Simple RL Example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "be59e66d",
   "metadata": {},
   "source": [
    "# Car Tank Leakage"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5a79730",
   "metadata": {},
   "source": [
    "A car has a tank leakage. The car is moving at constant speed v toward the mechanic shop. The air resistance is proportional to the cube of the velocity. The leakage rate is constant. Find the speed that minimizes fuel consumption and maximizes the chance of arriving at the mechanic in time before the car stops"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "365b9f51",
   "metadata": {},
   "source": [
    "![Car](./car.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffaf8a8c",
   "metadata": {},
   "source": [
    "The fuel consumption rate is than equal to: $$Consumption Rate = \\alpha v^3 + \\beta$$ \n",
    "\n",
    "where $\\alpha$ is a constant representing the air drug coefficient and $\\beta$ is a constant representing the leakage rate.\n",
    "\n",
    "If the distance to the mechanic is equal to $d$ than the time to arrive to the mechanic is $\\frac{d}{v}$ and the total fuel consumption is $$Total Consumption = (\\alpha v^3 + \\beta)\\times(\\frac{d}{v}) = d(\\alpha v^2 + \\frac{\\beta}{v})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f67621d",
   "metadata": {},
   "source": [
    "# Analytical solution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdfa449e",
   "metadata": {},
   "source": [
    "The solution is the value of $v$ that solves the equation: $$\\frac{d}{dv} TotalConsumption = 0$$\n",
    "since the function goes to infinity and there is only one minimum. Computing the derivative we obtain:\n",
    "$$2 \\alpha v - \\frac{\\beta}{v^2} = 0$$\n",
    "$$2\\alpha v = \\frac{\\beta}{v^2}$$\n",
    "$$2\\alpha v^3 = \\beta$$\n",
    "$$v = \\sqrt[3]{\\frac{\\beta}{2 \\alpha}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e84a52c2",
   "metadata": {},
   "source": [
    "# DDPG - Deep Deterministic Policy Gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "446fb586",
   "metadata": {},
   "source": [
    "It was first described in 2015 in the paper «Continuous control with deep reinforcement learning».\n",
    "It's a Deep Reinforcement Learning method used to solve optimization problems with continuous action space.\n",
    "The algorithm can be described as follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edca57b7",
   "metadata": {},
   "source": [
    "![DDPG1](./DDPG1.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5b90b36",
   "metadata": {},
   "source": [
    "However, in the example we are studying, there's just the present state. The action selected will not change the probability of which will be the future state, so there is no need to select a sub-optimal solution to maximize a future reward. We just have to optimize the current state. In a problem of this kind, where there is no future state (or the future state is independent of the action selected in the current state), the DDPG algorithm can be simplified as follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "574a0249",
   "metadata": {},
   "source": [
    "![DDPG1](./DDPG2.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "773d60df",
   "metadata": {},
   "source": [
    "The networks cooperate to find the solution to the optimization problem: the Actor and the Critic. The Actor predicts the best policy given the current state, the Critic must predict the value of the Q function given state and action."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "840708f4",
   "metadata": {},
   "source": [
    "### Let's train an agent that given $\\alpha$ and $\\beta$ finds the best speed to optimize fuel consumption"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ff3d2349",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\evezzali\\.conda\\envs\\my_env\\lib\\site-packages\\numpy\\_distributor_init.py:32: UserWarning: loaded more than 1 DLL from .libs:\n",
      "C:\\Users\\evezzali\\.conda\\envs\\my_env\\lib\\site-packages\\numpy\\.libs\\libopenblas.PYQHXLVVQ7VESDPUVUADXEVJOBGHJPAY.gfortran-win_amd64.dll\n",
      "C:\\Users\\evezzali\\.conda\\envs\\my_env\\lib\\site-packages\\numpy\\.libs\\libopenblas.WCDJNK7YVMPZQ2ME2ZZHJJRJ3JIKNDB7.gfortran-win_amd64.dll\n",
      "  stacklevel=1)\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "from tensorflow.keras import layers\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from glob import glob\n",
    "from tensorflow.keras.models import Sequential\n",
    "from tqdm import tqdm\n",
    "import cv2, json\n",
    "\n",
