Imitation_learning_2d.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "from Code.GDTW import gromov_dtw \n",
    "import torch.nn as nn\n",
    "from torch.utils.data import DataLoader\n",
    "import pickle\n",
    "from imageio import imread\n",
    "import sklearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Defining the Expert Policy $y_{exp}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def twospirals(linspace,n_points, noise=.01):\n",
    "    \"\"\"\n",
    "     Returns the two spirals dataset.\n",
    "    \"\"\"\n",
    "    n = np.sqrt(linspace.reshape(-1,1)) * 780 * (2*np.pi)/360\n",
    "    d1x = -np.cos(n)*n + np.random.rand(n_points,1) * noise\n",
    "    d1y = np.sin(n)*n + np.random.rand(n_points,1) * noise\n",
    "    return np.hstack((d1x,d1y))+1\n",
    "    \n",
    "\n",
    "y_exp=twospirals((torch.exp(torch.linspace(0,1.42,35))-1)/3.13,35,0)/20\n",
    "y_exp=torch.tensor(y_exp)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1234f1cd0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(y_exp[:,0],y_exp[:,1], c = np.arange(len(y_exp)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Defining the Actor's artitecture $\\pi_{\\theta}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "class MLP(nn.Module):\n",
    "\n",
    "        def __init__(self,state_dim=2,hidden_dim=128,action_dim=2):\n",
    "            super(MLP, self).__init__()\n",
    "\n",
    "            main = nn.Sequential(\n",
    "                nn.Linear(state_dim, hidden_dim),\n",
    "                nn.ReLU(True),\n",
    "                nn.Linear(hidden_dim, hidden_dim),\n",
    "                nn.ReLU(True),\n",
    "                nn.Linear(hidden_dim, action_dim),\n",
    "            )\n",
    "            self.main = main\n",
    "\n",
    "        def forward(self, state):\n",
    "\n",
    "            output = self.main(state)\n",
    "            return output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performing rollouts $x_\\theta \\in \\mathcal{X}^T$ under the current policy $\\pi_\\theta$ starting at $ x_0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agent rollouts under the current policy $\\pi_\\theta$ and transition dynamics $\\mathcal{T}$, and starting at $x_\\theta^{(0)}$ are generated in the following way:\n",
    "\n",
    "$$\\forall t=1,...,T: a_t = \\pi_{\\theta}(x_\\theta^{(t)}), \\quad x_\\theta^{(t+1)}= \\mathcal{T}(x_\\theta^{(t)},a_t)$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rollout(x0,actor,episode_len):\n",
    "    state=x0\n",
    "    states=state\n",
    "    \n",
    "    for step in range(episode_len):\n",
    "        action = actor(state)\n",
    "        new_state=action+state\n",
    "        states = torch.cat((states,new_state),0) \n",
    "        state=new_state\n",
    "        \n",
    "        \n",
    "    return(states)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experimental setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_epochs=6000\n",
    "\n",
    "#Length of rollouts T\n",
    "episode_len=37\n",
    "\n",
    "#Defining the policy $|pi_\\theta$'s architecture and optimizer\n",
    "actor=MLP(state_dim=2,hidden_dim=64,action_dim=2)\n",
    "optimizer = torch.optim.Adam(actor.parameters(), lr=5e-5, betas=(0.5, 0.99))\n",
    "\n",
    "#Defining the distance GDTW\n",
    "GDTW = gromov_dtw(max_iter=10,gamma=0.1,loss_only=1,dtw_approach='soft_GDTW',verbose=0)\n",
    "\n",
    "#Defining the agent's initial location (the same as the expert's initial location here)\n",
    "x0=y_exp[0].reshape(1,-1).float()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we train the model by minimizing the GDTW between the expert trajectory $y_{exp}$ and the agent's rollout $x_\\theta$ w.r.t the agent policy $\\pi_\\theta$'s parameters, namely:\n",
    "\n",
    "$$\\min_{\\theta}\\text{GDTW}(y_{exp},x_\\theta)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GDTW to ground truth 66998868.0\n",
      "GDTW to ground truth 16666.67578125\n",
      "GDTW to ground truth 1108.6484375\n",
      "GDTW to ground truth 303.228759765625\n",
      "GDTW to ground truth 180.45486450195312\n",
      "GDTW to ground truth 140.47142028808594\n",
      "GDTW to ground truth 6.091541290283203\n",
      "GDTW to ground truth 4.778125286102295\n",
      "GDTW to ground truth 3.913471221923828\n",
      "GDTW to ground truth 3.239980459213257\n",
      "GDTW to ground truth 3.099473476409912\n",
      "GDTW to ground truth 2.9121103286743164\n"
     ]
    }
   ],
   "source": [
    "\n",
    "episode_rewards = []\n",
    "\n",
    "for epoch in range(num_epochs):\n",
    "    optimizer.zero_grad()\n",
    "    new_episode = rollout(x0,actor,episode_len)\n",
    "\n",
    "\n",
    "    loss = GDTW(new_episode,y_exp)\n",
    "\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "\n",
    "    episode_rewards.append(loss.item())\n",
    "    \n",
    "    if epoch%500==0:\n",
    "\n",
    "        print('GDTW to ground truth',loss.item())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting a rollout $x_\\theta$ under the learned policy $\\pi_\\theta$ and comparing to the expert's $\\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad$ rollout $y_{exp}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We note that the learned policy has to be equivalent up to isometry (translations/rotations/reflections). We therefore observe in the following plot that the expert trajectory is recovered but up to some rotation of the ground space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Rollout under expert policy')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(1,2,figsize=[10,4])\n",
    "\n",
    "roll=rollout(x0,actor,episode_len)\n",
    "\n",
    "ax[0].scatter(roll.detach()[:,0],roll.detach()[:,1],c=np.arange(len(roll)),s=4)\n",
    "ax[0].set_title('Rollout under learned policy')\n",
    "\n",
    "ax[1].scatter(y_exp[:,0],y_exp[:,1],c=np.arange(len(y_exp)),s=4)\n",
    "ax[1].set_title('Rollout under expert policy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}