\pi, \\gamma} C_\\pi\\ \\ $ where \n",
    "$\\ \\ \\Phi_{\\pi, \\gamma} = (I - \\gamma P_\\pi)^{-1}$\n",
    "\n",
    "This means we can now learn a-priory the temporal behaviour of a policy in an environment and then calculate the GVF later by the desired cummulant function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from numpy.linalg import inv\n",
    "from math import sqrt\n",
    "import matplotlib.pyplot as plt\n",
    "from sr_main import run_experiment, compute_transition_mtx, compute_reward_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def init_default_config_tenbyten():\n",
    "    config = {'switch_reward': False,\n",
    "              'terminal_step' : 80000,\n",
    "              'switch_reward_at_step' : 40000,\n",
    "              'episode_length' : 50,\n",
    "              'maze_type' : 'tenbyten',\n",
    "              'maze_params' : {\n",
    "                  'row' : 10,\n",
    "                  'col' : 10,\n",
    "                  'start_row' : 1,\n",
    "                  'start_col' : 1\n",
    "              },\n",
    "              'learning_alg_params' : {\n",
    "                  'alpha' : 0.5,\n",
    "                  'gamma' : 0.9,\n",
    "              },              \n",
    "             }\n",
    "    return config"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Track 2: Question 1: Learning SR using TD(0)\n",
    "\n",
    "For this report we use a simple 10\\*10 gridworld with the starting position at (0,0) and goal position at (9,9). The action space consists of 4 actions in each of the four directions. All the transitions are considered deterministic. And the goal state (9,9) is an absorbing state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "config = init_default_config_tenbyten()\n",
    "result = run_experiment(config)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "terminal_step = config['terminal_step']\n",
    "approx_Phi_pi = result[terminal_step-1]['Phi_pi']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Calculate exact phi_pi for 10x10 gridworld\n",
    "state_len = config['maze_params']['row']*config['maze_params']['col']\n",
    "gamma = config['learning_alg_params']['gamma']\n",
    "P_pi = compute_transition_mtx(config)\n",
    "exact_Phi_pi = inv(np.identity(state_len)-gamma*P_pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fdf82c86668>"
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     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Phi_pi error\n",
    "err_sr = []\n",
    "\n",
    "for s in range(terminal_step):\n",
    "    est_Phi_pi = result[s]['Phi_pi']\n",
    "    err_sr.append(np.mean(np.square(est_Phi_pi - exact_Phi_pi)))\n",
    "    \n",
    "# Plotting Phi_pi error:\n",
    "plt.ylabel('Mean-squared error')\n",
    "plt.xlabel('Number of steps')\n",
    "plt.title('Phi_pi error')\n",
    "plt.plot(err_sr, label='SR')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph here presents the mean-squared error between the exact $\\Phi_\\pi$, calculated as: \n",
    "\n",
    "$\\Phi_\\pi = (I - \\gamma P_\\pi)^{-1}$\n",
    "\n",
    "and the $\\Phi_\\pi$ calculated by a one-step update rule given by:\n",
    "\n",
    "$\\Phi_\\pi(s,j) \\leftarrow \\Phi_\\pi(s,j) + \\alpha [\\mathbb{1}_{s=j} + \\gamma \\Phi_\\pi(\\acute{s},j) - \\Phi_\\pi(s,j)]$\n",
    "\n",
    "where $s$ is the current state, $\\acute{s}$ is the next state."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Track 2: Question 2: Value Prediction with SR\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "r1_pi, r2_pi = compute_reward_vector(config)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "exact_V_pi_R1 = exact_Phi_pi.dot(r1_pi)\n",
    "approx_V_pi = approx_Phi_pi.dot(r1_pi)\n",
    "td_V_pi = result[terminal_step-1]['V_pi']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "V_pi_sr = np.zeros((state_len,1))\n",
    "V_pi_td = np.zeros((state_len,1))\n",
    "\n",
    "err_sr = []\n",
    "err_regular_td = []\n",
    "\n",
    "for s in range(terminal_step):\n",
    "    V_pi_sr = result[s]['Phi_pi'].dot(r1_pi)\n",
    "    err_sr.append(np.mean(np.square(V_pi_sr - exact_V_pi_R1)))\n",
    "\n",
    "    V_pi_td = result[s]['V_pi']\n",
    "    err_regular_td.append(np.mean(np.square(V_pi_td - exact_V_pi_R1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fdf829b4668>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting value function error for the two algorithms:\n",
    "plt.ylabel('Mean-squared error')\n",
    "plt.xlabel('Number of steps')\n",
    "plt.title('Value Function error comparison between SR and regular TD(0)')\n",
    "plt.plot(err_sr, label='SR')\n",
    "plt.plot(err_regular_td, label='TD0')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This graph shows that mean-squared error for value-function calculated by two different methods:\n",
