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Commit 369e7d4

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xyliao
committed
finish q learning
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‎README.md

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@@ -63,10 +63,9 @@ Learn Deep Learning with PyTorch
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- [生成对抗网络](https://github.com/SherlockLiao/code-of-learn-deep-learning-with-pytorch/blob/master/chapter6_GAN/gan.ipynb)
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- 深度卷积对抗网络 (DCGANs) 生成人脸
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- Chapter 7: 深度增强学习
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- 深度增强学习的介绍
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- Policy gradient
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- Actor-critic gradient
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- Chapter 7: 深度强化学习
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- [Q Learning](https://github.com/SherlockLiao/code-of-learn-deep-learning-with-pytorch/blob/master/chapter7_RL/q-learning-intro.ipynb)
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- Open AI gym
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- Deep Q-networks
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- Chapter 8: PyTorch高级

‎chapter7_RL/q-learning-intro.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Q Learning 介绍\n",
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"在增强学习中,有一种很有名的算法,叫做 q-learning,我们下面会从原理入手,然后通过一个简单的小例子讲一讲 q-learning。\n",
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"\n",
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"## q-learning 的原理\n",
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"我们使用一个简单的例子来导入 q-learning,假设一个屋子有 5 个房间,某一些房间之间相连,我们希望能够走出这个房间,示意图如下\n",
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"\n",
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"![](https://ws2.sinaimg.cn/large/006tNc79ly1fn70q0n91lj30h40a8aaf.jpg)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"那么我们可以将其简化成一些节点和图的形式,每个房间作为一个节点,两个房间有门相连,就在两个节点之间连接一条线,可以得到下面的图片\n",
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"\n",
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"![](https://ws4.sinaimg.cn/large/006tNc79ly1fn70r6c6koj30h60b2gm0.jpg)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"为了模拟整个过程,我们放置一个智能体在任何一个房间,希望它能够走出这个房间,也就是说希望其能够走到了 5 号节点。为了能够让智能体知道 5 号节点是目标房间,我们需要设置一些奖励,对于每一条边,我们都关联一个奖励值:直接连到目标房间的边的奖励值设置为 100,其他的边可以设置为 0,注意 5 号房间有一个指向自己的箭头,奖励值也设置为 100,其他直接指向 5 号房间的也设置为 100,这样当智能体到达 5 号房间之后,他就会选择一只待在 5 号房间,这也称为吸收目标,效果如下\n",
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"\n",
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"![](https://ws4.sinaimg.cn/large/006tNc79ly1fn71gf4idrj30c207u74i.jpg)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"想想一下智能体可以不断学习,每次我们将其放在其中一个房间,然后它可以不断探索,根据奖励值走到 5 号房间,也就是走出这个屋子。比如现在这个智能体在 2 号房间,我们希望其能够不断探索走到 5 号房间。\n",
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"\n",
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"### 状态和动作\n",
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"q-learning 中有两个重要的概念,一个是状态,一个是动作,我们将每一个房间都称为一个状态,而智能体从一个房间走到另外一个房间称为一个动作,对应于上面的图就是每个节点是一个状态,每一个箭头都是一种行动。假如智能体处在状态 4,从状态 4 其可以选择走到状态 0,或者状态 3 或者状态 5,如果其走到了状态 3,也可以选择走到状态 2 或者状态 1 或者 状态 4。\n",
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"\n",
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"我们可以根据状态和动作得到的奖励来建立一个奖励表,用 -1 表示相应节点之间没有边相连,而没有到达终点的边奖励都记为 0,如下\n",
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"\n",
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"![](https://ws2.sinaimg.cn/large/006tNc79ly1fn71o8jlinj307t055wek.jpg)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"类似的,我们可以让智能体通过和环境的交互来不断学习环境中的知识,让智能体根据每个状态来估计每种行动可能得到的收益,这个矩阵被称为 Q 表,每一行表示状态,每一列表示不同的动作,对于状态未知的情景,我们可以随机让智能体从任何的位置出发,然后去探索新的环境来尽可能的得到所有的状态。刚开始智能体对于环境一无所知,所以数值全部初始化为 0,如下\n",
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"\n",
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"![](https://ws2.sinaimg.cn/large/006tNc79ly1fn71t3h3wnj306u053jrf.jpg)\n",
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"\n",
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"我们的智能体通过不断地学习来更新 Q 表中的结果,最后依据 Q 表中的值来做决策。"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Q-learning 算法\n",
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"有了奖励表和 Q 表,我们需要知道智能体是如何通过学习来更新 Q 表,以便最后能够根据 Q 表进行决策,这个时候就需要讲一讲 Q-learning 的算法。\n",
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"\n",
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"Q-learning 的算法特别简单,状态转移公式如下\n",
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"\n",
