Part_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First Part: MDP and optimal control\n",
    "### El Hassane Nour"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 1. Assume that V is constant in time and equal to $V_{max}$, and that moving left or right costs 'a' unit of energy. Model the problem as a MDP, and explain how to compute the optimal solution for a given discount factor $\\gamma$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.1. We define the three key elements of a MDP:\n",
    "- **State Space S**: represent the possible values of $\\theta$, which is the difference of angle between the wind orientation $\\theta_{wind}$ and the turbine orientation $\\theta_{turbine}$.\n",
    "$\\begin{equation}\n",
    "\\theta=\\theta_{wind} - \\theta_{turbine}\n",
    "\\end{equation}$\n",
    "where: $\\theta_{wind}, \\theta_{turbine} \\in [0,180]$\n",
    "\n",
    "    So, we define S as: \n",
    "\n",
    "$\\begin{equation}\n",
    "S=\\{-180, 179, ..., 0, 1, ... ,179, 180\\}\n",
    "\\end{equation}$\n",
    "\n",
    "- **Action Space A**: represent the possibles actions the wind turbine could do. That is, turn one degree left - means that $\\theta_{turbine}$ moves by minus one degree (action 0) , stay still (action 1), or turn one degree right - means that $\\theta_{turbine}$ moves by plus one degree (action 2).\n",
    "\n",
    "    So, A is defined as: \n",
    "\n",
    "$\\begin{equation}\n",
    "A=\\{0,1, 2\\}\n",
    "\\end{equation}$\n",
    "\n",
    "- **Reward Space R**: represent the reward of taking an action $a_t$ from a given state $s_t$, leading to a new state $s_{t+1}$. The reward would be equal to the energy produced during one time step which is: \n",
    "\n",
    "$\\begin{equation}\n",
    "\\begin{split}\n",
    "r(s_t,a_t) &= f(V)cos(\\theta_t)-\\alpha a \\\\\n",
    "&= cos(\\theta_t)-\\alpha a \\\\\n",
    "\\text{where: }\\alpha = \\begin{cases}\n",
    "1 & \\text{if action is 0 or 2}\\\\\n",
    "0 & \\text{if action is 1}\n",
    "\\end{cases} \n",
    "\\end{split}\n",
    "\\end{equation}$\n",
    "\n",
    "- **Transitions Probability P**: represent the Markovian transitions from a state $s_t$ by performing an action $a_t$, to a state $s_{t+1}$ with receipt of a reward $r_t$. Three actions are possible from a given state, so we assign a uniform probability distributions over these actions. That is:\n",
    "    $  P(S_{t+1} = \\theta+1 | s_t = \\theta,a_t = 0)=1/3\\\\\n",
    "    P(S_{t+1} = \\theta+1 | s_t = \\theta,a_t = 1)=0\\\\\n",
    "    P(S_{t+1} = \\theta+1 | s_t = \\theta,a_t = 2)=0\\\\\n",
    "    P(S_{t+1} = \\theta | s_t = \\theta,a_t = 0)=0\\\\\n",
    "    P(S_{t+1} = \\theta | s_t = \\theta,a_t = 1)=1/3\\\\\n",
    "    P(S_{t+1} = \\theta | s_t = \\theta,a_t = 2)=0\\\\\n",
    "    P(S_{t+1} = \\theta-1 | s_t = \\theta,a_t = 0)=0\\\\\n",
    "    P(S_{t+1} = \\theta-1 | s_t = \\theta,a_t = 1)=0\\\\\n",
    "    P(S_{t+1} = \\theta-1 | s_t = \\theta,a_t = 2)=1/3\\\\$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython import display\n",
    "display.Image(\"./mdp.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.2. Optimal solution computation for a given discount factor $\\gamma$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimal solution is defined by the best policy to follow in order to get the maximum value of power production. This could be found using the following value iteration algorithm:\n",
    "\n",
    "Algorithm: Value Iteration\n",
    "\n",
    "1 $\\epsilon$: a small number\n",
    "\n",
    "2 Initialize V(s) arbitrarily\n",
    "\n",
    "/* Loop until convergence\n",
    "\n",
    "3 $\\delta \\gets 1$\n",
    "\n",
    "4 While $\\delta > \\epsilon$\n",
    "\n",
    "5    for s $\\in$ S do\n",
    "\n",
    "6        v $\\gets$ V(s)\n",
    "\n",
    "7       V(s) $\\gets \\max_a \\sum_{s',r'}p(s',r'|s,a)[r+\\gamma V(s')]$\n",
    "\n",
    "8        $\\delta \\gets \\min(\\delta, |v-V(s)|)$\n",
    "\n",
    "9 return $\\pi$ s.t. $\\pi(s)=argmax_a V(s)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2. Implement an algorithm that finds the optimal solution and illustrate the optimal solution. You are free to choose your values of a and γ, but try to find ones that provide interesting results (Hint: Choose a close to 0 and γ close to 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [],
   "source": [
