CartPole/cartpole_v1@PG#pytorch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Policy Gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gym\n",
    "import numpy as np\n",
    "from collections import deque\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "from torch.distributions.categorical import Categorical\n",
    "from torch.optim import Adam"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make('CartPole-v1').env"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Box(4,)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.observation_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Discrete(2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.action_space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def network(*, n_input, n_output, n_hidden=32, hidden_layers=1, \n",
    "            activation=nn.Tanh, output_activation=nn.Identity):\n",
    "    layers = [nn.Linear(n_input, n_hidden), activation()]\n",
    "    for _ in range(hidden_layers):\n",
    "        layers += [nn.Linear(n_hidden, n_hidden), activation()]\n",
    "    layers += [nn.Linear(n_hidden, n_output), output_activation()]\n",
    "    return nn.Sequential(*layers)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "net = network(\n",
    "    n_input=env.observation_space.shape[0], \n",
    "    n_hidden=128, \n",
    "    n_output=env.action_space.n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Sequential(\n",
       "  (0): Linear(in_features=4, out_features=128, bias=True)\n",
       "  (1): Tanh()\n",
       "  (2): Linear(in_features=128, out_features=128, bias=True)\n",
       "  (3): Tanh()\n",
       "  (4): Linear(in_features=128, out_features=2, bias=True)\n",
       "  (5): Identity()\n",
       ")"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Buffer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Buffer:\n",
    "    def __init__(self, maxlen):\n",
    "        self._traj_rewards = 0\n",
    "        self._cache = []\n",
    "        self._memory = []\n",
    "    \n",
    "    @property\n",
    "    def size(self): return len(self._memory)\n",
    "    \n",
    "    def cache(self, state, action, reward, next_state, done):\n",
    "        self._traj_rewards += reward\n",
    "        self._cache.append([state, action, reward, next_state, done])\n",
    "    \n",
    "    def flush(self):\n",
    "        self._memory += [sample + [self._traj_rewards] for sample in self._cache]\n",
    "        self._traj_rewards = 0\n",
    "        self._cache = []\n",
    "        \n",
    "    def get_batch(self):\n",
    "        states, actions, rewards, next_states, dones, traj_rewards = np.array(self._memory).transpose()         \n",
    "        states, next_states = np.stack(states), np.stack(next_states)\n",
    "        actions, traj_rewards = actions.astype(int), traj_rewards.astype(float)\n",
    "        return states, actions, rewards, next_states, dones, traj_rewards\n",
    "    \n",
    "    def clear(self):\n",
    "        self._memory = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Agent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Agent:\n",
    "    def __init__(self, env):\n",
    "        self._env = env\n",
    "        self._buffer = Buffer(5000)\n",
    "        self._logits_net = network(n_input=env.observation_space.shape[0], \n",
    "                                   n_hidden=32, \n",
    "                                   n_output=env.action_space.n)\n",
    "        self._optimizer = Adam(self._logits_net.parameters(), lr=0.02)\n",
    "\n",
    "    def policy(self, state):\n",
    "        state = torch.as_tensor(state, dtype=torch.float32)\n",
    "        return Categorical(logits=self._logits_net(state))\n",
    "    \n",
    "    def choose_action(self, state, *, epilson=0.5):        \n",
    "        if np.random.random()>epilson:\n",
    "            return self._env.action_space.sample()\n",
    "        else:\n",
    "            return self.policy(state).sample().item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Agent(Agent):\n",
    "    def play(self, *, n_steps=500, render=False):\n",
    "        state = env.reset()\n",
    "        done = False\n",
    "        rewards = 0\n",
    "        for i_steps in range(1, n_steps+1):\n",
    "            action = self.choose_action(state, epilson=1)\n",
    "            next_state, reward, done, info = env.step(action)            \n",
    "            rewards += reward\n",
    "            state = next_state\n",
    "            if render: \n",
    "                env.render()\n",
    "            if done: \n",
    "                break\n",
    "        if render: \n",
    "            print(f'Steps taken: {i_steps}, rewards earned: {rewards}')\n",
    "            env.close()\n",
    "        else:\n",
    "            return rewards"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Agent(Agent):\n",
    "    def train(self):\n",
    "        states, actions, rewards, next_states, dones, traj_rewards = self._buffer.get_batch()\n",
    "        states = torch.as_tensor(states, dtype=torch.float32)\n",