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"$$Q(s, a) = R(s, a) + \\gamma \\mathop{max}_{\\tilde{a}}\\{ Q(\\tilde{s}, \\tilde{a}) \\}$$\n",
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"\n",
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"其中 s, a 表示当前的状态和行动,$\\tilde{s}, \\tilde{a}$ 分别表示 s 采取 a 的动作之后的下一个状态和该状态对应所有的行动,参数 $\\gamma$ 是一个常数,0ドル \\leq \\gamma \\le 1 $表示对未来奖励的一个衰减程度,形象地比喻就是一个人对于未来的远见程度。\n",
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"\n",
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"解释一下就是智能体通过经验进行自主学习,不断从一个状态转移到另外一个状态进行探索,并在这个过程中不断更新 Q 表,直到到达目标位置,Q 表就像智能体的大脑,更新越多就越强。我们称智能体的每一次探索为 episode,每个 episode 都表示智能体从任意初始状态到达目标状态,当智能体到达一个目标状态,那么当前的 episode 结束,进入下一个 episode。"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"下面给出 q-learning 的整个算法流程\n",
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"- step1 给定参数 $\\gamma$ 和奖励矩阵 R\n",
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"- step2 令 Q:= 0\n",
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"- step3 For each episode:\n",
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" - 3.1 随机选择一个初始状态 s\n",
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" - 3.2 若未到达目标状态,则执行以下几步\n",
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" - (1)在当前状态 s 的所有可能行动中选取一个行为 a\n",
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" - (2)利用选定的行为 a,得到下一个状态 $\\tilde{s}$\n",
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" - (3)按照前面的转移公式计算 Q(s, a)\n",
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" - (4)令 $s: = \\tilde{s}$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### 单步演示\n",
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"为了更好地理解 q-learning,我们可以示例其中一步。\n",
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"\n",
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"首先选择 $\\gamma = 0.8,ドル初始状态为 1,Q 初始化为零矩阵\n",
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"\n",
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"![](https://ws2.sinaimg.cn/large/006tNc79ly1fn71t3h3wnj306u053jrf.jpg)\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"![](https://ws2.sinaimg.cn/large/006tNc79ly1fn71o8jlinj307t055wek.jpg)\n",
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"\n",
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"因为是状态 1,所以我们观察 R 矩阵的第二行,负数表示非法行为,所以下一个状态只有两种可能,走到状态 3 或者走到状态 5,随机地,我们可以选择走到状态 5。\n",
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"\n",
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"当我们走到状态 5 之后,会发生什么事情呢?观察 R 矩阵的第 6 行可以发现,其对应于三个可能采取的动作:转至状态 1,4 或者 5,根据上面的转移公式,我们有\n",
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"\n",
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"$$Q(1, 5) = R(1, 5) + 0.8 * max\\{Q(5, 1), Q(5, 4), Q(5, 5)\\} = 100 + 0.8 * max\\{0, 0, 0\\} = 100$$\n",
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"\n",
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"所以现在 Q 矩阵进行了更新,变为了\n",
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"\n",
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"![](https://ws2.sinaimg.cn/large/006tNc79ly1fn8182u6xlj306y04mmx6.jpg)\n",
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"\n",
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"现在我们的状态由 1 变成了 5,因为 5 是最终的目标状态,所以一次 episode 便完成了,进入下一个 episode。\n",
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"\n",
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"在下一个 episode 中又随机选择一个初始状态开始,不断更新 Q 矩阵,在经过了很多个 episode 之后,矩阵 Q 接近收敛,那么我们的智能体就学会了从任意状态转移到目标状态的最优路径。"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"从上面的原理,我们知道了 q-learning 最重要的状态转移公式,这个公式也叫做 Bellman Equation,通过这个公式我们能够不断地进行更新 Q 矩阵,最后得到一个收敛的 Q 矩阵。\n",
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"\n",
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"下面我们通过代码来实现这个过程\n",
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"\n",
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"我们定义一个简单的走迷宫过程,也就是\n",
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"\n",
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"![](https://ws1.sinaimg.cn/large/006tNc79ly1fn82ja4dkwj308d08d3yj.jpg)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"初始位置随机在 state 0, state 1 和 state 2 上,然后希望智能体能够走到 state 3 获得宝藏,上面可行的行动路线已经用箭头标注了"
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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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"metadata": {
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"collapsed": true
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},
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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"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"下面定义奖励矩阵,一共是 4 行,5 列,每一行分别表示 state 0 到 state 3 这四个状态,每一列分别表示上下左右和静止 5 种状态,奖励矩阵中的 0 表示不可行的路线,比如第一个行,上走和左走都是不可行的路线,都用 0 表示,向下走会走到陷阱,所以使用 -10 表示奖励,向右走和静止都给与 -1 的奖励,因为既没有触发陷阱,也没有到达宝藏,但是过程中浪费了时间。"