    "STATE_SPACE = list(range(-180,181)) # theta, which is the relative wind heading (wind heading - wind turbine heading)\n",
    "ACTION_SPACE = [0,1,2]\n",
    "NB_ACTIONS=len(ACTION_SPACE)\n",
    "a=0.3\n",
    "disc_fact=0.98\n",
    "V_max=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(velocity):\n",
    "    return velocity**3 if velocity<=V_max else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate the rewards for all state,action pairs\n",
    "def rewards(v):\n",
    "  reward = {} # key (s,a)\n",
    "  for s in STATE_SPACE:\n",
    "    for action in ACTION_SPACE:\n",
    "      if action in [0,2]:\n",
    "        reward[(s,action)]=f(v)*np.cos(s*np.pi/180)-a\n",
    "      else:\n",
    "        reward[(s,action)]=f(v)*np.cos(s*np.pi/180)\n",
    "  return reward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [],
   "source": [
    "# caluculate Markovian transitions from a state to another \n",
    "def trans_probs():\n",
    "    probs = {}\n",
    "    for s in STATE_SPACE :\n",
    "        for a in ACTION_SPACE:\n",
    "            probs[(s,a)] = [ 0 for i in range(len(STATE_SPACE))]\n",
    "            if a == 0: #turn left == wind turbine heading minus one\n",
    "                probs[(s,a)][STATE_SPACE.index((s+1)%180)] = 1/3\n",
    "            if a == 1: #stay still\n",
    "                probs[(s,a)][STATE_SPACE.index(s)] = 1/3\n",
    "            if a == 2: #turn right == wind turbine heading plus one\n",
    "                probs[(s,a)][STATE_SPACE.index((s-1)%180)] = 1/3\n",
    "    return probs "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [],
   "source": [
    "# finds the optimal policy that gives the optimal solution V*\n",
    "class OptimalPolicy:\n",
    "    def __init__(self,rewards,probs,gamma=0.8):\n",
    "        self.rewards = rewards\n",
    "        self.probs = probs\n",
    "        self.gamma=gamma\n",
    "        self.policy= [1 for i in range(len(STATE_SPACE))] # initialize pi(s) \n",
    "  \n",
    "    def optimal_sol(self,nb_iter):\n",
    "        V = [0 for i in range(len(STATE_SPACE))] # initialize V(s)     \n",
    "        V_new = [0 for i in range(len(STATE_SPACE))]   # copy of V(s)\n",
    "        epsilon=1e-400\n",
    "        for i in range(nb_iter):\n",
    "            delta = 0  # initialize max difference\n",
    "            index=0\n",
    "            for s in STATE_SPACE: # compute state value\n",
    "                max_value = 0\n",
    "                for a in ACTION_SPACE:\n",
    "                    val = self.rewards[(s,a)]  # get the reward\n",
    "                    if a==0:\n",
    "                        S_next=STATE_SPACE.index((s+1)%180)\n",
    "                        val += self.gamma*self.probs[(s,a)][S_next]*V[S_next]# add discounted downstream values\n",
    "                    elif a==1:\n",
    "                        val += self.gamma*self.probs[(s,a)][s]*V[index]# add discounted downstream values\n",
    "                    elif a==2:\n",
    "                        S_next=STATE_SPACE.index((s-1)%180)\n",
    "                        val += self.gamma*self.probs[(s,a)][S_next]*V[S_next]# add discounted downstream values\n",
    "                        \n",
    "                    # store best value\n",
    "                    max_value = max(max_value, val)\n",
    "\n",
    "                    # Update best policy\n",
    "                    if V[index] < val:\n",
    "                        self.policy[index]=a  # store action with highest value\n",
    "\n",
    "                V_new[index]=max_value  # update value with highest value\n",
    "                # update maximum difference\n",
    "                delta = max(delta, abs(V[index] - V_new[index]))\n",
    "                index+=1\n",
    "\n",
    "            # Update value functions\n",
    "            V = V_new\n",
    "\n",
    "            # If diff smaller than threshold delta for all states, algorithm terminates\n",
    "            if delta < epsilon:\n",
    "                break\n",
    "        return V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rwds=rewards(v=V_max)\n",
    "probs=trans_probs()\n",
    "policy=OptimalPolicy(rwds,probs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [],
   "source": [
    "nbs_iters = list(range(10,50,10))\n",
    "differences = []\n",