    "from tensorflow.keras.layers import Dense\n",
    "from tensorflow.keras.models import Sequential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "50ef8be3",
   "metadata": {},
   "outputs": [],
   "source": [
    "config = tf.compat.v1.ConfigProto()\n",
    "config.gpu_options.allow_growth = True\n",
    "session =tf.compat.v1.InteractiveSession(config=config)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e67c953e",
   "metadata": {},
   "source": [
    "For this problem let's say that $\\alpha, \\beta \\in [0.1, 1.0]$. If we set the search boundary for $v$ as $[0.1, 2.0]$ the solution is always contained in the search boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3ad2c7aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_states = 2            # Number of state variables (alpha and beta)\n",
    "num_actions = 1           # Number of action variables (velocity)\n",
    "upper_bound = 2.0         # Action upper bound\n",
    "lower_bound = 0.1         # Action lower bound"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8854dd29",
   "metadata": {},
   "source": [
    "# We define the architectures for actor and critic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cc2dea89",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_actor():\n",
    "    # Initialize weights between -3e-3 and 3-e3\n",
    "    last_init = tf.random_uniform_initializer(minval=-0.003, maxval=0.003)\n",
    "\n",
    "    inputs = layers.Input(shape=(num_states,))\n",
    "    out = layers.Dense(16, activation=\"relu\", kernel_regularizer=tf.keras.regularizers.L2(l2=0.001))(inputs)\n",
    "    out = layers.Dense(16, activation=\"relu\", kernel_regularizer=tf.keras.regularizers.L2(l2=0.001))(out)\n",
    "    outputs = layers.Dense(num_actions, activation=\"sigmoid\", kernel_initializer=last_init)(out)\n",
    "\n",
    "    outputs = outputs * (upper_bound-lower_bound) + lower_bound\n",
    "    model = tf.keras.Model(inputs, outputs)\n",
    "    return model\n",
    "\n",
    "def get_critic():\n",
    "    # State as input\n",
    "    state_input = layers.Input(shape=(num_states))\n",
    "    state_out = layers.Dense(32, activation=\"relu\", kernel_regularizer=tf.keras.regularizers.L2(l2=0.001))(state_input)\n",
    "\n",
    "    # Action as input\n",
    "    action_input = layers.Input(shape=(num_actions))\n",
    "    action_out = layers.Dense(32, activation=\"relu\", kernel_regularizer=tf.keras.regularizers.L2(l2=0.001))(action_input)\n",
    "\n",
    "    # Both are passed through seperate layer before concatenating\n",
    "    concat = layers.Concatenate()([state_out, action_out])\n",
    "\n",
    "    out = layers.Dense(32, activation=\"relu\", kernel_regularizer=tf.keras.regularizers.L2(l2=0.001))(concat)\n",
    "    outputs = layers.Dense(1)(out)\n",
    "\n",
    "    # Outputs single value for give state-action\n",
    "    model = tf.keras.Model([state_input, action_input], outputs)\n",
    "\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c453f499",
   "metadata": {},
   "source": [
    "The replay buffer stores the las $n$ examples to keep in memory past examples and use them multiple times. The replay buffer is a circular buffer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "02c4ab5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Buffer:\n",
    "    def __init__(self, buffer_capacity=10000, batch_size=64):\n",
    "        # Number of \"experiences\" to store at max\n",
    "        self.buffer_capacity = buffer_capacity\n",
    "        # Num of tuples to train on.\n",
    "        self.batch_size = batch_size\n",
    "\n",
    "        # Its tells us num of times record() was called.\n",
    "        self.buffer_counter = 0\n",
    "\n",
    "        # Instead of list of tuples as the exp.replay concept go\n",
    "        # We use different np.arrays for each tuple element\n",
    "        self.state_buffer = np.zeros((self.buffer_capacity, num_states))\n",
    "        self.action_buffer = np.zeros((self.buffer_capacity, num_actions))\n",
    "        self.reward_buffer = np.zeros((self.buffer_capacity, 1))\n",
    "\n",
    "    # Takes (s,a,r) obervation tuple as input\n",
    "    def record(self, obs_tuple):\n",
    "        # Set index to zero if buffer_capacity is exceeded,\n",
    "        # replacing old records\n",
    "        index = self.buffer_counter % self.buffer_capacity\n",
    "\n",
    "        self.state_buffer[index] = np.squeeze(obs_tuple[0])\n",
    "        self.action_buffer[index] = np.squeeze(obs_tuple[1])\n",
    "        self.reward_buffer[index] = obs_tuple[2]\n",