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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": 2,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"reward = np.array([[0, -10, 0, -1, -1],\n",
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" [0, 10, -1, 0, -1],\n",
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" [-1, 0, 0, 10, -10],\n",
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" [-1, 0, -10, 0, 10]])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"接下来定义一个初始化为 0 的 q 矩阵"
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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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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"q_matrix = np.zeros((4, 5))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"然后定义一个转移矩阵,也就是从一个状态,采取一个可行的动作之后到达的状态,因为这里的状态和动作都是有限的,所以我们可以将他们存下来,比如第一行表示 state 0,向上和向左都是不可行的路线,所以给 -1 的值表示,向下走到达了 state 2,所以第二个值为 2,向右走到达了 state 1,所以第四个值是 1,保持不同还是在 state 0,所以最后一个标注为 0,另外几行类似。"
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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": 7,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"transition_matrix = np.array([[-1, 2, -1, 1, 0],\n",
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" [-1, 3, 0, -1, 1],\n",
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" [0, -1, -1, 3, 2],\n",
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" [1, -1, 2, -1, 3]])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"最后定义每个状态的有效行动,比如 state 0 的有效行动就是下、右和静止,对应于 1,3 和 4"
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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": 8,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"valid_actions = np.array([[1, 3, 4],\n",
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" [1, 2, 4],\n",
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" [0, 3, 4],\n",
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" [0, 2, 4]])"
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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": 9,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"# 定义 bellman equation 中的 gamma\n",
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"gamma = 0.8"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"最后开始让智能体与环境交互,不断地使用 bellman 方程来更新 q 矩阵,我们跑 10 个 episode"
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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": 10,
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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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"episode: 0, q matrix: \n",
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"[[ 0. 0. 0. -1. -1.]\n",
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" [ 0. 10. -1. 0. -1.]\n",
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" [ 0. 0. 0. 0. 0.]\n",
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" [ 0. 0. 0. 0. 0.]]\n",
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"\n",
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"episode: 1, q matrix: \n",
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"[[ 0. 0. 0. -1. -1.]\n",
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" [ 0. 10. -1. 0. -1.]\n",
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" [ 0. 0. 0. 10. 0.]\n",
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" [ 0. 0. 0. 0. 0.]]\n",
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"\n",
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"episode: 2, q matrix: \n",
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"[[ 0. -2. 0. 7. 4.6]\n",
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" [ 0. 10. 4.6 0. 7. ]\n",
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" [ -1.8 0. 0. 10. -2. ]\n",
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" [ 0. 0. 0. 0. 0. ]]\n",
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"\n",
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"episode: 3, q matrix: \n",
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"[[ 0. -2. 0. 7. 4.6]\n",
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" [ 0. 10. 4.6 0. 7. ]\n",
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" [ 4.6 0. 0. 10. -2. ]\n",
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" [ 0. 0. 0. 0. 0. ]]\n",
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"\n",
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"episode: 4, q matrix: \n",
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"[[ 0. -2. 0. 7. 4.6]\n",
