314 lines
102 KiB
Plaintext
314 lines
102 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "e0ac366f",
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"metadata": {},
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"source": [
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"# 第 5 章:蒙特卡洛方法 (Monte Carlo Methods)\n",
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"\n",
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"## 1. 什么是蒙特卡洛 (MC)?\n",
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"当智能体不知道环境的运作规律(无模型,Model-Free)时,它只能通过与环境真实交互来学习。\n",
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"蒙特卡洛方法的核心思想是:**“大数定律”**。既然我算不出某个状态的理论预期价值,那我就从这个状态出发,亲自跑几十次、几百次完整的**回合(Episode)**,然后把实际得到的**回报(Return, $G_t$)取平均值**。跑的次数越多,平均值就越接近真实的价值。\n",
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"\n",
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"## 2. 核心特征\n",
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"* **必须是分步的(Episodic)**:蒙特卡洛必须等一个完整的回合(比如一局游戏)彻底结束后,才能从后往前计算总回报并更新价值。\n",
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"* **计算动作价值 $q(s,a)$**:因为没有模型,光知道状态价值 $v(s)$ 没用了(你不知道选哪个动作能进入好状态)。因此,MC 直接估计**动作价值 $q(s,a)$**。\n",
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"\n",
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"## 3. 探索与利用 ($\\epsilon$-Greedy 策略)\n",
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"既然要靠“试错”来积累经验,智能体就绝不能总是死盯着当前看起来最好的动作(利用 Exploitation),它必须保留一定的概率去尝试其他动作(探索 Exploration)。\n",
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"**$\\epsilon$-贪心($\\epsilon$-Greedy)策略**:\n",
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"* 以 $1 - \\epsilon$ 的概率选择当前 Q 值最大的最佳动作。\n",
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"* 以 $\\epsilon$ 的概率在所有动作中**随机盲选**(这就是探索!)。"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "11448339",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import random\n",
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"from collections import defaultdict\n",
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"\n",
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"# 1. 简单的 1D 走廊环境 (黑盒)\n",
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"# 状态: 0, 1, 2, 3 (3 是目标宝箱)\n",
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"# 动作: 0 (向左), 1 (向右)\n",
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"def step(state, action):\n",
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" if state == 3: # 已经在终点\n",
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" return 3, 0, True \n",
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" \n",
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" if action == 1: # 向右走\n",
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" next_state = state + 1\n",
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" else: # 向左走\n",
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" next_state = max(0, state - 1)\n",
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" \n",
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" reward = 10 if next_state == 3 else -1\n",
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" done = (next_state == 3) # 是否结束回合\n",
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" return next_state, reward, done\n",
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"\n",
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"# 2. 定义 epsilon-greedy 策略\n",
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"def epsilon_greedy_policy(state, Q, epsilon, n_actions=2):\n",
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" # 以 epsilon 的概率随机探索\n",
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" if random.uniform(0, 1) < epsilon:\n",
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" return random.choice(range(n_actions))\n",
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" # 以 1 - epsilon 的概率贪心利用 (选择 Q 值最大的动作)\n",
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" else:\n",
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" # 如果 Q 值全是 0,也会默认选第一个,所以用 argmax\n",
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" return np.argmax(Q[state])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "7ecc277d",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"=== 开始蒙特卡洛控制 (Monte Carlo Control) ===\n",
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"完成第 100 个回合训练...\n",
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"完成第 200 个回合训练...\n",
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"完成第 300 个回合训练...\n",
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"完成第 400 个回合训练...\n",
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"完成第 500 个回合训练...\n",
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"\n",
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"--- 训练结束!揭晓学到的 Q 表 ---\n",
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"状态 0: 向左 Q=3.44, 向右 Q=5.38 -> 最优动作: 向右\n",
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"状态 1: 向左 Q=3.03, 向右 Q=7.49 -> 最优动作: 向右\n",
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"状态 2: 向左 Q=5.10, 向右 Q=10.00 -> 最优动作: 向右\n",
