minimal_agent_IFE.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ENV_SIZE = 16\n",
    "INITIAL_POSITION = 0\n",
    "FOOD_POSITION = 8\n",
    "MOVEMENT_PROBABILITY = 0.75\n",
    "\n",
    "# Sensory dynamics parameters\n",
    "MAX_SENSE_PROBABILITY = 4**(-1/16) # k\n",
    "SENSE_DECAY_RATE = np.log(4)/16 # omega\n",
    "\n",
    "# Number of epochs (simulation steps).\n",
    "EPOCHS = 100\n",
    "\n",
    "# Number of gradient descent steps made to update beliefs in each epoch.\n",
    "N_STEPS = 100\n",
    "LEARNING_RATE = 0.8\n",
    "\n",
    "# No preference for position\n",
    "#DESIRED_POSITIONS = [0.0] * ENV_SIZE\n",
    "\n",
    "# Fuzzy preference distributed around a specified position.\n",
    "pos = 2\n",
    "rng = np.arange(ENV_SIZE)\n",
    "DESIRED_POSITIONS = MAX_SENSE_PROBABILITY * np.exp(-SENSE_DECAY_RATE * np.minimum((rng - pos) % ENV_SIZE,\n",
    "                                                                                  (pos - rng) % ENV_SIZE))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "# Position (external state), Psi \\in (0,15)\n",
    "Psi = tf.Variable(initial_value=INITIAL_POSITION, trainable=False, dtype=tf.int32, name='external')\n",
    "\n",
    "# Sensory state, S \\in {0, 1}\n",
    "S = tf.Variable(initial_value=1, trainable=False, dtype=tf.int32, name='sensory')\n",
    "\n",
    "# Action state, A \\in {-1, 1}\n",
    "A = tf.Variable(initial_value=1, trainable=False, dtype=tf.int32, name='action')\n",
    "\n",
    "# Internal state, R \\in R^16\n",
    "R = tf.Variable(initial_value=[0.0]*ENV_SIZE, trainable=False, dtype=tf.float32, name='internal')\n",
    "\n",
    "# Internal state (as intention), Ri \\in R^16\n",
    "Ri = tf.Variable(initial_value=DESIRED_POSITIONS, trainable=False, dtype=tf.float32, name='internal_intention')\n",
    "\n",
    "# Internal state (as belief), Rb \\in R^16\n",
    "Rb = tf.Variable(initial_value=[0.0]*ENV_SIZE, trainable=True, dtype=tf.float32, name='internal_belief')\n",
    "\n",
    "\n",
    "def environmental_dynamics(psi, a):\n",
    "    \"\"\"\n",
    "    P(Psi' | Psi, A)\n",
    "    Probability of a new position given the old position and selected action.\n",
    "    \"\"\"\n",
    "    return tf.scatter_nd(tf.cast([[psi % ENV_SIZE], [(psi + a) % ENV_SIZE]], tf.int32),\n",
    "                         tf.stack([1 - MOVEMENT_PROBABILITY, MOVEMENT_PROBABILITY]),\n",
    "                         [ENV_SIZE])\n",
    "\n",
    "\n",
    "def sensory_dynamics(psi):\n",
    "    \"\"\"\n",
    "    P(S | Psi)\n",
    "    Probability of experiencing sensory state 1 given current position.\n",
    "    \"\"\"\n",
    "    return MAX_SENSE_PROBABILITY * tf.exp(-SENSE_DECAY_RATE * tf.cast(\n",
    "                        tf.minimum((psi - FOOD_POSITION) % ENV_SIZE,\n",
    "                                   (FOOD_POSITION - psi) % ENV_SIZE),\n",
    "                        tf.float32))\n",
    "\n",
    "\n",
    "def model_encoding(R):\n",
    "    \"\"\"\n",
    "    Probability of occupying specific position as encoded in the internal state.\n",
    "    \"\"\"\n",
    "    return tf.nn.softmax(R)\n",
    "\n",
    "\n",
    "def generative_density(R, a):\n",
    "    \"\"\"\n",
    "    P(Psi', S | R, A)\n",
    "    Agent's prediction of its new position given its internal state and selected action\n",
    "    (calculated separately for two sensory states).\n",
