From 826a625e13a87e71791a91f5bb4f481b44aca315 Mon Sep 17 00:00:00 2001 From: qiwang067 Date: Sat, 1 May 2021 23:24:55 +0800 Subject: [PATCH 1/3] fix ch1 --- docs/chapter1/chapter1.md | 17 +++++++---------- 1 file changed, 7 insertions(+), 10 deletions(-) diff --git a/docs/chapter1/chapter1.md b/docs/chapter1/chapter1.md index 7c62e00..d6c27c8 100644 --- a/docs/chapter1/chapter1.md +++ b/docs/chapter1/chapter1.md @@ -96,7 +96,7 @@ 强化学习是有一定的历史的,只是最近大家把强化学习跟深度学习结合起来,就形成了`深度强化学习(Deep Reinforcemet Learning)`。深度强化学习 = 深度学习 + 强化学习。这里做一个类比,把它类比于这个传统的计算机视觉以及深度计算机视觉。 * 传统的计算机视觉由两个过程组成。 - * 你给一张图,我们先要提取它的特征,用一些设计好的特征(feature),比如说 HOG、DPM。 + * 给定一张图,我们先要提取它的特征,用一些设计好的特征(feature),比如说 HOG、DPM。 * 提取这些特征后,我们再单独训练一个分类器。这个分类器可以是 SVM、Boosting,然后就可以辨别这张图片是狗还是猫。 * 2012 年过后,我们有了卷积神经网络,大家就把特征提取以及分类两者合到一块儿去了,就是训练一个神经网络。这个神经网络既可以做特征提取,也可以做分类。它可以实现这种端到端的训练,它里面的参数可以在每一个阶段都得到极大的优化,这样就得到了一个非常重要的突破。 @@ -120,10 +120,10 @@ ![](img/1.17.png) 接下来给大家再看一些强化学习里面比较有意思的例子。 -* **第一个例子是 [DeepMind 研发的一个走路的 agent](https://www.youtube.com/watch?v=gn4nRCC9TwQ)。**这个 agent 往前走一步,你就会得到一个 reward。这个 agent 有不同的这个形态,可以学到很多有意思的功能。比如怎么跨越这个障碍物,就像那个蜘蛛那样的 agent 。怎么跨越障碍物,像这个人有双腿一样, 这个 agent 往前走。以及像这个人形的 agent,怎么在一个曲折的道路上面往前走。这个结果也是非常有意思,这个人形 agent 会把手举得非常高,因为它这个手的功能就是为了使它身体保持平衡,这样它就可以更快地在这个环境里面往前跑,而且这里你也可以增加这个环境的难度,加入一些扰动,这个 agent 就会变得更鲁棒。 -* **第二个例子是[机械臂抓取](https://ai.googleblog.com/2016/03/deep-learning-for-robots-learning-from.html)。**因为机械臂的应用自动去强化学习需要大量的 rollout,所以它这里就有好多机械臂,分布式系统可以让这个机械臂尝试抓取不同的物体。你发现这个盘子里面物体的形状、形态其实都是不同的,这样就可以让这个机械臂学到一个统一的行为。然后在不同的抓取物下面都可以采取最优的一个抓取特征。你的这个抓取的物件形态存在很多不同,一些传统的这个抓取算法就没法把所有物体都抓起来,因为你对每一个物体都需要做一个建模,这样的话就是非常花时间。但是通过强化学习,你就可以学到一个统一的抓取算法,在不同物体上它都可以适用。 -* **第三个例子是 [OpenAI 做的一个机械臂翻魔方](https://www.youtube.com/watch?v=jwSbzNHGflM)。**这里它们 18 年的时候先设计了这个手指的一个机械臂,让它可以通过翻动手指,使得手中的这个木块达到一个预定的设定。人的手指其实非常精细,怎么使得这个机械手臂也具有这样灵活的能力就一直是个问题。它们通过这个强化学习在一个虚拟环境里面先训练,让 agent 能翻到特定的这个方向,再把它应用到真实的手臂之中。