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"\n",
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"结论:即使不知道环境具体规则,智能体仅凭不断试错取平均,也学会了一直向右走才是通关秘籍!\n"
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]
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}
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],
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"source": [
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"print(\"=== 开始蒙特卡洛控制 (Monte Carlo Control) ===\")\n",
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"\n",
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"# 初始化 Q 表 (状态数目为4,动作为2)\n",
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"# 使用 defaultdict 方便处理没见过的状态\n",
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"Q = defaultdict(lambda: np.zeros(2))\n",
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"# 用于记录每个 (状态, 动作) 组合被访问了多少次,以及获得的总回报\n",
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"returns_sum = defaultdict(float)\n",
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"returns_count = defaultdict(float)\n",
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"\n",
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"num_episodes = 500\n",
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"gamma = 0.9\n",
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"epsilon = 0.2\n",
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"\n",
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"for i in range(num_episodes):\n",
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" # --- 1. 生成一个完整的回合 (Episode) ---\n",
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" episode = []\n",
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" state = 0 # 每次都从起点开始\n",
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" \n",
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" # 智能体开始在黑盒里凭感觉走,直到碰壁或找到宝箱\n",
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" while True:\n",
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" action = epsilon_greedy_policy(state, Q, epsilon)\n",
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" next_state, reward, done = step(state, action)\n",
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" \n",
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" # 记录下这一步的“经验”: (状态, 动作, 奖励)\n",
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" episode.append((state, action, reward))\n",
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" state = next_state\n",
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" if done:\n",
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" break\n",
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" \n",
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" # --- 2. 回合结束后,从后往前算回报并更新 Q 表 ---\n",
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" G = 0.0 # G 代表累计回报 Return\n",
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" # 从轨迹的最后一步倒着往前算\n",
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" for t in reversed(range(len(episode))):\n",
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" state, action, reward = episode[t]\n",
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" \n",
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" # 计算折扣回报\n",
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" G = gamma * G + reward\n",
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" \n",
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" # First-Visit MC (初次访问蒙特卡洛): \n",
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" # 只在回合中首次遇到这个 (状态,动作) 时才更新\n",
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" state_action_pairs_before_t = [(x[0], x[1]) for x in episode[:t]]\n",
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" if (state, action) not in state_action_pairs_before_t:\n",
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" # 记录总回报并计数\n",
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" returns_sum[(state, action)] += G\n",
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" returns_count[(state, action)] += 1.0\n",
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" \n",
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" # 平均值法更新 Q 表: Q = sum(G) / count\n",
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" Q[state][action] = returns_sum[(state, action)] / returns_count[(state, action)]\n",
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"\n",
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" # 打印部分训练过程\n",
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" if (i + 1) % 100 == 0:\n",
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" print(f\"完成第 {i + 1} 个回合训练...\")\n",
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"\n",
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"print(\"\\n--- 训练结束!揭晓学到的 Q 表 ---\")\n",
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"for s in range(3):\n",
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" print(f\"状态 {s}: 向左 Q={Q[s][0]:.2f}, 向右 Q={Q[s][1]:.2f} -> 最优动作: {'向右' if np.argmax(Q[s])==1 else '向左'}\")\n",
