21como-intro-to-deeplearning/3a-policy-gradient.ipynb

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    "# Introduction to Deep Learning\n",
    "\n",
    "## Hands-on 3a: Reinforcement Learning with Policy Gradient\n",
    "Giuseppe Carleo and Filippo Vicentini\n",
    "\n",
    "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/PhilipVinc/Lectures/blob/master/21como-intro-to-deeplearning/3a-policy-gradient.ipynb) \n",
    "\n",
    "### Link to the GitHub repository:\n",
    "https://github.com/PhilipVinc/IntroDeepLearning   or  https://bit.ly/3ki90ki"
   ]
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    "## Intro\n",
    "\n",
    "It's christmas and Father Christmas need to pick up some presents, but we're in the 21st century so even Babbo Natale decided to solve the problems with some AI-controlled robot elfs.\n",
    "\n",
    "Our task today is to help father christmas's robotic elfs find their way across a frozen lake, avoiding ponds, to get to the presents.\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/PhilipVinc/IntroDeepLearning/master/images/lake_init.jpg\" alt=\"drawing\" width=\"300\"/>\n",
    "\n",
    "We will use OpenAI-gym, a python package that makes it easy to work with this kind of Reinforcement Learning problems and test different models.\n",
    "We will also use Jax, and coax, a small package that allows to use jax with gym.\n",
    "Lastly, we will use haiku to define neural networks.\n",
    "\n",
    "First we need to install all the required packages"
   ]
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  {
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   "id": "e291a1fd-b3e2-4d18-920a-e1b36f2519c8",
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   "source": [
    "#!pip install gym coax jax haiku flax optax matplotlib pygame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "eb14da3d-b46c-4c6d-ba9d-5cf930c28597",
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   "source": [
    "# Import all things\n",
    "import gym               # defines the problem\n",
    "import coax              # easy to use policy gradient learning\n",
    "import jax               # \n",
    "import jax.numpy as jnp  #\n",
    "import haiku as hk       # easy to define neural networks\n",
    "import optax             # optimisers\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "37d55f19-6ed5-4db3-867a-65cb1f1a6d67",
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   "source": [
    "# First, we define the problem\n",
    "env = gym.make('CartPole-v1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "c83bc62b-9151-4f93-9087-50ae06a9daff",
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    {
     "data": {
      "text/plain": [
       "True"
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     "execution_count": 65,
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    "# We can initialise a 'trajectory', or the 'state' of the system \n",
    "env.reset()\n",
    "# And then we can 'render' the current state with fancy graphics.\n",
    "env.render()"
   ]
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    "However, how do we store in memory the data representing the position of the elf, that of the target, and how do we encode our possible actions so that we can create a mathematical model of the problem?\n",
    "\n",
    "### Observation Space\n",
    "\n",
    "The observation is a value representing the agent's current position as `current_row * nrows + current_col` (where both the row and col start at 0).\n",
    "For example, the goal position in the $4\\times4$ map can be calculated as follows: $3 \\cdot 4 + 3 = 15$.\n",
    "The number of possible observations is dependent on the size of the map.\n",
    "For example, the $4\\times 4$ map has 16 possible observations.\n",
    "\n",
    "In mathematical terms, \n",
    "$$ s_t \\in [0,15]$$"
   ]
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     "text": [
      "The observation state is:  Box([-4.8000002e+00 -3.4028235e+38 -4.1887903e-01 -3.4028235e+38], [4.8000002e+00 3.4028235e+38 4.1887903e-01 3.4028235e+38], (4,), float32)\n"
     ]
    }
   ],
   "source": [
    "print(\"The observation state is: \", env.observation_space)"
   ]
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     "text": [