    "v_tmp = 0\n",
    "\n",
    "for i in nbs_iters:\n",
    "  v = policy.optimal_sol(i)\n",
    "  diff = np.linalg.norm(np.asarray(v)-np.asarray(v_tmp))\n",
    "  v_tmp = v.copy()\n",
    "  differences.append(diff)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to check the convergence of the value iteration algorithm, we plot the distances between the value-state arrays of all iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'State-value convergence')"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(nbs_iters,differences,color='red')\n",
    "plt.ylabel(\"distance\")\n",
    "plt.xlabel(\"nb iterations\")\n",
    "plt.title(\"State-value convergence\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The optimal solution is:  10.499650208971616\n",
      "The optimal policy is:  [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "print('The optimal solution is: ',max(v))\n",
    "print('The optimal policy is: ',policy.policy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 3. (*) Assume now that the wind at time t + 1 evolves as V (t + 1) = max(0, min(1.1, V (t) + b∆(t))),where ∆(t) is a value uniformly distributed between −1 and 1 and b > 0 is a parameter. Redo questions 1 and 2 above with the new model. Comment on the change of model that is needed.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, the wind velocity changes over time, which means that the rewards are also changing because they are calculated with $f(v)cos(\\theta)- ∂a$. This means that we need to calculate $V_{t+1}$ after each time step, using the formula: \n",
    "\n",
    "$V_{t+1} = max(0, min(1.1, V_t + b∆_t))$\n",
    "\n",
    "where $∆_t$ is a random value uniformly distributed between −1 and 1 and b > 0 is a parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [],
   "source": [
    "class VariableVelocityPolicy(OptimalPolicy):\n",
    "    def __init__(self, rewards, probs, speed,gamma=0.8):\n",
    "        super().__init__(rewards, probs, gamma)\n",
    "        self.speed=speed\n",
    "\n",
    "    def optimal_sol(self, nb_iter):\n",
    "        b=0.08\n",
    "        epsilon=1e-400\n",
    "        V = [0 for i in range(len(STATE_SPACE))] # initialize V(s)     \n",
    "        \n",
    "        for i in range(nb_iter):\n",
    "            delta = 0  # initialize max difference\n",
    "            index=0\n",
    "            V_new=V\n",
    "            for s in STATE_SPACE: # compute state value\n",
    "                max_value = 0\n",
    "                self.speed = max(0,min(1.1,self.speed+b*np.random.uniform(-1,1))) #calculate the new wind speed\n",
    "                for a in ACTION_SPACE:\n",
    "                    if a==0:\n",
    "                        self.rewards[(s,a)]= f(self.speed)*np.cos(s*np.pi/180)-a # update the new rewards\n",
    "                        val = self.rewards[(s,a)] \n",
    "                        S_next=STATE_SPACE.index((s+1)%180)\n",
    "                        val += self.gamma*self.probs[(s,a)][S_next]*V[S_next]# add discounted downstream values\n",
    "                    elif a==1:\n",
    "                        self.rewards[(s,a)]= f(self.speed)*np.cos(s*np.pi/180)# update the new rewards\n",
    "                        val = self.rewards[(s,a)] \n",
    "                        val += self.gamma*self.probs[(s,a)][index]*V[index]# add discounted downstream values\n",
    "                    elif a==2:\n",
    "                        self.rewards[(s,a)]= f(self.speed)*np.cos(s*np.pi/180)-a # update the new rewards\n",
    "                        val = self.rewards[(s,a)] \n",
    "                        S_next=STATE_SPACE.index((s-1)%180)\n",
    "                        val += self.gamma*self.probs[(s,a)][S_next]*V[S_next]# add discounted downstream values\n",
    "                        \n",
    "                    # store best value\n",
    "                    max_value = max(max_value, val)\n",
    "\n",
    "                    # update best policy\n",
    "                    if V[index] < val:\n",
    "                        self.policy[index]=a  # store action with highest value\n",
    "\n",
    "                V_new[index]=max_value  # update value with highest value\n",
    "                # update maximum difference\n",
    "                delta = max(delta, abs(V[index] - V_new[index]))\n",
    "                index+=1\n",