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" [ 0. 10. 4.6 0. 7. ]\n",
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" [ 4.6 0. 0. 10. -2. ]\n",
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" [ 0. 0. 0. 0. 0. ]]\n",
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"\n",
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"episode: 5, q matrix: \n",
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"[[ 0. -2. 0. 7. 4.6]\n",
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" [ 0. 10. 4.6 0. 7. ]\n",
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" [ 4.6 0. 0. 10. -2. ]\n",
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" [ 0. 0. 0. 0. 0. ]]\n",
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"\n",
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"episode: 6, q matrix: \n",
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"[[ 0. -2. 0. 7. 4.6]\n",
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" [ 0. 10. 4.6 0. 7. ]\n",
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" [ 4.6 0. 0. 10. -2. ]\n",
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" [ 0. 0. 0. 0. 0. ]]\n",
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"\n",
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"episode: 7, q matrix: \n",
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"[[ 0. -2. 0. 7. 4.6]\n",
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" [ 0. 10. 4.6 0. 7. ]\n",
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" [ 4.6 0. 0. 10. -2. ]\n",
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" [ 0. 0. 0. 0. 0. ]]\n",
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"\n",
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"episode: 8, q matrix: \n",
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"[[ 0. -2. 0. 7. 4.6]\n",
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" [ 0. 10. 4.6 0. 7. ]\n",
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" [ 4.6 0. 0. 10. -2. ]\n",
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" [ 0. 0. 0. 0. 0. ]]\n",
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"\n",
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"episode: 9, q matrix: \n",
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"[[ 0. -2. 0. 7. 4.6]\n",
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" [ 0. 10. 4.6 0. 7. ]\n",
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" [ 4.6 0. 0. 10. -2. ]\n",
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" [ 0. 0. 0. 0. 0. ]]\n",
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"\n"
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]
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}
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],
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"source": [
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"for i in range(10):\n",
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" start_state = np.random.choice([0, 1, 2], size=1)[0] # 随机初始起点\n",
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" current_state = start_state\n",
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" while current_state != 3: # 判断是否到达终点\n",
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" action = random.choice(valid_actions[current_state]) # greedy 随机选择当前状态下的有效动作\n",
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" next_state = transition_matrix[current_state][action] # 通过选择的动作得到下一个状态\n",
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" future_rewards = []\n",
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" for action_nxt in valid_actions[next_state]:\n",
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" future_rewards.append(q_matrix[next_state][action_nxt]) # 得到下一个状态所有可能动作的奖励\n",
338+
" q_state = reward[current_state][action] + gamma * max(future_rewards) # bellman equation\n",
339+
" q_matrix[current_state][action] = q_state # 更新 q 矩阵\n",
340+
" current_state = next_state # 将下一个状态变成当前状态\n",
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" \n",
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" print('episode: {}, q matrix: \\n{}'.format(i, q_matrix))\n",
343+
" print()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"可以看到在第一次 episode 之后,智能体就学会了在 state 2 的时候向下走能够得到奖励,通过不断地学习,在 10 个 episode 之后,智能体知道,在 state 0,向右走能得到奖励,在 state 1 向下走能够得到奖励,在 state 3 向右 走能得到奖励,这样在这个环境中任何一个状态智能体都能够知道如何才能够最快地到达宝藏的位置\n",
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"\n",
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"从上面的例子我们简单的演示了 q-learning,可以看出自己来构建整个环境是非常麻烦的,所以我们可以通过一些第三方库来帮我们搭建强化学习的环境,其中最有名的就是 open-ai 的 gym 模块,下一章我们将介绍一下 gym。"
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