lspi.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Least Squares Policy Iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = 10, 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Environment\n",
    "\n",
    "Let's get a really simple environment going -- we'll try to replicate\n",
    "the paper's results with the [NChain-v0](https://gym.openai.com/envs/NChain-v0/) \n",
    "environment.  The environment wrapped up in OpenAI puts a large reward at the\n",
    "end of the chain, so the optimal strategy is always to go right.  The problem\n",
    "is made slightly more difficult in that there is a high probability of \n",
    "movement error, and you always receive a small reward for going left.\n",
    "\n",
    "We can solve this pretty easily (1-3 iterations of LSPI with only quadratic \n",
    "basis functions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gym"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length = 10\n",
    "\n",
    "env = gym.make('NChain-v0', n=length)\n",
    "env.reset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Discrete(2)"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.action_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Discrete(10)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.observation_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "obs, reward, done, _ = env.step(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LSTDQ: Least Squares Temporal Difference Q-Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lspi.policy import RandomPolicy, DiscreteActionBasisPolicy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lspi.basis import IndActionPolyStateBasis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  1.,  2.,  4.])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis = IndActionPolyStateBasis(action_space=gym.spaces.Discrete(2), observation_space=gym.spaces.Discrete(10), order=2)\n",
    "basis(2, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,\n",
       "        0.  ,  0.  ,  0.  ,  1.  ,  1.  ,  1.  ,  1.  ,  0.1 ,  0.1 ,\n",
       "        0.1 ,  0.1 ,  0.01,  0.01,  0.01,  0.01])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis = IndActionPolyStateBasis(action_space=gym.spaces.Discrete(2), observation_space=gym.make(\"CartPole-v0\").observation_space, order=2)\n",
    "basis(np.ones(4) * 0.1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lspi.optim import LSTDQ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lspi.util import generate_sample_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = generate_sample_data(1e3, env, RandomPolicy(env))\n",
    "\n",
    "basis = IndActionPolyStateBasis(env.action_space, env.observation_space, order=2)\n",
    "lstdq = LSTDQ(basis, discount=0.1)\n",
    "lstdq = lstdq.fit(data, RandomPolicy(env))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lspi.policy import DiscreteActionBasisPolicy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis = IndActionPolyStateBasis(env.action_space, env.observation_space, order=2)\n",
    "dabp = DiscreteActionBasisPolicy(env.action_space, basis, lstdq.weights_)\n",
    "dabp(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lspi.optim import LSPI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running LSPI on OpenAI's NChain-v0 environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = generate_sample_data(1e3, env, RandomPolicy(env))\n",