    "\n",
    "        self.buffer_counter += 1\n",
    "\n",
    "\n",
    "    @tf.function\n",
    "    def update(self, state_batch, action_batch, reward_batch):\n",
    "        # Critic Training Step\n",
    "        with tf.GradientTape() as tape:\n",
    "            target_actions = target_actor(state_batch, training=True)\n",
    "            critic_value = critic_model([state_batch, action_batch], training=True)\n",
    "            critic_loss = tf.math.reduce_mean(tf.math.square(reward_batch - critic_value))\n",
    "\n",
    "        critic_grad = tape.gradient(critic_loss, critic_model.trainable_variables)\n",
    "        critic_optimizer.apply_gradients(\n",
    "            zip(critic_grad, critic_model.trainable_variables)\n",
    "        )\n",
    "        \n",
    "        # Actor Training Step\n",
    "        with tf.GradientTape() as tape:\n",
    "            actions = actor_model(state_batch, training=True)\n",
    "            critic_value = critic_model([state_batch, actions], training=True)\n",
    "            actor_loss = -tf.math.reduce_mean(critic_value)\n",
    "\n",
    "        actor_grad = tape.gradient(actor_loss, actor_model.trainable_variables)\n",
    "        actor_optimizer.apply_gradients(\n",
    "            zip(actor_grad, actor_model.trainable_variables)\n",
    "        )\n",
    "\n",
    "    # We compute the loss and update parameters\n",
    "    def learn(self):\n",
    "        # Get sampling range\n",
    "        record_range = min(self.buffer_counter, self.buffer_capacity)\n",
    "        # Randomly sample indices\n",
    "        batch_indices = np.random.choice(record_range, self.batch_size)\n",
    "\n",
    "        # Convert to tensors\n",
    "        state_batch = tf.convert_to_tensor(self.state_buffer[batch_indices])\n",
    "        action_batch = tf.convert_to_tensor(self.action_buffer[batch_indices])\n",
    "        reward_batch = tf.convert_to_tensor(self.reward_buffer[batch_indices])\n",
    "        reward_batch = tf.cast(reward_batch, dtype=tf.float32)\n",
    "\n",
    "        self.update(state_batch, action_batch, reward_batch)\n",
    "\n",
    "\n",
    "# This update target parameters slowly (weight averaging)\n",
    "# Based on rate `tau`, which is much less than one.\n",
    "@tf.function\n",
    "def update_target(target_weights, weights, tau):\n",
    "    for (a, b) in zip(target_weights, weights):\n",
    "        a.assign(b * tau + a * (1 - tau))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a7ef13a",
   "metadata": {},
   "source": [
    "As policy we take the actions selected by the actor plus gaussian noise. Noise is used to make the agent explore the solution space. The standard deviation can be constant or can change during training (usually it gets progressively small, like in this notebook).\n",
    "Noise is not applied during inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6940a078",
   "metadata": {},
   "outputs": [],
   "source": [
    "def policy(state, std):\n",
    "    sampled_actions = tf.squeeze(actor_model(state)).numpy()\n",
    "\n",
    "    sampled_actions = sampled_actions + np.random.normal(0, std, sampled_actions.shape).astype('float32')\n",
    "\n",
    "    # We make sure action is within bounds\n",
    "    legal_action = np.clip(sampled_actions, lower_bound, upper_bound)\n",
    "\n",
    "    return [np.squeeze(legal_action)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cc94a4c",
   "metadata": {},
   "source": [
    "The reward must increase when the total consumption goes down. A function that is inversely proportional to the total consumption will do.\n",
    "In particular, if we divide the total consuption by $-d$ we remove the need to know $d$.\n",
    "\n",
    "$$Reward = -\\alpha v^2 - \\frac{b}{v}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "07376df1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_reward(state, action):\n",
    "    a, b = np.squeeze(state)\n",
    "    v = np.squeeze(action)\n",
    "    return -a*(v**2)-b/v"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d99ad84a",
   "metadata": {},
   "source": [
    "# Definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "17dda60b",
   "metadata": {},
   "outputs": [],
   "source": [
    "policy_std_dev = 0.3 #Initial Action Noise\n",
    "batch_size = 128\n",
    "\n",
    "#Actor and critics used to compute the policy during training\n",
    "actor_model = get_actor()\n",
    "critic_model = get_critic()\n",
    "\n",
    "#Actual model obtained through weight averaging\n",
    "target_actor = get_actor()\n",