    "\n",
    "            # Update value functions\n",
    "            V = V_new\n",
    "\n",
    "            # If diff smaller than threshold delta for all states, algorithm terminates\n",
    "            if delta < epsilon:\n",
    "                break\n",
    "        return V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_speed=0.5\n",
    "V_max=2\n",
    "policy_var_speed=VariableVelocityPolicy(rewards=rewards(initial_speed),probs=probs,speed=initial_speed,gamma=0.98)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [],
   "source": [
    "nbs_iters = list(range(10,500,10))\n",
    "differences = []\n",
    "v_tmp = 0\n",
    "\n",
    "for i in nbs_iters:\n",
    "  v = policy_var_speed.optimal_sol(i)\n",
    "  diff = np.linalg.norm(np.asarray(v)-np.asarray(v_tmp))\n",
    "  v_tmp = v.copy()\n",
    "  differences.append(diff)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to check the convergence of the value iteration algorithm, we plot the distances between the value-state arrays of all iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'State-value convergence')"
      ]
     },
     "execution_count": 280,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(nbs_iters,differences,color='red')\n",
    "plt.ylabel(\"distance\")\n",
    "plt.xlabel(\"nb iterations\")\n",
    "plt.title(\"State-value convergence\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The optimal solution is:  1.4073054991559033\n",
      "The optimal policy is:  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]\n"
     ]
    }
   ],
   "source": [
    "print('The optimal solution is: ',max(v))\n",
    "print('The optimal policy is: ',policy_var_speed.policy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 4. (*) In addition to the above, assume that the wind has some momentum: with 90% chances, the change in the orientation of the wind will be the same as the one during the last time step. Redo question 1 and 2 above and comment."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the wind orientation at time ti, is now conditioned by the previous orientation, the transitions probabilities will change as the following:\n",
    "\n",
    " $  P(S_{t+1} = \\theta+1 | s_t = \\theta,a_t = 0, wo_t=1)=0.9*1/3\\\\\n",
    "    P(S_{t+1} = \\theta+1 | s_t = \\theta,a_t = 0, wo_t=0)=0.1*1/3\\\\\n",
    "    P(S_{t+1} = \\theta | s_t = \\theta,a_t = 1,wo_t=1)=0.9*1/3\\\\\n",
    "    P(S_{t+1} = \\theta | s_t = \\theta,a_t = 1,wo_t=0)=0.1*1/3\\\\\n",
    "    P(S_{t+1} = \\theta-1 | s_t = \\theta,a_t = 2,wo_t=1)=0.9*1/3\\\\\n",
    "    P(S_{t+1} = \\theta-1 | s_t = \\theta,a_t = 2,wo_t=0)=0.1*1/3\\\\$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [],
   "source": [
    "def trans_probs_conditioned():\n",
    "    probs = {}\n",
    "    wind_orientation=[0,1]\n",
    "    for s in STATE_SPACE :\n",
    "        for a in ACTION_SPACE:\n",
    "            for w in wind_orientation:\n",
    "                probs[(s,a,w)] = [ 0 for i in range(len(STATE_SPACE))]\n",
    "                if a == 0 and w==0: #turn left == wind turbine heading minus one\n",
    "                    probs[(s,a,w)][STATE_SPACE.index((s+1)%180)] = 0.1*1/3\n",
    "                elif a == 0 and w==1:\n",
    "                    probs[(s,a,w)][STATE_SPACE.index((s+1)%180)] = 0.9*1/3\n",
    "                elif a == 1 and w==0: #stay still\n",
    "                    probs[(s,a,w)][STATE_SPACE.index(s)] = 0.1*1/3\n",
    "                elif a==1 and w==1:\n",
    "                    probs[(s,a,w)][STATE_SPACE.index(s)] = 0.9*1/3\n",
    "                if a == 2 and w==0: #turn right == wind turbine heading plus one\n",
    "                    probs[(s,a,w)][STATE_SPACE.index((s-1)%180)] = 0.1*1/3\n",
    "                if a == 2 and w==1: #turn right == wind turbine heading plus one\n",
    "                    probs[(s,a,w)][STATE_SPACE.index((s-1)%180)] = 0.9*1/3  \n",
    "\n",
    "    return probs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MomentumPolicy(OptimalPolicy):\n",
    "    def __init__(self, rewards, probs, speed,gamma=0.8):\n",
    "        super().__init__(rewards, probs, gamma)\n",
    "        self.speed=speed\n",
    "        self.wind_orientation=[0,1]\n",
    "\n",
    "    def optimal_sol(self, nb_iter):\n",
    "        b=0.08\n",
    "        epsilon=1e-400\n",