    "lstdq = LSTDQ(basis, discount=0.7)\n",
    "basis = IndActionPolyStateBasis(env.action_space, env.observation_space, order = 2)\n",
    "dabp = DiscreteActionBasisPolicy(env.action_space, basis, np.zeros(basis.rank))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<lspi.optim.LSPI at 0x7fb6f20b2198>"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lspi = LSPI(lstdq, dabp, max_iter=50, epsilon=1e-5)\n",
    "lspi.fit(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lspi.itr_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "1\n",
      "1\n",
      "1\n",
      "1\n",
      "1\n",
      "1\n",
      "1\n",
      "1\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "for state in range(env.observation_space.n):\n",
    "    print(lspi.policy(state))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As desired, the learned optimal action for all states is to move to the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb6f1f04128>"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for ind, line in enumerate(lspi.policy.history_):\n",
    "    plt.plot(line, label=f\"{ind}\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More complicated chain problems\n",
    "\n",
    "In the [LSPI paper](https://www2.cs.duke.edu/research/AI/LSPI/) they test on some more complex chains:  \n",
    "\n",
    "* chains with rewards on either end \n",
    "* chains with rewards in the middle\n",
    "\n",
    "I grabbed [the NChain-v0 code](https://github.com/openai/gym/blob/master/gym/envs/toy_text/nchain.py)\n",
    "from OpenAI's github, and modified it \n",
    "to support chains of this structure in the file \n",
    "[environments.py](./environments.py)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "from environments import NChainEnv\n",
    "\n",
    "length = 10\n",
    "\n",
    "# first and last states have a reward\n",
    "reward = np.zeros(length)\n",
    "reward[2] = 1\n",
    "reward[7] = 1\n",
    "\n",
    "env = NChainEnv(reward, slip=0.0, wrap=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = generate_sample_data(1e4, env, RandomPolicy(env))\n",
    "basis = IndActionPolyStateBasis(env.action_space, env.observation_space, order=3)\n",
    "lstdq = LSTDQ(basis, discount=0.7)\n",
    "dabp = DiscreteActionBasisPolicy(env.action_space, basis, np.zeros(basis.rank))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<lspi.optim.LSPI at 0x7fb6f20a8198>"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lspi = LSPI(lstdq, dabp, max_iter=100, epsilon=1e-3)\n",
    "lspi.fit(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lspi.itr_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 1, 0, 0, 0, 1, 1, 1, 0, 0]"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "policy = [lspi.policy(state) for state in range(env.observation_space.n)]\n",
    "policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "expected = np.array([1, 1, 0, 0, 0, 1, 1, 1, 0, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "policies = []\n",
    "for test in range(20):\n",
    "    lspi.fit(data)\n",
    "    policy = [lspi.policy(state) for state in range(env.observation_space.n)]\n",