    "target_critic = get_critic()\n",
    "\n",
    "# Making the weights equal initially\n",
    "target_actor.set_weights(actor_model.get_weights())\n",
    "target_critic.set_weights(critic_model.get_weights())\n",
    "\n",
    "# Learning rate for actor-critic models\n",
    "critic_lr = 0.002\n",
    "actor_lr = 0.001\n",
    "\n",
    "critic_optimizer = tf.keras.optimizers.Adam(critic_lr)\n",
    "actor_optimizer = tf.keras.optimizers.Adam(actor_lr)\n",
    "\n",
    "# Used to update target networks\n",
    "tau = 0.05\n",
    "\n",
    "buffer = Buffer(10000, batch_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb6f88e1",
   "metadata": {},
   "source": [
    "# Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cb38e630",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode * 100 * Avg Consumption: 1.471\n",
      "Episode * 200 * Avg Consumption: 1.819\n",
      "Episode * 300 * Avg Consumption: 1.613\n",
      "Episode * 400 * Avg Consumption: 1.522\n",
      "Episode * 500 * Avg Consumption: 1.491\n",
      "Episode * 600 * Avg Consumption: 1.453\n",
      "Episode * 700 * Avg Consumption: 1.417\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_20812/4110755287.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     11\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     12\u001b[0m     \u001b[0mstate\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'float32'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 13\u001b[1;33m     \u001b[0maction\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpolicy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpolicy_std_dev\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     14\u001b[0m     \u001b[0mreward\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcompute_reward\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maction\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     15\u001b[0m     \u001b[0mreward_list\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mreward\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_20812/3392143551.py\u001b[0m in \u001b[0;36mpolicy\u001b[1;34m(state, std)\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mpolicy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstd\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m     \u001b[0msampled_actions\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msqueeze\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mactor_model\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[0msampled_actions\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msampled_actions\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnormal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstd\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msampled_actions\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'float32'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\.conda\\envs\\my_env\\lib\\site-packages\\tensorflow\\python\\keras\\engine\\base_layer.py\u001b[0m in \u001b[0;36m__call__\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1028\u001b[0m         with autocast_variable.enable_auto_cast_variables(\n\u001b[0;32m   1029\u001b[0m             self._compute_dtype_object):\n\u001b[1;32m-> 1030\u001b[1;33m           \u001b[0moutputs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcall_fn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0minputs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1031\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1032\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_activity_regularizer\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\.conda\\envs\\my_env\\lib\\site-packages\\tensorflow\\python\\keras\\engine\\functional.py\u001b[0m in \u001b[0;36mcall\u001b[1;34m(self, inputs, training, mask)\u001b[0m\n\u001b[0;32m    419\u001b[0m     \"\"\"\n\u001b[0;32m    420\u001b[0m     return self._run_internal_graph(\n\u001b[1;32m--> 421\u001b[1;33m         inputs, training=training, mask=mask)\n\u001b[0m\u001b[0;32m    422\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    423\u001b[0m   \u001b[1;32mdef\u001b[0m \u001b[0mcompute_output_shape\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minput_shape\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\.conda\\envs\\my_env\\lib\\site-packages\\tensorflow\\python\\keras\\engine\\functional.py\u001b[0m in \u001b[0;36m_run_internal_graph\u001b[1;34m(self, inputs, training, mask)\u001b[0m\n\u001b[0;32m    554\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    555\u001b[0m         \u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwargs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnode\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmap_arguments\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtensor_dict\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 556\u001b[1;33m         \u001b[0moutputs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnode\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlayer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    557\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    558\u001b[0m         \u001b[1;31m# Update tensor_dict.