    "        actions = torch.as_tensor(actions, dtype=torch.int32)\n",
    "        traj_rewards = torch.as_tensor(traj_rewards, dtype=torch.float32)\n",
    "        # gradient ascent\n",
    "        self._optimizer.zero_grad()        \n",
    "        logp = self.policy(states).log_prob(actions)\n",
    "        batch_loss = -(logp*traj_rewards).mean()\n",
    "        batch_loss.backward()\n",
    "        self._optimizer.step()\n",
    "        return batch_loss.detach().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Agent(Agent):\n",
    "    def run(self, n_eps=1000, n_steps=500, batch_size=6000):\n",
    "        scores = deque(maxlen=10)\n",
    "        for i_eps in range(1, n_eps+1):\n",
    "            while True:\n",
    "                state = env.reset()\n",
    "                done = False\n",
    "                for i_steps in range(1,n_steps+1):\n",
    "                    action = self.choose_action(state, epilson=1)\n",
    "                    next_state, reward, done, info = env.step(action)\n",
    "                    self._buffer.cache(state, action, reward, next_state, done)\n",
    "                    state = next_state \n",
    "                    if done: break\n",
    "                self._buffer.flush()\n",
    "                if self._buffer.size>=batch_size: \n",
    "                    break\n",
    "            self.train()\n",
    "            self._buffer.clear()\n",
    "            if i_eps%2==0:\n",
    "                scores.append(self.play())\n",
    "            if i_eps%1==0:\n",
    "                print('#', end='')\n",
    "            if i_eps%10==0:\n",
    "                mean_score = sum(scores)/len(scores)\n",
    "                print(f' | Episode {i_eps:>4d} | mean rewards: {mean_score:.1f}')\n",
    "                if mean_score>=495:\n",
    "                    print(f'\\nMean score of {mean_score:.1f} is considered solved.')\n",
    "                    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "agent = Agent(env)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "########## | Episode   10 | mean rewards: 41.8\n",
      "########## | Episode   20 | mean rewards: 95.5\n",
      "########## | Episode   30 | mean rewards: 182.2\n",
      "########## | Episode   40 | mean rewards: 177.9\n",
      "########## | Episode   50 | mean rewards: 147.1\n",
      "########## | Episode   60 | mean rewards: 150.9\n",
      "########## | Episode   70 | mean rewards: 148.3\n",
      "########## | Episode   80 | mean rewards: 203.7\n",
      "########## | Episode   90 | mean rewards: 230.0\n",
      "########## | Episode  100 | mean rewards: 219.9\n",
      "########## | Episode  110 | mean rewards: 254.6\n",
      "########## | Episode  120 | mean rewards: 248.1\n",
      "########## | Episode  130 | mean rewards: 198.2\n",
      "########## | Episode  140 | mean rewards: 206.3\n",
      "########## | Episode  150 | mean rewards: 130.2\n",
      "########## | Episode  160 | mean rewards: 146.6\n",
      "########## | Episode  170 | mean rewards: 335.9\n",
      "########## | Episode  180 | mean rewards: 421.5\n",
      "########## | Episode  190 | mean rewards: 358.7\n",
      "########## | Episode  200 | mean rewards: 290.7\n",
      "########## | Episode  210 | mean rewards: 405.0\n",
      "########## | Episode  220 | mean rewards: 500.0\n",
      "\n",
      "Mean score of 500.0 is considered solved.\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Continue training? (y/[N])  n\n"
     ]
    }
   ],
   "source": [
    "agent.run()\n",
    "while input('Continue training? (y/[N]) ').upper()=='Y':\n",
    "    agent.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steps taken: 500, rewards earned: 500.0\n"
     ]
    }
   ],
   "source": [
    "agent.play(render=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I used the tutorial from Openai Spinning Up to implement the policy gradient method. In each training loop, we adjust the gradient of the policy neural network according to:"
   ]
  },
  {
   "attachments": {
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     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:5476763c-5627-4ea1-91f6-d497c065752c.png)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Source: <https://spinningup.openai.com/en/latest/spinningup/rl_intro3.html#part-3-intro-to-policy-optimization>"
   ]
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    "* Still robust when training v1\n",
    "* Because a longer time to terminal stage and larger observation space, training time is also much longer than v0.\n",
    "* Using GP can boost total rewards to 400+, and therefore superior than DQN.\n",
    "* Tuning hyper parameters is important, some settings may work much better than others, such as learning rate and batch size.\n",
    "* Larger batch let the current policy see much more sample of the environment, but will take longer training time. If an environment observation space is large, a larger batch size is necessary."
   ]
  }
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