    "        V = [0 for i in range(len(STATE_SPACE))] # initialize V(s)     \n",
    "        \n",
    "        for i in range(nb_iter):\n",
    "            delta = 0  # initialize max difference\n",
    "            index=0\n",
    "            V_new=V\n",
    "            for s in STATE_SPACE: # compute state value\n",
    "                max_value = 0\n",
    "                self.speed = max(0,min(1.1,self.speed+b*np.random.uniform(-1,1))) #calculate the new wind speed\n",
    "                for a in ACTION_SPACE:\n",
    "                    for w in self.wind_orientation:\n",
    "                        if a==0:\n",
    "                            self.rewards[(s,a)]= f(self.speed)*np.cos(s*np.pi/180)-a # update the new rewards\n",
    "                            val = self.rewards[(s,a)] \n",
    "                            S_next=STATE_SPACE.index((s+1)%180)\n",
    "                            val += self.gamma*self.probs[(s,a,w)][S_next]*V[S_next]# add discounted downstream values\n",
    "                        elif a==1:\n",
    "                            self.rewards[(s,a)]= f(self.speed)*np.cos(s*np.pi/180)# update the new rewards\n",
    "                            val = self.rewards[(s,a)] \n",
    "                            val += self.gamma*self.probs[(s,a,w)][index]*V[index]# add discounted downstream values\n",
    "                        elif a==2:\n",
    "                            self.rewards[(s,a)]= f(self.speed)*np.cos(s*np.pi/180)-a # update the new rewards\n",
    "                            val = self.rewards[(s,a)] \n",
    "                            S_next=STATE_SPACE.index((s-1)%180)\n",
    "                            val += self.gamma*self.probs[(s,a,w)][S_next]*V[S_next]# add discounted downstream values\n",
    "                            \n",
    "                    # store best value\n",
    "                    max_value = max(max_value, val)\n",
    "\n",
    "                    # update best policy\n",
    "                    if V[index] < val:\n",
    "                        self.policy[index]=a  # store action with highest value\n",
    "\n",
    "                V_new[index]=max_value  # update value with highest value\n",
    "                # update maximum difference\n",
    "                delta = max(delta, abs(V[index] - V_new[index]))\n",
    "                index+=1\n",
    "\n",
    "            # Update value functions\n",
    "            V = V_new\n",
    "\n",
    "            # If diff smaller than threshold delta for all states, algorithm terminates\n",
    "            if delta < epsilon:\n",
    "                break\n",
    "        return V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_speed=0.5\n",
    "V_max=2\n",
    "policy_momentum=MomentumPolicy(rewards=rewards(initial_speed),probs=trans_probs_conditioned(),speed=initial_speed,gamma=0.98)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [],
   "source": [
    "nbs_iters = list(range(10,110,10))\n",
    "differences = []\n",
    "v_tmp = 0\n",
    "\n",
    "for i in nbs_iters:\n",
    "  v = policy_momentum.optimal_sol(i)\n",
    "  diff = np.linalg.norm(np.asarray(v)-np.asarray(v_tmp))\n",
    "  v_tmp = v.copy()\n",
    "  differences.append(diff)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to check the convergence of the value iteration algorithm, we plot the distances between the value-state arrays of all iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'State-value convergence')"
      ]
     },
     "execution_count": 289,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(nbs_iters,differences,color='red')\n",
    "plt.ylabel(\"distance\")\n",
    "plt.xlabel(\"nb iterations\")\n",
    "plt.title(\"State-value convergence\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The optimal solution is:  0.7366559873917403\n",
      "The optimal policy is:  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]\n"
     ]
    }
   ],
   "source": [
    "print('The optimal solution is: ',max(v))\n",
    "print('The optimal policy is: ',policy_momentum.policy)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.7.11 ('myenv')",
   "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": "3.7.15"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "7f8cba5f5f0d0cb017b85e934e89380a2ce707bec4d9c1b9f06b2dc18e7eb81a"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}