这在强化学习里面是一个比较常用的做法,就是你先在虚拟环境里面得到一个很好的 agent,然后再把它使用到真实的这个机器人中。因为真实的机械手臂通常都是非常容易坏,而且非常贵,你没法大批量地购买。2019 年对手臂进一步改进了,这个手臂可以玩魔方了。这个结果也非常有意思,到后面,这个魔方就被恢复成了个六面都是一样的结构了。 -* **第四个例子是[一个穿衣服的 agent](https://www.youtube.com/watch?v=ixmE5nt2o88) ,就是训练这个 agent 穿衣服。**因为很多时候你要在电影或者一些动画实现人穿衣服的场景,通过手写执行命令让机器人穿衣服其实非常困难。很多时候穿衣服也是一个非常精细的操作,那么它们这个工作就是训练这个强化学习 agent,然后就可以实现这个穿衣功能。你还可以在这里面加入一些扰动,然后 agent 可以抗扰动。可能会有失败的情况(failure case), agent 就穿不进去,就卡在这个地方。 +1. **[DeepMind 研发的一个走路的 agent](https://www.youtube.com/watch?v=gn4nRCC9TwQ)。**这个 agent 往前走一步,你就会得到一个 reward。这个 agent 有不同的这个形态,可以学到很多有意思的功能。比如怎么跨越这个障碍物,就像那个蜘蛛那样的 agent 。怎么跨越障碍物,像这个人有双腿一样, 这个 agent 往前走。以及像这个人形的 agent,怎么在一个曲折的道路上面往前走。这个结果也是非常有意思,这个人形 agent 会把手举得非常高,因为它这个手的功能就是为了使它身体保持平衡,这样它就可以更快地在这个环境里面往前跑,而且这里你也可以增加这个环境的难度,加入一些扰动,这个 agent 就会变得更鲁棒。 +2. **[机械臂抓取](https://ai.googleblog.com/2016/03/deep-learning-for-robots-learning-from.html)。**因为机械臂的应用自动去强化学习需要大量的 rollout,所以它这里就有好多机械臂,分布式系统可以让这个机械臂尝试抓取不同的物体。你发现这个盘子里面物体的形状、形态其实都是不同的,这样就可以让这个机械臂学到一个统一的行为。然后在不同的抓取物下面都可以采取最优的一个抓取特征。你的这个抓取的物件形态存在很多不同,一些传统的这个抓取算法就没法把所有物体都抓起来,因为你对每一个物体都需要做一个建模,这样的话就是非常花时间。但是通过强化学习,你就可以学到一个统一的抓取算法,在不同物体上它都可以适用。 +3. **[OpenAI 做的一个机械臂翻魔方](https://www.youtube.com/watch?v=jwSbzNHGflM)。**这里它们 18 年的时候先设计了这个手指的一个机械臂,让它可以通过翻动手指,使得手中的这个木块达到一个预定的设定。人的手指其实非常精细,怎么使得这个机械手臂也具有这样灵活的能力就一直是个问题。它们通过这个强化学习在一个虚拟环境里面先训练,让 agent 能翻到特定的这个方向,再把它应用到真实的手臂之中。这在强化学习里面是一个比较常用的做法,就是你先在虚拟环境里面得到一个很好的 agent,然后再把它使用到真实的这个机器人中。因为真实的机械手臂通常都是非常容易坏,而且非常贵,你没法大批量地购买。2019 年对手臂进一步改进了,这个手臂可以玩魔方了。这个结果也非常有意思,到后面,这个魔方就被恢复成了个六面都是一样的结构了。 +4. **[一个穿衣服的 agent](https://www.youtube.com/watch?v=ixmE5nt2o88) ,就是训练这个 agent 穿衣服。**因为很多时候你要在电影或者一些动画实现人穿衣服的场景,通过手写执行命令让机器人穿衣服其实非常困难。很多时候穿衣服也是一个非常精细的操作,那么它们这个工作就是训练这个强化学习 agent,然后就可以实现这个穿衣功能。你还可以在这里面加入一些扰动,然后 agent 可以抗扰动。可能会有失败的情况(failure case), agent 就穿不进去,就卡在这个地方。 ## Introduction to Sequential Decision Making @@ -337,14 +337,9 @@ A: 针对是否需要对真实环境建模,强化学习可以分为有模型 Learning 和 Planning 是序列决策的两个基本问题。 -### Reinforcement Learning - ![](img/learning.png) 在强化学习中,环境初始时是未知的,agent 不知道环境如何工作,agent 通过不断地与环境交互,逐渐改进策略。 - -### Planning - ![](img/planning.png) 在 plannning 中,环境是已知的,我们被告知了整个环境的运作规则的详细信息。Agent 能够计算出一个完美的模型,并且在不需要与环境进行任何交互的时候进行计算。Agent 不需要实时地与环境交互就能知道未来环境,只需要知道当前的状态,就能够开始思考,来寻找最优解。 @@ -680,3 +675,5 @@ print('平均回合奖励 = {}'.format(np.mean(episode_rewards))) + + From 1e5da365475ef1a905daf47d5341ecfb86bd4448 Mon Sep 17 00:00:00 2001 From: qiwang067 Date: Mon, 3 May 2021 20:17:57 +0800 Subject: [PATCH 2/3] fix ch1 --- docs/chapter1/chapter1.md | 40 ++++++++++++++++++--------------- docs/chapter1/img/1.1.png | Bin 143653 -> 29867 bytes docs/chapter1/img/1.3.png | Bin 223139 -> 125946 bytes docs/chapter1/img/1.36.png | Bin 317269 -> 252544 bytes docs/chapter1/img/1.46.png | Bin 303412 -> 263567 bytes docs/chapter1/img/1.47.png | Bin 435254 -> 405029 bytes docs/chapter1/img/1.9.png | Bin 258220 -> 146510 bytes docs/chapter1/img/learning.png | Bin 742443 -> 566607 bytes docs/chapter1/img/planning.png | Bin 287585 -> 92341 bytes 9 files changed, 22 insertions(+), 18 deletions(-) diff --git a/docs/chapter1/chapter1.md b/docs/chapter1/chapter1.md index d6c27c8..c9bbddb 100644 --- a/docs/chapter1/chapter1.md +++ b/docs/chapter1/chapter1.md @@ -4,10 +4,7 @@ ![](img/1.1.png) -* **强化学习讨论的问题是一个智能体(agent) 怎么在一个复杂不确定的环境(environment)里面去极大化它能获得的奖励。** - -* 示意图由两部分组成:agent 和 environment。 -* 在强化学习过程中,agent 跟 environment 一直在交互。Agent 在环境里面获取到状态,agent 会利用这个状态输出一个动作(action),一个决策。然后这个决策会放到环境之中去,环境会根据 agent 采取的决策,输出下一个状态以及当前的这个决策得到的奖励。Agent 的目的就是为了尽可能多地从环境中获取奖励。 +**强化学习讨论的问题是一个智能体(agent) 怎么在一个复杂不确定的环境(environment)里面去极大化它能获得的奖励。** 示意图由两部分组成:agent 和 environment。在强化学习过程中,agent 跟 environment 一直在交互。Agent 在环境里面获取到状态,agent 会利用这个状态输出一个动作(action),一个决策。然后这个决策会放到环境之中去,环境会根据 agent 采取的决策,输出下一个状态以及当前的这个决策得到的奖励。Agent 的目的就是为了尽可能多地从环境中获取奖励。 ![](img/1.2.png) @@ -24,7 +21,7 @@ ![](img/1.3.png) -在强化学习里面,这两点其实都不满足。