      "And a random cofiguration will be:  10\n"
     ]
    }
   ],
   "source": [
    "print(\"And a random cofiguration will be: \", env.observation_space.sample())"
   ]
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    "### Action Space\n",
    "The agent takes a 1-element vector (aka, a scalar) for actions.\n",
    "The action space is `(dir)`, where `dir` decides direction to move in which can be:\n",
    "- 0: LEFT\n",
    "- 1: DOWN\n",
    "- 2: RIGHT\n",
    "- 3: UP\n",
    "\n",
    "In mathematical terms, \n",
    "$$ a_t \\in [0,3]$$"
   ]
  },
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   "cell_type": "code",
   "execution_count": 67,
   "id": "c50649e3-29bc-469a-8104-d5e0053c9ca6",
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    {
     "name": "stdout",
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     "text": [
      "The action space is:  Discrete(2)\n"
     ]
    }
   ],
   "source": [
    "print(\"The action space is: \", env.action_space)"
   ]
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    "### Reward\n",
    "\n",
    "Reward schedule $r_t(s_t)$:\n",
    "- Reach goal(G): +1\n",
    "- Reach hole(H): 0\n",
    "- Reach frozen(F): 0\n",
    "\n",
    "Note that the rewards for a succesful run will therefore be $r_0 = 0$, $r_1=0$ ... $r_T = 1$, so any succesful run will have\n",
    "$$\n",
    "R = \\sum_{t=0}^T r_t = 1,\n",
    "$$\n",
    "because we're giving a reward only when we hit the goa.\n",
    "\n",
    "This means that the reward for solving the puzzle in the smallest amount of moves, or infinitely main moves, is the same. To bias the policy to solve in fewer moves the puzzle, we can add some negative reward at every step."
   ]
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    "## Defining the policy\n",
    "\n",
    "We want to define the policy $ pi(a | s_t) $ that gives the probability of each move $a={0,1,2,3}$ given a current state configuration $s_t$.\n",
    "\n",
    "To have a simpler implentation we will define $\\pi : {0,1\\dots 15} \\rightarrow \\mathbb{R}^4 $, which will return the unnormalized log-probability of every action. "
   ]
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   "id": "080b59ec-3238-4866-9828-4a6b5d6c8e76",
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   "source": [
    "def π_fun(S, is_training):\n",
    "    logits = hk.Linear(env.action_space.n, w_init=jnp.zeros)\n",
    "    return {'logits': logits(S)}"
   ]
  },
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   "cell_type": "markdown",
   "id": "b67fefbb-7f72-4418-8594-8a281e9cf165",
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   "source": [
    "We can investigate how that works..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "a0aa8269-300e-40c7-9956-cc7192cd8416",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'logits': DeviceArray([0., 0.], dtype=float32)}"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For example, this gives us\n",
    "forward = hk.transform(π_fun)\n",
    "pars = forward.init(jax.random.PRNGKey(1), jax.numpy.ones(16), True)\n",
    "forward.apply(pars, jax.random.PRNGKey(1), jax.numpy.ones(16), True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3c0e4953-7bc3-4367-bca6-6d2f3b44f627",
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    "### Using Coax\n",
    "\n",
    "In principle we'd have to sample from the log-distribution above at every time $t$ to determine a trajectory ${s_1, a_1, s_2, a_2...}$, and we'd have to define the REINFORCE/Policy gradient algorithm ourselves.\n",
    "\n",
    "However, it turns out that somebody already did the hard work for ourselves. See for example https://coax.readthedocs.io/ so we're going to use this package going forward.\n",
    "\n",
    "We can create a Policy from the function `π_fun` and the environment description/state.\n",
    "THis is an object that encapsulates the current parameters of the policy, as well as the current state of the environment. \n",
    "It exposes a few useful functions such as:\n",
    " - `Policy.sample`, which samples a possible configuration given the state the environment is in\n",
    " - `Policy.update`, which updates the weights according to the REINFORCE gradient update"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "85f70e6c-d8b5-4427-9747-1a2f5863fb5a",