    "    \"\"\"\n",
    "    return tf.stack([\n",
    "        tf.reduce_sum(\n",
    "            tf.stack([environmental_dynamics(psi, a) * (1-sensory_dynamics(psi)) * model_encoding(R)[psi]\n",
    "                      for psi in range(ENV_SIZE)], axis=0), axis=0),\n",
    "        tf.reduce_sum(\n",
    "            tf.stack([environmental_dynamics(psi, a) * sensory_dynamics(psi) * model_encoding(R)[psi]\n",
    "                      for psi in range(ENV_SIZE)], axis=0), axis=0)])\n",
    "\n",
    "\n",
    "def variational_density(R):\n",
    "    \"\"\"\n",
    "    P(Psi | R)\n",
    "    Agent's belief about the external states (i.e. its current position in the \n",
    "    world) or intention (i.e. desired position in the world) as encoded in the\n",
    "    internal state.\n",
    "    \"\"\"\n",
    "    return model_encoding(R)\n",
    "\n",
    "\n",
    "def KL(a, b):\n",
    "    \"\"\"\n",
    "    Kullback-Leibler divergence between densities a and b.\n",
    "    \"\"\"\n",
    "    return tf.reduce_sum(a * tf.log(a/b))\n",
    "\n",
    "\n",
    "def free_energy(R1, R, s, a):\n",
    "    \"\"\"\n",
    "    KL divergence between variational density and generative density for a fixed\n",
    "    sensory state s.\n",
    "    \"\"\"\n",
    "    return KL(variational_density(R1), generative_density(R, a)[s])\n",
    "\n",
    "\n",
    "update_sensor = S.assign(tf.cond(tf.less(tf.random_uniform([1])[0], sensory_dynamics(Psi)), lambda: 1, lambda: 0))\n",
    "choose_action = A.assign(tf.cond(tf.less(free_energy(Ri, R, S, -1), free_energy(Ri, R, S, 1)), lambda: -1, lambda: 1))\n",
    "\n",
    "clear_belief = Rb.assign(tf.constant([0.0]*16))\n",
    "update_belief = R.assign(Rb)\n",
    "\n",
    "update_position = Psi.assign(tf.cond(tf.less(tf.random_uniform([1])[0], MOVEMENT_PROBABILITY),\n",
    "                                     lambda: (Psi + A) % ENV_SIZE, lambda: Psi))\n",
    "\n",
    "belief_optimizer_step = tf.train.GradientDescentOptimizer(LEARNING_RATE).minimize(free_energy(Rb, R, S, A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initializing the variables\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "Psi_trace = []\n",
    "R_trace = []\n",
    "\n",
    "# Launch the graph\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "    \n",
    "    for epoch in range(EPOCHS):\n",
    "        sess.run([update_sensor, choose_action, clear_belief])\n",
    "        for step in range(N_STEPS):\n",
    "            sess.run(belief_optimizer_step)\n",
    "        sess.run([update_belief, update_position]) \n",
    "        \n",
    "        Psi_trace.append(Psi.eval())\n",
    "        R_trace.append(R.eval())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {},
   "outputs": [
    {
     "data": {
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M4k0ZERERERFRBo0p0Ifb7bYBeArAHABhAP/q8XiOpLBeRERERERE08JYn5Rd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f67e559b470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15, 4))\n",
    "ax = fig.gca()\n",
    "\n",
    "ax.imshow(np.exp(R_trace).T / np.sum(np.exp(R_trace), axis=1), interpolation=\"nearest\", aspect=\"auto\")\n",
    "ax.scatter(list(range(EPOCHS)), Psi_trace, color=\"red\")\n",
    "ax.invert_yaxis()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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