    "    policies.append(policy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean([pol == expected for pol in policies])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cartpole"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make(\"CartPole-v0\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<TimeLimit<CartPoleEnv<CartPole-v0>>>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Discrete(2)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.action_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Box(4,)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.observation_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "state = env.reset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.00139939, -0.03437892,  0.02808837, -0.04591466])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = generate_sample_data(1e4, env, RandomPolicy(env))\n",
    "basis = IndActionPolyStateBasis(env.action_space, env.observation_space, order=10)\n",
    "lstdq = LSTDQ(basis, discount=0.7)\n",
    "dabp = DiscreteActionBasisPolicy(env.action_space, basis, np.zeros(basis.rank))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<__main__.LSPI at 0x7fb6f5657b38>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lspi = LSPI(lstdq, dabp, max_iter=50, epsilon=1e-3)\n",
    "lspi.fit(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lspi.itr_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb6f35ba748>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for ind, line in enumerate(lspi.policy.history_):\n",
    "    plt.plot(line, label=f\"{ind}\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "numsteps = []\n",
    "actions = []\n",
    "\n",
    "for episode in range(1000):\n",
    "    state = env.reset()\n",
    "    done = False\n",
    "    steps = 0\n",
    "    while not done:\n",
    "        action = lspi.policy(state)\n",
    "        actions.append(action)\n",
    "        state, reward, done, _ = env.step(action)\n",
    "        steps += 1\n",
    "    numsteps.append(steps)\n",
    "#     print(f\"Episode {episode}, Steps: {steps}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(actions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we're just moving left at every iteration... Which is basically the \n",
    "worst policy you could learn haha.  Obviously something is going wrong\n",
    "either with basis evaluation / weighting or we're not using complex\n",
    "enough bases.  I'm going to implement RBF bases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 155.,    0.,    0.,  415.,    0.,    0.,  404.,    0.,    0.,   26.]),\n",
       " array([  8. ,   8.3,   8.6,   8.9,   9.2,   9.5,   9.8,  10.1,  10.4,\n",
       "         10.7,  11. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlkAAAFpCAYAAACvaj13AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAFzVJREFUeJzt3X+wZnV9H/D3p6yiJqmAXCzuYpbqduKPqWi3hMaZjBXHIDouttJi20gtzcYZnGiTaYN2psZMnepMEhw7LR0UyppJRWpMoUpiCGqNf4BZDCKIlo1S2bADN4KoY0MDfvrHPavXy13uw9773Xvv7us1c+Y553u+53k+z5fD5c359VR3BwCAtfXX1rsAAICjkZAFADCAkAUAMICQBQAwgJAFADCAkAUAMICQBQAwgJAFADCAkAUAMICQBQAwwJb1LiBJTj755N6+fft6lwEAsKJbbrnlL7p7bqV+GyJkbd++PXv37l3vMgAAVlRV/2eWfk4XAgAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMsGW9C4CjxfZLPrHeJayJu9/z6vUuAeCo4EgWAMAAQhYAwABCFgDAAEIWAMAAQhYAwABCFgDAADOHrKo6rqr+tKo+Pi2fXlU3V9VdVfWRqnry1H78tLxvWr99TOkAABvXE3lO1luT3Jnkr0/L701yaXdfXVX/JclFSS6bXh/s7udW1QVTv3+8hjUDHHOOluewJZ7FxrFjpiNZVbUtyauTfHBariQvT/LRqcueJOdN87um5Uzrz576AwAcM2Y9Xfi+JP8myfen5Wck+VZ3PzIt70+ydZrfmuSeJJnWPzT1BwA4ZqwYsqrqNUnu7+5bFjcv07VnWLf4fXdX1d6q2js/Pz9TsQAAm8UsR7JemuS1VXV3kquzcJrwfUlOqKqD13RtS3LvNL8/yWlJMq1/epIHlr5pd1/e3Tu7e+fc3NyqvgQAwEazYsjq7rd397bu3p7kgiSf6u5/muTTSV4/dbswybXT/HXTcqb1n+ruxxzJAgA4mq3mOVm/muSXq2pfFq65umJqvyLJM6b2X05yyepKBADYfJ7IIxzS3Z9J8plp/mtJzlymz18mOX8NagMA2LQ88R0AYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBggBVDVlU9pao+X1VfrKo7qupdU/tVVfX1qrp1ms6Y2quq3l9V+6rqtqp6yegvAQCw0WyZoc/DSV7e3d+tqicl+VxV/f607l9390eX9H9Vkh3T9NNJLpteAQCOGSseyeoF350WnzRN/Tib7EryoWm7m5KcUFWnrr5UAIDNY6ZrsqrquKq6Ncn9SW7o7punVe+eTgleWlXHT21bk9yzaPP9UxsAwDFjppDV3Y929xlJtiU5s6pemOTtSX4qyd9NclKSX52613JvsbShqnZX1d6q2js/P39YxQMAbFRP6O7C7v5Wks8kOae7D0ynBB9O8l+TnDl125/ktEWbbUty7zLvdXl37+zunXNzc4dVPADARjXL3YVzVXXCNP/UJK9I8pWD11lVVSU5L8nt0ybXJXnjdJfhWUke6u4DQ6oHANigZrm78NQke6rquCyEsmu6++NV9amqmsvC6cFbk7x56n99knOT7EvyvSRvWvuyAQA2thVDVnffluTFy7S//BD9O8nFqy8NAGDz8sR3AIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABVgxZVfWUqvp8VX2xqu6oqndN7adX1c1VdVdVfaSqnjy1Hz8t75vWbx/7FQAANp5ZjmQ9nOTl3f2iJGckOaeqzkry3iSXdveOJA8muWjqf1GSB7v7uUkunfoBABxTVgxZveC70+KTpqmTvDzJR6f2PUnOm+Z3TcuZ1p9dVbVmFQMAbAIzXZNVVcdV1a1J7k9yQ5I/S/Kt7n5k6rI/ydZpfmuSe5JkWv9QkmesZdEAABvdTCGrux/t7jOSbEtyZpLnLddtel3uqFUvbaiq3VW1t6r2zs/Pz1ovAMCm8ITuLuzubyX5TJKzkpxQVVumVduS3DvN709yWpJM65+e5IFl3uvy7t7Z3Tvn5uYOr3oAgA1qlrsL56rqhGn+qUlekeTOJJ9O8vqp24VJrp3mr5uWM63/VHc/5kgWAMDRbMvKXXJqkj1VdVwWQtk13f3xqvpykqur6t8n+dMkV0z9r0jy21W1LwtHsC4YUDcAwIa2Ysjq7tuSvHiZ9q9l4fqspe1/meT8NakOAGCT8sR3AIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAFWDFlVdVpVfbqq7qyqO6rqrVP7r1XVn1fVrdN07qJt3l5V+6rqq1X1cyO/AADARrRlhj6PJPmV7v5CVf1Ekluq6oZp3aXd/RuLO1fV85NckOQFSZ6V5I+q6m9196NrWTgAwEa24pGs7j7Q3V+Y5r+T5M4kWx9nk11Jru7uh7v760n2JTlzLYoFANgsntA1WVW1PcmLk9w8Nb2lqm6rqiur6sSpbWuSexZttj+PH8oAAI46M4esqvrxJL+b5G3d/e0klyV5TpIzkhxI8psHuy6zeS/zfruram9V7Z2fn3/ChQMAbGQzhayqelIWAtbvdPfHkqS77+vuR7v7+0k+kB+eEtyf5LRFm29Lcu/S9+zuy7t7Z3fvnJubW813AADYcGa5u7CSXJHkzu7+rUXtpy7q9rokt0/z1yW5oKqOr6rTk+xI8vm1KxkAYOOb5e7Clyb5+SRfqqpbp7Z3JHlDVZ2RhVOBdyf5xSTp7juq6pokX87CnYkXu7MQADjWrBiyuvtzWf46q+sfZ5t3J3n3KuoCANjUPPEdAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGAAIQsAYAAhCwBgACELAGCAFUNWVZ1WVZ+uqjur6o6qeuvUflJV3VBVd02vJ07tVVXvr6p9VXVbVb1k9JcAANhoZjmS9UiSX+nu5yU5K8nFVfX8JJckubG7dyS5cVpOklcl2TFNu5NctuZVAwBscCuGrO4+0N1fmOa/k+TOJFuT7EqyZ+q2J8l50/yuJB/qBTclOaGqTl3zygEANrAndE1WVW1P8uIkNyd5ZncfSBaCWJJTpm5bk9yzaLP9UxsAwDFj5pBVVT+e5HeTvK27v/14XZdp62Xeb3dV7a2qvfPz87OWAQCwKcwUsqrqSVkIWL/T3R+bmu87eBpwer1/at+f5LRFm29Lcu/S9+zuy7t7Z3fvnJubO9z6AQA2pFnuLqwkVyS5s7t/a9Gq65JcOM1fmOTaRe1vnO4yPCvJQwdPKwIAHCu2zNDnpUl+PsmXqurWqe0dSd6T5JqquijJN5KcP627Psm5SfYl+V6SN61pxQAAm8CKIau7P5flr7NKkrOX6d9JLl5lXQAAm5onvgMADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMsGWlDlV1ZZLXJLm/u184tf1akl9IMj91e0d3Xz+te3uSi5I8muSXuvuTA+o+LNsv+cR6l7Am7n7Pq9e7BABgBbMcyboqyTnLtF/a3WdM08GA9fwkFyR5wbTNf66q49aqWACAzWLFkNXdn03ywIzvtyvJ1d39cHd/Pcm+JGeuoj4AgE1pNddkvaWqbquqK6vqxKlta5J7FvXZP7UBABxTDjdkXZbkOUnOSHIgyW9O7bVM317uDapqd1Xtraq98/Pzy3UBANi0Ditkdfd93f1od38/yQfyw1OC+5OctqjrtiT3HuI9Lu/und29c25u7nDKAADYsA4rZFXVqYsWX5fk9mn+uiQXVNXxVXV6kh1JPr+6EgEANp9ZHuHw4SQvS3JyVe1P8s4kL6uqM7JwKvDuJL+YJN19R1Vdk+TLSR5JcnF3PzqmdACAjWvFkNXdb1im+YrH6f/uJO9eTVEAAJudJ74DAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAywYsiqqiur6v6qun1R20lVdUNV3TW9nji1V1W9v6r2VdVtVfWSkcUDAGxUsxzJuirJOUvaLklyY3fvSHLjtJwkr0qyY5p2J7lsbcoEANhcVgxZ3f3ZJA8sad6VZM80vyfJeYvaP9QLbkpyQlWdulbFAgBsFod7TdYzu/tAkkyvp0ztW5Pcs6jf/qkNAOCYstYXvtcybb1sx6rdVbW3qvbOz8+vcRkAAOvrcEPWfQdPA06v90/t+5OctqjftiT3LvcG3X15d+/s7p1zc3OHWQYAwMZ0uCHruiQXTvMXJrl2Ufsbp7sMz0ry0MHTigAAx5ItK3Woqg8neVmSk6tqf5J3JnlPkmuq6qIk30hy/tT9+iTnJtmX5HtJ3jSgZgCADW/FkNXdbzjEqrOX6dtJLl5tUQAAm50nvgMADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADCBkAQAMIGQBAAwgZAEADLBlNRtX1d1JvpPk0SSPdPfOqjopyUeSbE9yd5J/1N0Prq5MAIDNZS2OZP397j6ju3dOy5ckubG7dyS5cVoGADimjDhduCvJnml+T5LzBnwGAMCGttqQ1Un+sKpuqardU9szu/tAkkyvp6zyMwAANp1VXZOV5KXdfW9VnZLkhqr6yqwbTqFsd5I8+9nPXmUZAAAby6qOZHX3vdPr/Ul+L8mZSe6rqlOTZHq9/xDbXt7dO7t759zc3GrKAADYcA47ZFXVj1XVTxycT/LKJLcnuS7JhVO3C5Ncu9oiAQA2m9WcLnxmkt+rqoPv89+6+w+q6k+SXFNVFyX5RpLzV18mAMDmctghq7u/luRFy7R/M8nZqykKAGCz88R3AIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABhCwAgAGELACAAYQsAIABtqx3AQDA+tp+ySfWu4Q1c/d7Xr3eJfyAI1kAAAMIWQAAAwhZAAADCFkAAAMIWQAAAwhZAAADCFkAAAMIWQAAAwhZAAADCFkAAAMIWQAAAwhZAAADCFkAAAMIWQAAAwhZAAADDAtZVXVOVX21qvZV1SWjPgcAYCMaErKq6rgk/ynJq5I8P8kbqur5Iz4LAGAjGnUk68wk+7r7a939/5JcnWTXoM8CANhwRoWsrUnuWbS8f2oDADgmbBn0vrVMW/9Ih6rdSXZPi9+tqq8OqmWxk5P8xRH4nKHqvetdwQ8cFeO5waz7mG6g/WstrPt4HoVWPaZH2T62WvbRNVbvPSJj+pOzdBoVsvYnOW3R8rYk9y7u0N2XJ7l80Ocvq6r2dvfOI/mZRzPjufaM6doynmvPmK4t47n2NtKYjjpd+CdJdlTV6VX15CQXJLlu0GcBAGw4Q45kdfcjVfWWJJ9MclySK7v7jhGfBQCwEY06XZjuvj7J9aPe/zAd0dOTxwDjufaM6doynmvPmK4t47n2NsyYVnev3AsAgCfEz+oAAAxw1IWsqvpXVXVHVd1eVR+uqqcsWX98VX1k+rmfm6tq+/pUunnMMKb/vKrmq+rWafqX61XrZlBVb53G8o6qetsy66uq3j/to7dV1UvWo87NZIYxfVlVPbRoH/1361HnRlZVV1bV/VV1+6K2k6rqhqq6a3o98RDbXjj1uauqLjxyVW9cqxzPRxftq24amxxiTM+f/r3/flUd8o7C9fqpv6MqZFXV1iS/lGRnd78wCxfdX7Ck20VJHuzu5ya5NIkntjyOGcc0ST7S3WdM0wePaJGbSFW9MMkvZOFXEV6U5DVVtWNJt1cl2TFNu5NcdkSL3GRmHNMk+eNF++ivH9EiN4erkpyzpO2SJDd2944kN07LP6KqTkryziQ/nYV/Bu88VHg4xlyVwxjPyf9dtK++dmCNm81VeeyY3p7kHyT57KE2Ws+f+juqQtZkS5KnVtWWJE/LkudzZeHnffZM8x9NcnZVLffwVH5opTFlds9LclN3f6+7H0nyv5K8bkmfXUk+1AtuSnJCVZ16pAvdRGYZU1bQ3Z9N8sCS5sV/L/ckOW+ZTX8uyQ3d/UB3P5jkhjz2P4THnFWMJ4ew3Jh2953dvdLDzNftp/6OqpDV3X+e5DeSfCPJgSQPdfcfLun2g5/8mf4gP5TkGUeyzs1kxjFNkn84ndr6aFWdtsx6Ftye5Ger6hlV9bQk5+ZHH9yb+FmqJ2qWMU2Sv1dVX6yq36+qFxzZEjetZ3b3gSSZXk9Zpo/9dXazjGeSPKWq9lbVTVUliK3euu2jR1XImg5R70pyepJnJfmxqvpnS7sts6lbLA9hxjH9n0m2d/ffTvJH+eH/qbFEd9+ZhVPUNyT5gyRfTPLIkm720SdgxjH9QpKf7O4XJfmPSf7HES3y6GZ/XXvPnp5Y/k+SvK+qnrPeBW1y67aPHlUhK8krkny9u+e7+6+SfCzJzyzp84Of/JlOfz09jz2kyw+tOKbd/c3ufnha/ECSv3OEa9xUuvuK7n5Jd/9sFva9u5Z0WfFnqfhRK41pd3+7u787zV+f5ElVdfI6lLrZ3HfwVPX0ev8yfeyvs5tlPNPd906vX0vymSQvPlIFHqXWbR892kLWN5KcVVVPm66zOjvJnUv6XJfk4N0vr0/yqfawsMez4pguuV7otUvX86Oq6pTp9dlZuGDzw0u6XJfkjdNdhmdl4RTtgSNc5qay0phW1d84eO1lVZ2Zhb993zzSdW5Ci/9eXpjk2mX6fDLJK6vqxOnI9yunNh5rxfGcxvH4af7kJC9N8uUjVuHRaf1+6q+7j6opybuSfCUL12n8dpLjk/x6ktdO65+S5L8n2Zfk80n+5nrXvNGnGcb0PyS5IwunaT6d5KfWu+aNPCX54yz80fxikrOntjcnefM0X1m4E+bPknwpC3d2rnvdG3maYUzfsmgfvSnJz6x3zRttykIwPZDkr7Lwf/4XZeF61RuzcGTwxiQnTX13Jvngom3/xfQ3dV+SN633d9kI0+GOZxbOFHxp2le/lOSi9f4uG2U6xJi+bpp/OMl9ST459X1WkusXbXtukv89/V39t0eqZk98BwAY4Gg7XQgAsCEIWQAAAwhZAAADCFkAAAMIWQAAAwhZAAADCFkAAAMIWQAAA/x/Z5uW88k1umAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(numsteps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "numsteps = []\n",
    "policy = RandomPolicy(env)\n",
    "\n",