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\.conda\\envs\\my_env\\lib\\site-packages\\tensorflow\\python\\keras\\engine\\base_layer.py\u001b[0m in \u001b[0;36m__call__\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1028\u001b[0m         with autocast_variable.enable_auto_cast_variables(\n\u001b[0;32m   1029\u001b[0m             self._compute_dtype_object):\n\u001b[1;32m-> 1030\u001b[1;33m           \u001b[0moutputs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcall_fn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0minputs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1031\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1032\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_activity_regularizer\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\.conda\\envs\\my_env\\lib\\site-packages\\tensorflow\\python\\keras\\layers\\core.py\u001b[0m in \u001b[0;36mcall\u001b[1;34m(self, inputs)\u001b[0m\n\u001b[0;32m   1240\u001b[0m             self.kernel, ids, weights, combiner='sum')\n\u001b[0;32m   1241\u001b[0m       \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1242\u001b[1;33m         \u001b[0moutputs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgen_math_ops\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mMatMul\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0minputs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkernel\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1243\u001b[0m     \u001b[1;31m# Broadcast kernel to inputs.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1244\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\.conda\\envs\\my_env\\lib\\site-packages\\tensorflow\\python\\util\\tf_export.py\u001b[0m in \u001b[0;36mwrapper\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m    402\u001b[0m           \u001b[1;34m'Please pass these args as kwargs instead.'\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    403\u001b[0m           .format(f=f.__name__, kwargs=f_argspec.args))\n\u001b[1;32m--> 404\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    405\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    406\u001b[0m   \u001b[1;32mreturn\u001b[0m \u001b[0mtf_decorator\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmake_decorator\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdecorator_argspec\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mf_argspec\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\.conda\\envs\\my_env\\lib\\site-packages\\tensorflow\\python\\ops\\gen_math_ops.py\u001b[0m in \u001b[0;36mmat_mul\u001b[1;34m(a, b, transpose_a, transpose_b, name)\u001b[0m\n\u001b[0;32m   5694\u001b[0m       _result = pywrap_tfe.TFE_Py_FastPathExecute(\n\u001b[0;32m   5695\u001b[0m         \u001b[0m_ctx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"MatMul\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mname\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"transpose_a\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtranspose_a\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"transpose_b\"\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 5696\u001b[1;33m         transpose_b)\n\u001b[0m\u001b[0;32m   5697\u001b[0m       \u001b[1;32mreturn\u001b[0m \u001b[0m_result\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   5698\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0m_core\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_NotOkStatusException\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# To store reward history of each episode\n",
    "reward_list = []\n",
    "avg_reward_list = []\n",
    "\n",
    "for i in range(20000):\n",
    "    \n",
    "    #Drag coefficient\n",
    "    a = np.random.uniform(0.1, 1.0)\n",
    "    #Leakage rate\n",
    "    b = np.random.uniform(0.1, 1.0)\n",
    "    \n",
    "    state = np.array([[a,b]]).astype('float32')\n",
    "    action = policy(state, policy_std_dev)\n",
    "    reward = compute_reward(state, action)\n",
    "    reward_list.append(reward)\n",
    "    \n",