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   "source": [
    "# First we wrap the environment into a training monitor wrapper, so we can automatically log at every step some information\n",
    "env = coax.wrappers.TrainMonitor(env)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "620e4cbf-1582-4ef6-a0a3-92199a5094dd",
   "metadata": {},
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   "source": [
    "# We create the Policy funciton\n",
    "pi = coax.Policy(π_fun, env)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "40685cbb-bc83-4e3f-8833-3422d0306fa5",
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    {
     "ename": "InconclusiveDimensionOperation",
     "evalue": "Cannot divide evenly the sizes of shapes (1,) and (-1, 4)",
     "output_type": "error",
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      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mInconclusiveDimensionOperation\u001b[0m            Traceback (most recent call last)",
      "Input \u001b[0;32mIn [72]\u001b[0m, in \u001b[0;36m<cell line: 2>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# For example, what move can we have if we are in 0?\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m actions \u001b[38;5;241m=\u001b[39m [pi(\u001b[38;5;241m0\u001b[39m) \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m1000\u001b[39m)]\n",
      "Input \u001b[0;32mIn [72]\u001b[0m, in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# For example, what move can we have if we are in 0?\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m actions \u001b[38;5;241m=\u001b[39m [\u001b[43mpi\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m)\u001b[49m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m1000\u001b[39m)]\n",
      "File \u001b[0;32m~/Documents/pythonenvs/teach-rl/python-3.10.2/lib/python3.10/site-packages/coax/_core/policy.py:86\u001b[0m, in \u001b[0;36mPolicy.__call__\u001b[0;34m(self, s, return_logp)\u001b[0m\n\u001b[1;32m     59\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__call__\u001b[39m(\u001b[38;5;28mself\u001b[39m, s, return_logp\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m):\n\u001b[1;32m     60\u001b[0m     \u001b[38;5;124mr\u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     61\u001b[0m \n\u001b[1;32m     62\u001b[0m \u001b[38;5;124;03m    Sample an action :math:`a\\sim\\pi_\\theta(.|s)`.\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     84\u001b[0m \n\u001b[1;32m     85\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m---> 86\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__call__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43ms\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mreturn_logp\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mreturn_logp\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Documents/pythonenvs/teach-rl/python-3.10.2/lib/python3.10/site-packages/coax/_core/base_stochastic_func_type2.py:31\u001b[0m, in \u001b[0;36mStochasticFuncType2Mixin.__call__\u001b[0;34m(self, s, return_logp)\u001b[0m\n\u001b[1;32m     30\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__call__\u001b[39m(\u001b[38;5;28mself\u001b[39m, s, return_logp\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m):\n\u001b[0;32m---> 31\u001b[0m     S \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mobservation_preprocessor\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrng\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43ms\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     32\u001b[0m     X, logP \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39msample_func(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mparams, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfunction_state, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mrng, S)\n\u001b[1;32m     33\u001b[0m     x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mproba_dist\u001b[38;5;241m.\u001b[39mpostprocess_variate(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mrng, X)\n",