    "for episode in range(1000):\n",
    "    state = env.reset()\n",
    "    done = False\n",
    "    steps = 0\n",
    "    while not done:\n",
    "        action = policy(state)\n",
    "        state, reward, done, _ = env.step(action)\n",
    "        steps += 1\n",
    "    numsteps.append(steps)\n",
    "#     print(f\"Episode {episode}, Steps: {steps}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 447.,  346.,  107.,   58.,   22.,   13.,    4.,    2.,    0.,    1.]),\n",
       " array([   8. ,   17.8,   27.6,   37.4,   47.2,   57. ,   66.8,   76.6,\n",
       "          86.4,   96.2,  106. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(numsteps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CartPole Debugging\n",
    "\n",
    "OK, so cartpole isn't working at all.  The policy learnts to move left\n",
    "in all states.  I might try to get some rendering working real quick just\n",
    "to make sure I'm not doing anything crazy... I'm missing an OpenGL library \n",
    "in this container...  But then I'd have to recreate the container... This\n",
    "is probably why @cannon used so much docker commit hahaah"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Better Bases\n",
    "\n",
    "While that's installing / building, let's check out what features we should \n",
    "be using.  Shamelessly going to pull from @jack here.  Looks like \n",
    "these are the features that work best for CartPole:\n",
    "\n",
    "```python\n",
    "def get_cartpole_basis_functions_v2():\n",
    "    '''\n",
    "    Returns a list of basis functions that seem \n",
    "    to work well for the simplified (no singularity, starting above the horizon)\n",
    "    cartpole problem.\n",
    "    \n",
    "    Note: this one seems to work the best so far.\n",
    "    '''\n",
    "    s1 = np.array([1,1,1,1])\n",
    "    s2 = np.array([0,0,0,0])\n",
    "    s3 = np.array([1,0,1,0])\n",
    "\n",
    "    bf1 = lambda s,a: 1\n",
    "\n",
    "    bf2 = lambda s,a: int(a==0)*np.exp( - np.linalg.norm(s-s1)/2.0)\n",
    "    bf3 = lambda s,a: int(a==1)*np.exp( - np.linalg.norm(s-s1)/2.0)\n",
    "\n",
    "    bf4 = lambda s,a: int(a==0)*np.exp( - np.linalg.norm(s-s2)/2.0)\n",
    "    bf5 = lambda s,a: int(a==1)*np.exp( - np.linalg.norm(s-s2)/2.0)\n",
    "\n",
    "    bf6 = lambda s,a: int(a==0)*np.exp( - np.linalg.norm(s-s3)/2.0)\n",
    "    bf7 = lambda s,a: int(a==1)*np.exp( - np.linalg.norm(s-s3)/2.0)\n",
    "    \n",
    "    \n",
    "    bfs = [bf1,bf2, bf3, bf4, bf5, bf6, bf7]\n",
    "    \n",
    "    return bfs\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "from environments import NChainEnv\n",
    "\n",
    "length = 10\n",
    "\n",
    "# first and last states have a reward\n",
    "reward = np.zeros(length)\n",
    "reward[2] = 1\n",
    "reward[7] = 1\n",
    "\n",
    "env = NChainEnv(reward, slip=0.0, wrap=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = generate_sample_data(1e4, env, RandomPolicy(env))\n",
    "basis = IndActionPolyStateBasis(env.action_space, env.observation_space, order=3)\n",
    "lstdq = LSTDQ(basis, discount=0.7)\n",
    "dabp = DiscreteActionBasisPolicy(env.action_space, basis, np.zeros(basis.rank))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.60653066,  0.36787944,  0.22313016,  0.13533528,\n",