    "    #Save (state, action, reward) into the replay buffer\n",
    "    buffer.record((state, action, reward))\n",
    "    \n",
    "    #Computing a training step with a random batch taken from the replay buffer\n",
    "    buffer.learn()\n",
    "    update_target(target_actor.variables, actor_model.variables, tau)\n",
    "    update_target(target_critic.variables, critic_model.variables, tau)\n",
    "    \n",
    "    # Reduce policy noise (reduces exploration, increases exploitation)\n",
    "    policy_std_dev = max(policy_std_dev/(1+2e-4), 0.05)\n",
    "    \n",
    "    \n",
    "    if (i+1)%100 == 0:\n",
    "        avg_reward_list.append(np.mean(reward_list[-1000:]))\n",
    "        print(\"Episode * {} * Avg Consumption: {}\".format(str(i+1), -np.round(avg_reward_list[-1],3)))\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f379ed5",
   "metadata": {},
   "source": [
    "# Check Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ef48ad43",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Blue Curve: consumption per unit of distance travelled\n",
      "Red Line: Predicted Solution\n",
      "Green Line: Optimal Solution\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('Blue Curve: consumption per unit of distance travelled')\n",
    "print('Red Line: Predicted Solution')\n",
    "print('Green Line: Optimal Solution')\n",
    "def optimal_result(a,b):\n",
    "    return np.cbrt(b/(2*a))\n",
    "\n",
    "from matplotlib.widgets import Slider, Button, CheckButtons\n",
    "%matplotlib notebook\n",
    "\n",
    "\n",
    "# The parametrized function to be plotted\n",
    "def f(v,a,b):\n",
    "    return a*(v**2)+b/v\n",
    "\n",
    "\n",
    "t = np.linspace(0.1, 2, 200)\n",
    "\n",
    "# Define initial parameters\n",
    "init_a = 0.25\n",
    "init_b = 0.25\n",
    "state = np.array([[init_a,init_b]]).astype('float32')\n",
    "v_pred = np.squeeze(target_actor(state).numpy())\n",
    "v_opt = optimal_result(init_a, init_b)\n",
    "\n",
    "# Create the figure and the line that we will manipulate\n",
    "fig, ax = plt.subplots()\n",
    "line, = plt.plot(t, f(t, init_a, init_b), lw=2)\n",
    "v_line = plt.axvline(x=v_pred, linewidth=1, color='r', label='line1')\n",
    "v_line_opt = plt.axvline(x=v_opt, linewidth=1, color='g', label='line2')\n",
    "v_line_opt.set_visible(not v_line_opt.get_visible())\n",
    "ax.set_xlabel('Velocity')\n",
    "\n",
    "# adjust the main plot to make room for the sliders\n",
    "plt.subplots_adjust(left=0.25, bottom=0.25)\n",
    "\n",
    "# Make a vertically oriented slider to control alpha\n",
    "axamp = plt.axes([0.1, 0.25, 0.0225, 0.63])\n",
    "a_slider = Slider(\n",
    "    ax=axamp,\n",
    "    label=\"alpha\",\n",
    "    valmin=0.1,\n",
    "    valmax=1,\n",
    "    valinit=init_a,\n",
    "    orientation=\"vertical\"\n",
    ")\n",
    "\n",
    "# Make a horizontal slider to control the beta\n",
    "axfreq = plt.axes([0.25, 0.1, 0.65, 0.03])\n",
    "b_slider = Slider(\n",
    "    ax=axfreq,\n",
    "    label='beta',\n",
    "    valmin=0.1,\n",
    "    valmax=1,\n",
    "    valinit=init_b,\n",
    ")\n",
    "\n",
    "#Draw Checkbox\n",
    "rax = plt.axes([0.7, 0.78, 0.25, 0.2])\n",
    "check = CheckButtons(rax, ['Draw Solution'], [False])\n",
    "\n",
    "\n",
    "# The function to be called anytime a slider's value changes\n",
    "def update(val):\n",
    "    \n",
    "    state = np.array([[a_slider.val, b_slider.val]]).astype('float32')\n",
    "    v_pred = np.squeeze(target_actor(state).numpy())\n",
    "    v_opt = optimal_result(a_slider.val, b_slider.val)\n",
    "    line.set_ydata(f(t, a_slider.val, b_slider.val))\n",
    "    v_line.set_xdata(v_pred)\n",
    "    v_line_opt.set_xdata(v_opt)\n",
    "    fig.canvas.draw_idle()\n",
    "\n",
    "\n",
    "# register the update function with each slider\n",
    "b_slider.on_changed(update)\n",
    "a_slider.on_changed(update)\n",
    "\n",
    "# Create a `matplotlib.widgets.Button` to reset the sliders to initial values.\n",
    "resetax = plt.axes([0.8, 0.025, 0.1, 0.04])\n",
    "button = Button(resetax, 'Reset', hovercolor='0.975')\n",
    "\n",
    "def toggle(event):\n",
    "    v_line_opt.set_visible(not v_line_opt.get_visible())\n",
    "    \n",
    "def reset(event):\n",
    "    b_slider.reset()\n",
    "    a_slider.reset()\n",
    "    v_line_opt.set_visible(True)\n",
    "\n",
    "button.on_clicked(reset)\n",
    "check.on_clicked(toggle)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5dbdfa4f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}