      "File \u001b[0;32m~/Documents/pythonenvs/teach-rl/python-3.10.2/lib/python3.10/site-packages/coax/utils/_array.py:332\u001b[0m, in \u001b[0;36mdefault_preprocessor.<locals>.func\u001b[0;34m(rng, X)\u001b[0m\n\u001b[1;32m    330\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mfunc\u001b[39m(rng, X):\n\u001b[1;32m    331\u001b[0m     X \u001b[38;5;241m=\u001b[39m jnp\u001b[38;5;241m.\u001b[39masarray(X, dtype\u001b[38;5;241m=\u001b[39mspace\u001b[38;5;241m.\u001b[39mdtype)   \u001b[38;5;66;03m# ensure ndarray\u001b[39;00m\n\u001b[0;32m--> 332\u001b[0m     X \u001b[38;5;241m=\u001b[39m \u001b[43mjnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mreshape\u001b[49m\u001b[43m(\u001b[49m\u001b[43mX\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mspace\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshape\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m  \u001b[38;5;66;03m# ensure batch axis\u001b[39;00m\n\u001b[1;32m    333\u001b[0m     X \u001b[38;5;241m=\u001b[39m jnp\u001b[38;5;241m.\u001b[39mclip(X, space\u001b[38;5;241m.\u001b[39mlow, space\u001b[38;5;241m.\u001b[39mhigh)  \u001b[38;5;66;03m# clip to be safe\u001b[39;00m\n\u001b[1;32m    334\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m X\n",
      "File \u001b[0;32m~/Documents/pythonenvs/teach-rl/python-3.10.2/lib/python3.10/site-packages/jax/_src/numpy/lax_numpy.py:711\u001b[0m, in \u001b[0;36mreshape\u001b[0;34m(a, newshape, order)\u001b[0m\n\u001b[1;32m    709\u001b[0m _stackable(a) \u001b[38;5;129;01mor\u001b[39;00m _check_arraylike(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mreshape\u001b[39m\u001b[38;5;124m\"\u001b[39m, a)\n\u001b[1;32m    710\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 711\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43ma\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mreshape\u001b[49m\u001b[43m(\u001b[49m\u001b[43mnewshape\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43morder\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43morder\u001b[49m\u001b[43m)\u001b[49m  \u001b[38;5;66;03m# forward to method for ndarrays\u001b[39;00m\n\u001b[1;32m    712\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mAttributeError\u001b[39;00m:\n\u001b[1;32m    713\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m _reshape(a, newshape, order\u001b[38;5;241m=\u001b[39morder)\n",
      "File \u001b[0;32m~/Documents/pythonenvs/teach-rl/python-3.10.2/lib/python3.10/site-packages/jax/_src/numpy/lax_numpy.py:729\u001b[0m, in \u001b[0;36m_reshape\u001b[0;34m(a, order, *args)\u001b[0m\n\u001b[1;32m    728\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_reshape\u001b[39m(a, \u001b[38;5;241m*\u001b[39margs, order\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mC\u001b[39m\u001b[38;5;124m\"\u001b[39m):\n\u001b[0;32m--> 729\u001b[0m   newshape \u001b[38;5;241m=\u001b[39m \u001b[43m_compute_newshape\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43mlen\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m==\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    730\u001b[0m   \u001b[38;5;28;01mif\u001b[39;00m order \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mC\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[1;32m    731\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m lax\u001b[38;5;241m.\u001b[39mreshape(a, newshape, \u001b[38;5;28;01mNone\u001b[39;00m)\n",
      "File \u001b[0;32m~/Documents/pythonenvs/teach-rl/python-3.10.2/lib/python3.10/site-packages/jax/_src/numpy/lax_numpy.py:723\u001b[0m, in \u001b[0;36m_compute_newshape\u001b[0;34m(a, newshape)\u001b[0m\n\u001b[1;32m    721\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m: iterable \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[1;32m    722\u001b[0m newshape \u001b[38;5;241m=\u001b[39m core\u001b[38;5;241m.\u001b[39mcanonicalize_shape(newshape \u001b[38;5;28;01mif\u001b[39;00m iterable \u001b[38;5;28;01melse\u001b[39;00m [newshape])\n\u001b[0;32m--> 723\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mtuple\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mcore\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdivide_shape_sizes\u001b[49m\u001b[43m(\u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshape\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnewshape\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    724\u001b[0m \u001b[43m             \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mcore\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msymbolic_equal_dim\u001b[49m\u001b[43m(\u001b[49m\u001b[43md\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43md\u001b[49m\n\u001b[1;32m    