sarsa_acme.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1-Step SARSA Using Acme\n",
    "\n",
    "This notebook shows the tabular reinforcement learning algorithm, 1-step SARSA applied to the Taxi problem (it also works on CliffWalking and FrozenLake) from Open AI's gym. 1-step SARSA is an on-policy Temporal Difference control algorithm. The algorithm is defined by: \n",
    "$$Q(S_t, A_t) \\leftarrow Q(S_t, A_t) + \\alpha [R_{t + 1} + \\gamma Q(S_{t + 1}, A_{t + 1}) - Q(S_t, A_t)]$$\n",
    ", where $Q$ is the learned action-value function, $R$ is the reward, $A$ is the action, $\\alpha$ is the step size, $\\gamma$ is the discount rate and $t$ is the time step.\n",
    "\n",
    "For more information on the SARSA algorithm see section 6.4 of [Reinforcement Learning: An Introduction](http://incompleteideas.net/book/RLbook2018.pdf). For alternative implementations of 1-step SARSA see: [SARSA Example by Denny Britz](https://github.com/dennybritz/reinforcement-learning/blob/master/TD/SARSA%20Solution.ipynb), [Intro to DeepMind’s Reinforcement Learning Framework “Acme”](https://towardsdatascience.com/deepminds-reinforcement-learning-framework-acme-87934fa223bf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import acme\n",
    "from acme import types\n",
    "from acme.wrappers import GymWrapper\n",
    "from acme.environment_loop import EnvironmentLoop\n",
    "from acme.utils.loggers import InMemoryLogger\n",
    "import pandas as pd\n",
    "import gym\n",
    "import dm_env\n",
    "import numpy as np\n",
    "import tree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Patch The Acme GymWrapper Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def patched_step(self, action: types.NestedArray) -> dm_env.TimeStep:\n",
    "    \"\"\"Steps the environment.\"\"\"\n",
    "    if self._reset_next_step:\n",
    "        return self.reset()\n",
    "\n",
    "    # Added change to include truncated paramater\n",
    "    observation, reward, done, truncated, info = self._environment.step(action)\n",
    "    self._reset_next_step = done\n",
    "    self._last_info = info\n",
    "\n",
    "    # Convert the type of the reward based on the spec, respecting the scalar or\n",
    "    # array property.\n",
    "    reward = tree.map_structure(\n",
    "        lambda x, t: (  # pylint: disable=g-long-lambda\n",
    "            t.dtype.type(x)\n",
    "            if np.isscalar(x) else np.asarray(x, dtype=t.dtype)),\n",
    "        reward,\n",
    "        self.reward_spec())\n",
    "\n",
    "    if done:\n",
    "        if truncated:\n",
    "            return dm_env.truncation(reward, observation)\n",
    "        return dm_env.termination(reward, observation)\n",
    "    return dm_env.transition(reward, observation)\n",
    "\n",
    "def patched_reset(self) -> dm_env.TimeStep:\n",
    "    \"\"\"Resets the episode.\"\"\"\n",
    "    self._reset_next_step = False\n",
    "    observation, info = self._environment.reset()\n",
    "    # Reset the diagnostic information.\n",
    "    self._last_info = None\n",
    "    return dm_env.restart(observation)\n",
    "\n",
    "\n",
    "GymWrapper.step = patched_step\n",
    "GymWrapper.reset = patched_reset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Select Environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Type of environment, options include:\n",
    "# Taxi-v3, CliffWalking-v0, FrozenLake-v1\n",
    "env_type = \"Taxi-v3\"\n",
    "# Create the environment\n",
    "env = GymWrapper(gym.make(env_type, render_mode=None))\n",
    "\n",
    "# Number of possible states and actions\n",
    "num_states = env.observation_space.n \n",
    "num_actions = env.action_space.n\n",
    "\n",
    "# Action-value function, \n",
    "# initialized to 0 for all states and actions\n",
    "Q = np.zeros([num_states, num_actions])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observation Spec: Discrete(500)\n",
      "Action Spec: Discrete(6)\n",
      "Reward Spec: (-inf, inf)\n"
     ]
    }
   ],
   "source": [
    "# print env specs\n",
    "env_specs = env.observation_space, env.action_space, env.reward_range # env.observation_spec()\n",
    "print('Observation Spec:', env.observation_space)\n",
    "print('Action Spec:', env.action_space)\n",
    "print('Reward Spec:', env.reward_range)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create SARSA Agent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class SARSAAgent(acme.Actor):\n",
    "\n",
    "    def __init__(self, Q, num_states, num_actions, gamma=0.99, epsilon=0.01, alpha=0.618):\n",
    "\n",
    "        self.Q = Q\n",
    "\n",
    "        self.num_states = num_states\n",
    "        self.num_actions = num_actions \n",
    "        self.gamma = gamma\n",
    "        self.epsilon = epsilon\n",