    "1. Using the successor representation as described in the previous section, repeated here:\n",
    "First we calculate the $\\Phi_\\pi$ using the one-step update rule:\n",
    "\n",
    "  $\\Phi_\\pi(s,j) \\leftarrow \\Phi_\\pi(s,j) + \\alpha [\\mathbb{1}_{s=j} + \\gamma \\Phi_\\pi(\\acute{s},j) - \\Phi_\\pi(s,j)]$\n",
    "\n",
    "  following which we can calculate the value function as:\n",
    "\n",
    "  $V_\\pi = \\Phi_\\pi R_\\pi\\$\n",
    "\n",
    "2. By vanilla TD(0) method:\n",
    "\n",
    "  $V_\\pi(s) \\leftarrow V_\\pi(s) + \\alpha [R_t + \\gamma V_\\pi(\\acute{s}) - V_\\pi(s)]$\n",
    "\n",
    "The baseline used for the error computation is the calculated directly from the matrix computation given by:\n",
    "\n",
    "$V_\\pi = \\Phi_\\pi R_\\pi\\ \\ $ where $\\ \\ \\Phi_\\pi = (I - \\gamma P_\\pi)^{-1}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 3: Tracking with SR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "config = init_default_config_tenbyten()\n",
    "config['switch_reward'] = True\n",
    "result = run_experiment(config)\n",
    "\n",
    "state_len = config['maze_params']['row']*config['maze_params']['col']\n",
    "terminal_step = config['terminal_step']\n",
    "switch_step = config['switch_reward_at_step']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Calculate exact phi_pi for 10x10 gridworld\n",
    "gamma = config['learning_alg_params']['gamma']\n",
    "P_pi = compute_transition_mtx(config)\n",
    "exact_Phi_pi = inv(np.identity(state_len)-gamma*P_pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r1_pi, r2_pi = compute_reward_vector(config)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "exact_V_R1 = exact_Phi_pi.dot(r1_pi) \n",
    "exact_V_R2 = exact_Phi_pi.dot(r2_pi)\n",
    "\n",
    "err_sr = []\n",
    "err_regular_td = []\n",
    "\n",
    "for s in range(terminal_step):\n",
    "    if s <= switch_step:\n",
    "        pass\n",
    "        V_pi_sr = result[s]['Phi_pi'].dot(r1_pi)\n",
    "        err_sr.append(np.mean(np.square(V_pi_sr - exact_V_R1)))\n",
    "        \n",
    "        V_pi_td = result[s]['V_pi']\n",
    "        err_regular_td.append(np.mean(np.square(V_pi_td - exact_V_R1)))\n",
    "    else:\n",
    "        V_pi_sr = result[s]['Phi_pi'].dot(r2_pi)\n",
    "        err_sr.append(np.mean(np.square(V_pi_sr - exact_V_R2)))\n",
    "    \n",
    "        V_pi_td = result[s]['V_pi']\n",
    "        err_regular_td.append(np.mean(np.square(V_pi_td - exact_V_R2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fdfa094a668>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting value function error for the two algorithms:\n",
    "plt.ylabel('Mean-squared error')\n",
    "plt.xlabel('Number of steps')\n",
    "plt.title('Value Function error comparison between SR and regular TD(0)')\n",
    "plt.plot(err_sr, label='SR')\n",
    "plt.plot(err_regular_td, label='TD0')\n",
    "plt.axvline(x=switch_step, color='grey', linestyle='--')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot represents the errors same as in previous section. But in this case we change the reward function at 39000th step. From 0 to 40000th step the reward function is given by:\n",
    "\n",
    "$R(\\acute{s}) = 0 \\ \\ $ if $\\ \\ \\acute{s} == (9,9) \\ \\ $  $-1$ otherwise\n",
    "\n",
    "And from 40000th step till the end the reward is given by:\n",
    "\n",
    "$R(\\acute{s}) = 1 \\ \\ $ if $\\ \\ \\acute{s} == (9,9) \\ \\ $  $0$ otherwise.\n",
    "\n",
    "As we can see, since the successor representation method learns temporal behaviour of the policy, it's estimate of the value function is still very accurate after the change in the reward function. But TD(0) develops a big error in it's estimate of the value function during the switch in reward, but given some time, its is able to adapt to the change."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 4: Eigendecomposition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We compute 20 eigenvectors of our SR representation and plot them. While our environment does not contain obstacles we do observe the geometrical decomposition as seen in the empty room examples of the paper. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x1440 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nrow, ncol = config['maze_params']['row'], config['maze_params']['col']\n",
    "eig_vals, eig_vecs = np.linalg.eig(exact_Phi_pi)\n",
    "\n",
    "vec_ids = np.flip(np.argsort(eig_vals), 0)[:20]\n",
    "\n",
    "fig = plt.figure(figsize=(16, 20))\n",
    "\n",
    "for n, i in enumerate(vec_ids):\n",
    "    new_vec = eig_vecs[:,i].reshape([nrow,ncol])\n",
    "    \n",
    "    ax1 = fig.add_subplot(5, 4, n+1)   \n",
    "    ax1.imshow(new_vec)"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}