725\u001b[0m \u001b[43m             \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43md\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mnewshape\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Documents/pythonenvs/teach-rl/python-3.10.2/lib/python3.10/site-packages/jax/_src/numpy/lax_numpy.py:723\u001b[0m, in \u001b[0;36m<genexpr>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m    721\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m: iterable \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[1;32m    722\u001b[0m newshape \u001b[38;5;241m=\u001b[39m core\u001b[38;5;241m.\u001b[39mcanonicalize_shape(newshape \u001b[38;5;28;01mif\u001b[39;00m iterable \u001b[38;5;28;01melse\u001b[39;00m [newshape])\n\u001b[0;32m--> 723\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mtuple\u001b[39m(\u001b[38;5;241m-\u001b[39m \u001b[43mcore\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdivide_shape_sizes\u001b[49m\u001b[43m(\u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshape\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnewshape\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    724\u001b[0m              \u001b[38;5;28;01mif\u001b[39;00m core\u001b[38;5;241m.\u001b[39msymbolic_equal_dim(d, \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m) \u001b[38;5;28;01melse\u001b[39;00m d\n\u001b[1;32m    725\u001b[0m              \u001b[38;5;28;01mfor\u001b[39;00m d \u001b[38;5;129;01min\u001b[39;00m newshape)\n",
      "File \u001b[0;32m~/Documents/pythonenvs/teach-rl/python-3.10.2/lib/python3.10/site-packages/jax/core.py:1544\u001b[0m, in \u001b[0;36mdivide_shape_sizes\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m   1542\u001b[0m s2 \u001b[38;5;241m=\u001b[39m s2 \u001b[38;5;129;01mor\u001b[39;00m (\u001b[38;5;241m1\u001b[39m,)\n\u001b[1;32m   1543\u001b[0m handler, ds \u001b[38;5;241m=\u001b[39m _dim_handler_and_canonical(\u001b[38;5;241m*\u001b[39ms1, \u001b[38;5;241m*\u001b[39ms2)\n\u001b[0;32m-> 1544\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mhandler\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdivide_shape_sizes\u001b[49m\u001b[43m(\u001b[49m\u001b[43mds\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[38;5;28;43mlen\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43ms1\u001b[49m\u001b[43m)\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mds\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;28;43mlen\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43ms1\u001b[49m\u001b[43m)\u001b[49m\u001b[43m:\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Documents/pythonenvs/teach-rl/python-3.10.2/lib/python3.10/site-packages/jax/core.py:1448\u001b[0m, in \u001b[0;36mDimensionHandler.divide_shape_sizes\u001b[0;34m(self, s1, s2)\u001b[0m\n\u001b[1;32m   1446\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;241m1\u001b[39m\n\u001b[1;32m   1447\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m sz1 \u001b[38;5;241m%\u001b[39m sz2:\n\u001b[0;32m-> 1448\u001b[0m   \u001b[38;5;28;01mraise\u001b[39;00m InconclusiveDimensionOperation(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mCannot divide evenly the sizes of shapes \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mtuple\u001b[39m(s1)\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m and \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mtuple\u001b[39m(s2)\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m   1449\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m sz1 \u001b[38;5;241m/\u001b[39m\u001b[38;5;241m/\u001b[39m sz2\n",
      "\u001b[0;31mInconclusiveDimensionOperation\u001b[0m: Cannot divide evenly the sizes of shapes (1,) and (-1, 4)"
     ]
    }
   ],
   "source": [
    "# For example, what move can we have if we are in 0?\n",
    "actions = [pi(0) for i in range(1000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0565e6e5-4658-4712-9130-0f99d74dd102",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"log probabilities: \", pi.dist_params(0))\n",
    "plt.hist(actions);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9fb1623-35e4-4975-bda7-c5f445464746",
   "metadata": {},
   "source": [
    "This is consistent with the fact that our initialisation of the weights is all 0s."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9695b8ee-724d-4907-9818-392152b7e5c5",