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"\n",
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"print(\"\\n结论:即使不知道环境具体规则,智能体仅凭不断试错取平均,也学会了一直向右走才是通关秘籍!\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8e92690e",
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"metadata": {},
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"source": [
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"加一个小测试,引入$\\epsilon$ 衰减(Epsilon Decay)的机制,并与之前的方法进行对比"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "142b7542",
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"metadata": {},
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"outputs": [
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{
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"data": {
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",
|
||
"text/plain": [
|
||
"<Figure size 1000x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"ename": "",
|
||
"evalue": "",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[1;31m在当前单元格或上一个单元格中执行代码时 Kernel 崩溃。\n",
|
||
"\u001b[1;31m请查看单元格中的代码,以确定故障的可能原因。\n",
|
||
"\u001b[1;31m单击<a href='https://aka.ms/vscodeJupyterKernelCrash'>此处</a>了解详细信息。\n",
|
||
"\u001b[1;31m有关更多详细信息,请查看 Jupyter <a href='command:jupyter.viewOutput'>log</a>。"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import random\n",
|
||
"from collections import defaultdict\n",
|
||
"\n",
|
||
"# 1. 简单的 1D 走廊黑盒环境\n",
|
||
"def step(state, action):\n",
|
||
" if state == 3:\n",
|
||
" return 3, 0, True\n",
|
||
" if action == 1:\n",
|
||
" next_state = state + 1\n",
|
||
" else:\n",
|
||
" next_state = max(0, state - 1)\n",
|
||
" reward = 10 if next_state == 3 else -1\n",
|
||
" done = (next_state == 3)\n",
|
||
" return next_state, reward, done\n",
|
||
"\n",
|
||
"# 2. epsilon-greedy 策略\n",
|
||
"def epsilon_greedy_policy(state, Q, epsilon, n_actions=2):\n",
|
||
" if random.uniform(0, 1) < epsilon:\n",
|
||
" return random.choice(range(n_actions))\n",
|
||
" else:\n",
|
||
" return np.argmax(Q[state])\n",
|
||
"\n",
|
||
"# 3. 封装好的蒙特卡洛控制算法\n",
|
||
"def run_mc_control(num_episodes, gamma, initial_epsilon, decay_epsilon=False):\n",
|
||
" Q = defaultdict(lambda: np.zeros(2))\n",
|
||
" returns_sum = defaultdict(float)\n",
|
||
" returns_count = defaultdict(float)\n",
|
||
" episode_returns = [] # 记录每一局的最终回报,用来画图\n",
|
||
"\n",
|
||
" # 循环执行多次回合\n",
|
||
" for i in range(num_episodes):\n",
|
||
" \n",
|
||
" # --- 【彩蛋核心逻辑:Epsilon 衰减】 ---\n",
|
||
" # 如果开启衰减,每一局的 epsilon 都会按照比例减小,但最低不低于 0.01\n",
|
||
" if decay_epsilon:\n",
|
||
" epsilon = max(0.01, initial_epsilon * (1 - i / num_episodes))\n",
|
||
" else:\n",
|
||
" epsilon = initial_epsilon\n",
|
||
" \n",
|
||
" episode = []\n",
|
||
" state = 0\n",
|
||
" episode_return = 0\n",
|
||
" \n",
|
||
" # 跑完一个完整的回合\n",
|
||
" while True:\n",
|
||
" action = epsilon_greedy_policy(state, Q, epsilon)\n",
|
||
" next_state, reward, done = step(state, action)\n",
|
||
" episode.append((state, action, reward))\n",
|
||
" episode_return += reward\n",
|
||
" state = next_state\n",
|
||
" if done: break\n",
|
||
" \n",
|
||
" episode_returns.append(episode_return)\n",
|
||
" \n",
|
||
" # 从最后一步倒算回报并更新 Q 表 (初次访问 MC)\n",
|
||
" G = 0.0\n",
|
||
" for t in reversed(range(len(episode))):\n",
|
||
" s, a, r = episode[t]\n",
|
||
" G = gamma * G + r\n",
|
||
" \n",
|
||
" # 检查是否初次访问\n",
|
||
" is_first_visit = True\n",
|
||
" for prev_t in range(t):\n",
|
||
" if episode[prev_t][0] == s and episode[prev_t][1] == a:\n",
|
||
" is_first_visit = False\n",
|
||
" break\n",
|
||
" \n",
|
||
" if is_first_visit:\n",
|
||
" returns_sum[(s, a)] += G\n",
|
||
" returns_count[(s, a)] += 1.0\n",
|
||
" Q[s][a] = returns_sum[(s, a)] / returns_count[(s, a)]\n",
|
||
" \n",
|
||
" return episode_returns\n",
|
||
"\n",
|
||
"# --- 4. 运行对比实验并绘图 ---\n",
|
||
"num_episodes = 500\n",
|
||
"gamma = 0.9\n",
|
||
"\n",
|
||
"# 实验一:恒定 epsilon = 0.2\n",
|
||
"returns_const = run_mc_control(num_episodes, gamma, initial_epsilon=0.2, decay_epsilon=False)\n",
|
||
"\n",
|
||
"# 实验二:衰减 epsilon (初始值大胆设为 0.5,慢慢降到 0.01)\n",
|
||
"returns_decay = run_mc_control(num_episodes, gamma, initial_epsilon=0.5, decay_epsilon=True)\n",
|
||
"\n",
|
||
"# 计算滑动平均 (平滑曲线,看起来更直观)\n",
|
||
"def moving_average(a, n=20):\n",
|
||
" ret = np.cumsum(a, dtype=float)\n",
|
||
" ret[n:] = ret[n:] - ret[:-n]\n",
|
||
" return ret[n - 1:] / n\n",
|
||
"\n",
|
||
"# 绘图\n",
|
||
"plt.figure(figsize=(10, 6))\n",
|
||
"plt.plot(moving_average(returns_const), label='Constant Epsilon (0.2)')\n",
|
||
"plt.plot(moving_average(returns_decay), label='Decaying Epsilon (0.5 -> 0.01)')\n",
|
||
"plt.title('Monte Carlo Control: Constant vs Decaying Epsilon')\n",
|
||
"plt.xlabel('Episodes (Smoothed over 20 episodes)')\n",
|
||
"plt.ylabel('Average Return per Episode')\n",
|
||
"plt.legend()\n",
|
||
"plt.grid(True)\n",
|
||
"plt.show()"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "GymRL",
|
||
"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": "3.13.9"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|