    "        self.alpha = alpha\n",
    "\n",
    "\n",
    "    def policy_fn(self, state):\n",
    "        # Create a distribution of actions and divide the epsilon probability between all actions\n",
    "        action_dist = np.ones(self.num_actions, dtype=float) * self.epsilon / self.num_actions\n",
    "        # Find the best action\n",
    "        best_action = np.argmax(self.Q[state, :])\n",
    "        # Set probability for the best action to (1 - epsilon)\n",
    "        action_dist[best_action] += (1.0 - self.epsilon)\n",
    "        return action_dist\n",
    "\n",
    "\n",
    "    def select_action(self, observation: types.NestedArray):\n",
    "        state = observation\n",
    "        action_dist = self.policy_fn(state)\n",
    "        action = np.random.choice(np.arange(num_actions), p=action_dist)\n",
    "        return action\n",
    "\n",
    "    def observe_first(self, timestep: dm_env.TimeStep):\n",
    "        self.timestep = timestep\n",
    "\n",
    "    def observe(self, action: types.NestedArray, next_timestep: dm_env.TimeStep):\n",
    "        self.action = action\n",
    "        self.next_timestep = next_timestep\n",
    "\n",
    "    def update(self, wait: bool = False):\n",
    "        # get variables for convenience\n",
    "        state = self.timestep.observation\n",
    "        _, reward, discount, next_state = self.next_timestep\n",
    "        action = self.action\n",
    "        \n",
    "        # sample a next action\n",
    "        next_action_dist = self.policy_fn(next_state)\n",
    "        next_action = np.random.choice(np.arange(self.num_actions), p=next_action_dist)\n",
    "\n",
    "        # compute and apply the TD error\n",
    "        self.Q[state][action] += self.alpha * (reward + self.gamma * self.Q[next_state, next_action] - self.Q[state, action]) \n",
    "        \n",
    "        # finally, set timestep to next_timestep\n",
    "        self.timestep = self.next_timestep        \n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "sarsa = SARSAAgent(Q, num_states, num_actions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learn The Optimal Action-Value Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ubuntu22/repos/reinforcement-learning-algorithms/venv/lib/python3.10/site-packages/gym/utils/passive_env_checker.py:233: DeprecationWarning: `np.bool8` is a deprecated alias for `np.bool_`.  (Deprecated NumPy 1.24)\n",
      "  if not isinstance(terminated, (bool, np.bool8)):\n"
     ]
    }
   ],
   "source": [
    "loop = EnvironmentLoop(env, sarsa, logger=InMemoryLogger())\n",
    "loop.run(500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot The Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "      <th>episode_return</th>\n",
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       "      <td>1043</td>\n",
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      "text/plain": [
       "   episode_length episode_return  steps_per_second  episodes  steps\n",
       "0            1043        -2327.0      22929.785214         1   1043\n",
       "1             705        -1548.0      28340.706748         2   1748\n",
       "2             494        -1211.0      27955.990285         3   2242\n",
       "3             935        -1958.0      28030.378820         4   3177\n",
       "4             272         -269.0      26384.761165         5   3449"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logger_df = pd.DataFrame(loop._logger.data)\n",
    "logger_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(logger_df[\"episodes\"], logger_df[\"episode_return\"])\n",
    "plt.title(\"Returns Over Episodes\")\n",
    "plt.xlabel(\"Episodes\")\n",
    "plt.ylabel(\"Returns\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run $q_{\\pi}$ On An Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total Reward: 5, Steps Taken: 16\n"
     ]
    }
   ],
   "source": [
    "# Run the algorithm in inferencing mode and \n",
    "# observe its performance\n",
    "env = gym.make(env_type, render_mode=\"human\")\n",
    "state, info = env.reset(seed=48)\n",
    "G = 0\n",
    "num_steps = 0\n",
    "terminated = False\n",
    "\n",
    "while not terminated:\n",
    "    action = np.argmax(Q[state, :]) \n",
    "    state, reward, terminated, truncated, info = env.step(action)\n",
    "    G += reward\n",
    "    num_steps += 1\n",
    "\n",
    "print(f'Total Reward: {G}, Steps Taken: {num_steps}')\n",
    "\n",
    "env.close()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.4 ('jax0.3')",
   "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": "3.10.12"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "9cc3e2285d016734416124682a618282b04f438db98398baa547b8d92dfbc772"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}