   "metadata": {},
   "source": [
    "### Reward tracing \n",
    "\n",
    "We create a reward tracing object, which collects at every time $t$ the reward $r_t$ and eventually discounts it by a factor $\\gamma$ so that\n",
    "\n",
    "$$ R = \\sum_{t=0}^T \\gamma^t r_t $$\n",
    "\n",
    "This is basically a smarter version of a list, that we will use later. Using a $\\gamma < 1$ allows us to give higher rewards to shorter trajectories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "56f18828-48de-4be2-ae9b-d1da27fac46b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# experience tracer\n",
    "tracer = coax.reward_tracing.MonteCarlo(gamma=0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f898caa8-e9b9-4c39-a7c1-02d988bc2668",
   "metadata": {},
   "source": [
    "### Policy Gradient objective\n",
    "\n",
    "Coax has several objects functions used to train RL algorithms.\n",
    "`VanillaPG` is a A vanilla policy-gradient objective, a.k.a. REINFORCE-style objective.\n",
    "$$J(\\theta; s,a)\\ =\\ \\mathcal{A}(s,a)\\,\\log\\pi_\\theta(a|s)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "73f28490-cc51-44cf-a865-1c6c36a32268",
   "metadata": {},
   "outputs": [],
   "source": [
    "vanilla_pg = coax.policy_objectives.VanillaPG(pi, optimizer=optax.adam(0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95e6ed19-b5bc-412b-adb6-244f66d84a1b",
   "metadata": {},
   "source": [
    "### Writing down the 'RL' loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "56bf947a-1f11-4092-8e5a-6317224de524",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.03715683  0.04894755 -0.00799295  0.04374625]\n"
     ]
    }
   ],
   "source": [
    "# First we reset the environment so we get the initial state\n",
    "s_t = env.reset()\n",
    "print(s_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "aaf4f789-8262-46ab-a3f2-1b3e8699a05e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "action a_t = 1\n"
     ]
    }
   ],
   "source": [
    "a_t = pi(s_t)\n",
    "print(f\"action a_t = {a_t}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "e27aa9e5-49df-4b89-a4ec-818e88682eb1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "s_tnext: [-0.03617788  0.24418321 -0.00711802 -0.25144777], r_t:1.0, is_done:False, info:{'monitor': {'T': 1, 'ep': 1}}\n"
     ]
    }
   ],
   "source": [
    "s_tnext, r_t, is_done, info = env.step(a_t)\n",
    "print(f\"s_tnext: {s_tnext}, r_t:{r_t}, is_done:{is_done}, info:{info}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "e94573e8-af9a-4798-a180-1ad5aad08f49",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We add to the reward tracer this last step\n",
    "tracer.add(s_t, a_t, r_t, is_done)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "080d0a06-3ec0-4956-8def-9771bdf49ce3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# And now, we repeat many times:\n",
    "tracer.reset()\n",
    "s_t = env.reset()\n",
    "env.render()\n",
    "for t in range(env.spec.max_episode_steps):\n",
    "    a_t = pi(s_t)\n",
    "    s_tnext, r_t, is_done, info = env.step(a_t)\n",
    "    tracer.add(s_t, a_t, r_t, is_done)\n",
    "    env.render()\n",
    "    \n",
    "    if is_done:\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "066b979c-42ef-49e8-b813-2e4d26b98446",
   "metadata": {},
   "outputs": [],
   "source": [
    "# and we then update the weights according to this\n",
    "while tracer:\n",
    "    transition_batch = tracer.pop()\n",
    "    vanilla_pg.update(transition_batch, Adv=transition_batch.Rn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "d062d809-89c3-414f-aeb5-3c9dce09aafb",
   "metadata": {},
   "outputs": [],
   "source": [
    "#vanilla_pg.pi.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "2afe4726-869a-4d31-a5f6-7b0408087f78",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Finally, we do this many times\n",
    "pi = coax.Policy(π_fun, env)\n",
    "vanilla_pg = coax.policy_objectives.VanillaPG(pi, optimizer=optax.adam(0.01))\n",
    "tracer.reset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "419f1060-1268-4705-b768-9071e2108aed",
   "metadata": {},
   "outputs": [],
   "source": [
    "# train\n",
    "Rvals = []\n",
    "Tsteps = []\n",
    "\n",
    "for ep in range(500):\n",