       "        0.082085  ,  0.04978707,  0.03019738,  0.01831564,  0.011109  ,\n",
       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lspi.basis import IndActionRBFStateBasis\n",
    "\n",
    "basis = IndActionRBFStateBasis(list(range(env.observation_space.n)), env.action_space, env.observation_space)\n",
    "basis(0, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "        1.        ,  0.60653066,  0.36787944,  0.22313016,  0.13533528,\n",
       "        0.082085  ,  0.04978707,  0.03019738,  0.01831564,  0.011109  ])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make(\"CartPole-v0\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "ename": "AssertionError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-126-e7ad91edffae>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m ], env.action_space, env.observation_space)\n\u001b[0m\u001b[1;32m      7\u001b[0m \u001b[0mlstdq\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mLSTDQ\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbasis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdiscount\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.7\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mdabp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mDiscreteActionBasisPolicy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0menv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maction_space\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbasis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbasis\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrank\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/work/lspi/basis.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, anchors, action_space, observation_space, metric)\u001b[0m\n\u001b[1;32m    116\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_anchors\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0manchors\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    117\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0manch\u001b[0m \u001b[0;32min\u001b[0m \u001b[0manchors\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 118\u001b[0;31m             \u001b[0;32massert\u001b[0m \u001b[0manch\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_observation_space\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    119\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    120\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_num_actions\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_action_space\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAssertionError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "data = generate_sample_data(1e4, env, RandomPolicy(env))\n",
    "basis = IndActionRBFStateBasis([\n",
    "    np.array([1,1,1,1]),\n",
    "    np.array([0,0,0,0]),\n",
    "    np.array([1,0,1,0])\n",
    "], env.action_space, env.observation_space)\n",
    "lstdq = LSTDQ(basis, discount=0.7)\n",
    "dabp = DiscreteActionBasisPolicy(env.action_space, basis, np.zeros(basis.rank))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<__main__.LSPI at 0x7fb6f5657b38>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lspi = LSPI(lstdq, dabp, max_iter=50, epsilon=1e-3)\n",
    "lspi.fit(data)"
   ]
  }
 ],
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