    "    s_t = env.reset()\n",
    "    do_render = ep % 50 == 0\n",
    "    if do_render:\n",
    "        env.render()\n",
    "\n",
    "    for t in range(env.spec.max_episode_steps):\n",
    "        a_t = pi(s_t)\n",
    "        s_tnext, r_t, is_done, info = env.step(a_t)\n",
    "\n",
    "        # update\n",
    "        tracer.add(s_t, a_t, r_t, is_done)\n",
    "        \n",
    "        while tracer:\n",
    "            transition_batch = tracer.pop()\n",
    "            vanilla_pg.update(transition_batch, Adv=transition_batch.Rn)\n",
    "\n",
    "        if do_render:\n",
    "            env.render()\n",
    "\n",
    "        if is_done:\n",
    "            Rvals.append(env.G)\n",
    "            Tsteps.append(t)\n",
    "            #print(vanilla_pg.pi.params)\n",
    "            break\n",
    "\n",
    "        s_t = s_tnext\n",
    "\n",
    "    # early stopping\n",
    "    if env.avg_G > env.spec.reward_threshold:\n",
    "        break\n",
    "        \n",
    "Rvals = jnp.array(Rvals)\n",
    "Tsteps = jnp.array(Tsteps)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf707cf7-4019-4a7b-b681-3d1b5560db27",
   "metadata": {},
   "source": [
    "Let's visualize the performance and plot the final reward (1 if it succeded, 0 if it did not)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "fd61f083-9ec1-4eac-9c66-cbed313eaab4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x158dbbb50>]"
      ]
     },
     "execution_count": 41,
     "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.plot(Rvals)\n",
    "plt.plot(jnp.cumsum(Rvals)/jnp.arange(Rvals.size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "06e6fb0f-2ce8-4646-9a51-ef4f2f7d4121",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x158f6e770>]"
      ]
     },
     "execution_count": 42,
     "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.plot(Rvals*Tsteps)\n",
    "plt.plot(jnp.cumsum(Rvals*Tsteps)/jnp.arange(Rvals.size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "bda615c7-ebb6-4242-8c14-ca976b214e0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# You see that this did not work well. It's because there is no signal at the beginning as the reward is always 0!\n",
    "# Let's try to set the reward to non zero. For example, let's make him not take the useless moves such as up when he's at the top already.\n",
    "\n",
    "pi = coax.Policy(π_fun, env)\n",
    "vanilla_pg = coax.policy_objectives.VanillaPG(pi, optimizer=optax.adam(0.01))\n",
    "tracer.reset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "9bad307e-e4b8-460b-a76b-c03707c5ab17",
   "metadata": {},
   "outputs": [],
   "source": [
    "# train\n",
    "Rvals = []\n",
    "Tsteps = []\n",
    "\n",
    "for ep in range(500):\n",
    "    s_t = env.reset()\n",
    "    do_render = ep % 50 == 0\n",
    "    if do_render:\n",
    "        env.render()\n",
    "\n",
    "    for t in range(env.spec.max_episode_steps):\n",
    "        a_t = pi(s_t)\n",
    "        s_tnext, r_t, is_done, info = env.step(a_t)\n",
    "\n",
    "        if jnp.array_equal(s_tnext, s_t):\n",
    "            r_t = r_t - 0.01\n",
    "\n",
    "        # update\n",
    "        tracer.add(s_t, a_t, r_t, is_done)\n",
    "        \n",
    "        while tracer:\n",
    "            transition_batch = tracer.pop()\n",
    "            vanilla_pg.update(transition_batch, Adv=transition_batch.Rn)\n",
    "\n",
    "        if do_render:\n",
    "            env.render()\n",
    "\n",
    "        if is_done:\n",
    "            Rvals.append(env.G)\n",
    "            Tsteps.append(t)\n",
    "            #print(vanilla_pg.pi.params)\n",
    "            break\n",
    "\n",
    "        s_t = s_tnext\n",
    "\n",
    "    # early stopping\n",
    "    if env.avg_G > env.spec.reward_threshold:\n",
    "        break\n",
    "        \n",
    "Rvals = jnp.array(Rvals)\n",
    "Tsteps = jnp.array(Tsteps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "0ca406b5-1c68-44ea-9c9f-c2c640ab0157",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x15917af20>]"
      ]
     },
     "execution_count": 46,
     "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.plot(Rvals)\n",
    "plt.plot(jnp.cumsum(Rvals)/jnp.arange(Rvals.size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "9f38d438-2eda-4468-8520-b7d70866d3ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1592052a0>]"
      ]
     },
     "execution_count": 47,
     "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.plot(Rvals*Tsteps)\n",
    "plt.plot(jnp.cumsum(Rvals*Tsteps)/jnp.arange(Rvals.size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "556bf89f-1651-4473-9b3d-576b3d14cba0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# You see that this did not work well again because he is not learning to get to the objective, and keeps falling on the holes.\n",
    "# Let's give him a penalty if he falls on the holes\n",
    "\n",
    "pi = coax.Policy(π_fun, env)\n",
    "vanilla_pg = coax.policy_objectives.VanillaPG(pi, optimizer=optax.adam(0.01))\n",
    "tracer.reset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "5600dd50-5944-4deb-8e3b-ddc6552f6f6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# train\n",
    "Rvals = []\n",
    "Tsteps = []\n",
    "\n",
    "for ep in range(500):\n",
    "    s_t = env.reset()\n",
    "    do_render = ep % 50 == 0\n",
    "    if do_render:\n",
    "        env.render()\n",
    "\n",
    "    for t in range(env.spec.max_episode_steps):\n",
    "        a_t = pi(s_t)\n",
    "        s_tnext, r_t, is_done, info = env.step(a_t)\n",
    "\n",
    "        if jnp.array_equal(s_tnext, s_t):\n",
    "            r_t = r_t - 0.01\n",
    "        if is_done and s_tnext != 15:\n",
    "            r_t = r_t - 0.05\n",
    "        #if not is_done:\n",
    "        #    r_t = r_t + 0.005\n",
    "        \n",
    "        # update\n",
    "        tracer.add(s_t, a_t, r_t, is_done)\n",
    "        \n",
    "        while tracer:\n",
    "            transition_batch = tracer.pop()\n",
    "            vanilla_pg.update(transition_batch, Adv=transition_batch.Rn)\n",
    "\n",
    "        if do_render:\n",
    "            env.render()\n",
    "\n",
    "        if is_done:\n",
    "            Rvals.append(env.G)\n",
    "            Tsteps.append(t)\n",
    "            #print(vanilla_pg.pi.params)\n",
    "            break\n",
    "\n",
    "        s_t = s_tnext\n",
    "\n",
    "    # early stopping\n",
    "    if env.avg_G > env.spec.reward_threshold:\n",
    "        break\n",
    "        \n",
    "Rvals = jnp.array(Rvals)\n",
    "Tsteps = jnp.array(Tsteps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "379df1ac-a522-477f-b1ac-3d1ee6eb56fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray([[0.0578948 , 0.8252751 , 0.00968201, 0.10714805],\n",
       "             [0.32782987, 0.15143633, 0.25879538, 0.26193845],\n",
       "             [0.28314325, 0.24622405, 0.2400847 , 0.23054805],\n",
       "             [0.31219593, 0.1988406 , 0.27051812, 0.21844535],\n",
       "             [0.09291917, 0.8126031 , 0.00812364, 0.08635408],\n",
       "             [0.25      , 0.25      , 0.25      , 0.25      ],\n",
       "             [0.20227171, 0.3257466 , 0.2809326 , 0.19104916],\n",
       "             [0.25      , 0.25      , 0.25      , 0.25      ],\n",
       "             [0.18065251, 0.01060159, 0.7183045 , 0.09044136],\n",
       "             [0.12255215, 0.5699346 , 0.26276183, 0.04475139],\n",
       "             [0.15752916, 0.77743167, 0.01530033, 0.04973885],\n",
       "             [0.25      , 0.25      , 0.25      , 0.25      ],\n",
       "             [0.25      , 0.25      , 0.25      , 0.25      ],\n",
       "             [0.0285945 , 0.05520048, 0.84025043, 0.07595465],\n",
       "             [0.07922566, 0.05320261, 0.7686978 , 0.09887398],\n",
       "             [0.25      , 0.25      , 0.25      , 0.25      ]],            dtype=float32)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jnp.exp(pi.params['linear']['w'])/jnp.sum(jnp.exp(pi.params['linear']['w']), axis=-1, keepdims=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "48ba603e-2c9a-480a-b923-e3569f220f8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x15a4aa080>]"
      ]
     },
     "execution_count": 147,
     "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.plot(Rvals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a65c5ebe-affa-405f-8150-6db2359cdfa8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (RL)",
   "language": "python",
   "name": "py-rl"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}