举一个 Atari Breakout 游戏的例子,这是一个打砖块的游戏,控制木板,然后把这个球反弹到上面来消除这些砖块。 +在强化学习里面,这两点其实都不满足。举一个 Atari Breakout 游戏的例子,这是一个打砖块的游戏,控制木板左右移动把球反弹到上面来消除砖块。 * 在游戏过程中,大家可以发现这个 agent 得到的观测不是个独立同分布的分布,上一帧下一帧其实有非常强的连续性。这就是说,得到的数据是相关的时间序列数据,不满足独立同分布。 * 另外一点,在玩游戏的过程中,你并没有立刻获得反馈,没有告诉你哪个动作是正确动作。比如你现在把这个木板往右移,那么只会使得这个球往上或者往左上去一点,你并不会得到立刻的反馈。所以强化学习这么困难的原因是没有得到很好的反馈,然后你依然希望 agent 在这个环境里面学习。 @@ -196,11 +193,11 @@ POMDP 可以用一个 7 元组描述:$(S,A,T,R,\Omega,O,\gamma)$,其中 $S$ 对于一个强化学习 agent,它可能有一个或多个如下的组成成分: -* 首先 agent 有一个 `策略函数(policy function)`,agent 会用这个函数来选取下一步的动作。 +* `策略函数(policy function)`,agent 会用这个函数来选取下一步的动作。 -* 然后它也可能生成一个`价值函数(value function)`。我们用价值函数来对当前状态进行估价,它就是说你进入现在这个状态,可以对你后面的收益带来多大的影响。当这个价值函数大的时候,说明你进入这个状态越有利。 +* `价值函数(value function)`,我们用价值函数来对当前状态进行估价,它就是说你进入现在这个状态,可以对你后面的收益带来多大的影响。当这个价值函数大的时候,说明你进入这个状态越有利。 -* 另外一个组成成分是`模型(model)`。模型表示了 agent 对这个环境的状态进行了理解,它决定了这个世界是如何进行的。 +* `模型(model)`,模型表示了 agent 对这个环境的状态进行了理解,它决定了这个世界是如何进行的。 ### Policy @@ -237,12 +234,19 @@ $$ 所以你未来可以获得多少的奖励,它的这个期望取决于你当前的状态和当前的行为。这个 Q 函数是强化学习算法里面要学习的一个函数。因为当我们得到这个 Q 函数后,进入某一种状态,它最优的行为就可以通过这个 Q 函数来得到。 ### Model -![](img/1.28.png) 第三个组成部分是模型,**模型决定了下一个状态会是什么样的,就是说下一步的状态取决于你当前的状态以及你当前采取的行为。**它由两个部分组成, -* 概率:这个转移状态之间是怎么转移的。 +* 概率:这个转移状态之间是怎么转移的,如下式所示: + +$$ +\mathcal{P}_{s s^{\prime}}^{a}=\mathbb{P}\left[S_{t+1}=s^{\prime} \mid S_{t}=s, A_{t}=a\right] +$$ + +* 奖励函数:当你在当前状态采取了某一个行为,可以得到多大的奖励,如下式所示: +$$ +\mathcal{R}_{s}^{a}=\mathbb{E}\left[R_{t+1} \mid S_{t}=s, A_{t}=a\right] +$$ -* 奖励函数:当你在当前状态采取了某一个行为,可以得到多大的奖励。 ![](img/1.29.png) @@ -252,9 +256,9 @@ $$ 我们来看一个走迷宫的例子。 -* 这个例子要求 agent 从 start 开始,然后到达 goal 的位置。 -* 这里设定的奖励是每走一步,你就会得到一个负的奖励。 -* 这里可以采取的动作是往上下左右走。 +* 要求 agent 从 start 开始,然后到达 goal 的位置。 +* 每走一步,你就会得到一个负的奖励。 +* 可以采取的动作是往上下左右走。 * 当前状态用现在 agent 所在的位置来描述。 ![](img/1.31.png) @@ -295,8 +299,8 @@ A: 对于一个状态转移概率已知的马尔可夫决策过程,我们可 **另外,我们是可以通过 agent 到底有没有学习这个环境模型来分类。** -* 第一种是 `model-based(有模型)` RL agent,它通过学习这个状态的转移来采取动作。 -* 另外一种是 ` model-free(免模型)` RL agent,它没有去直接估计这个状态的转移,也没有得到环境的具体转移变量。它通过学习价值函数和策略函数进行决策。Model-free 的模型里面没有一个环境转移的模型。 +* `model-based(有模型)` RL agent,它通过学习这个状态的转移来采取动作。 +* ` model-free(免模型)` RL agent,它没有去直接估计这个状态的转移,也没有得到环境的具体转移变量。它通过学习价值函数和策略函数进行决策。Model-free 的模型里面没有一个环境转移的模型。 我们可以用马尔可夫决策过程来定义强化学习任务,并表示为四元组 $$,即状态集合、动作集合、状态转移函数和奖励函数。如果这四元组中所有元素均已知,且状态集合和动作集合在有限步数内是有限集,则机器可以对真实环境进行建模,构建一个虚拟世界来模拟真实环境的状态和交互反应。 @@ -450,8 +454,8 @@ for step in range(100): ![](img/1.46.png) 在 OpenAI Gym 里面有很经典的控制类游戏。 -* 比如说 Acrobot,就是把这个两节铁杖,然后甩了立起来。 -* CartPole 是通过控制一个平板,让这个木棍立起来。 +* 比如说 Acrobot 就是把两节铁杖甩了立起来。 +* CartPole 是通过控制一个平板,让木棍立起来。 * MountainCar 是通过前后移动这个车,让它到达这个旗子的位置。 大家可以点[这个链接](https://gym.openai.com/envs/#classic_control)看一看这些环境。在刚开始测试强化学习的时候,可以选择这些简单环境,因为这些环境可以在一两分钟之内见到一个效果。 diff --git a/docs/chapter1/img/1.1.png b/docs/chapter1/img/1.1.png index 5b62908641bb58e79c3c8d2d7fc5af61abfc208c..9b23653a71044dd6f66c3289bbe0bb7df734bf5a 100644 GIT binary patch literal 29867 zcmc$`by$^M^esxWk=lTChal2OcZZZkcXxM4cXu~}N;gu1G}2wt2#PdF$6ed+`+n!# z^PKzl#Rqr1wbuL2HDio1iFm0ji}{G;5gZ&Gro5cgYdAOrJ@Ebzf&%`heY)reUXaYi 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From 08e1a365e2e7fde5f3f75b31e9dd4c71ea4494bf Mon Sep 17 00:00:00 2001 From: qiwang067 Date: Mon, 3 May 2021 21:10:01 +0800 Subject: [PATCH 3/3] fix #27 --- docs/chapter2/chapter2.md | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/docs/chapter2/chapter2.md b/docs/chapter2/chapter2.md index c88610c..308860c 100644 --- a/docs/chapter2/chapter2.md +++ b/docs/chapter2/chapter2.md @@ -274,9 +274,13 @@ $$ * 我们就可以从 $s_4$ 状态开始,随机产生很多轨迹,就是说产生很多小船,把小船扔到这个转移矩阵里面去,然后它就会随波逐流,产生轨迹。 * 每个轨迹都会得到一个 return,我们得到大量的 return,比如说一百个、一千个 return ,然后直接取一个平均,那么就可以等价于现在 $s_4$ 这个价值,因为 $s_4$ 的价值 $V(s_4)$ 定义了你未来可能得到多少的奖励。这就是蒙特卡罗采样的方法。 -![](img/2.17.png)**我们也可以用这个动态规划的办法**,一直去迭代它的 Bellman equation,让它最后收敛,我们就可以得到它的一个状态。所以在这里算法二就是一个迭代的算法,通过 bootstrapping(拔靴自助) 的办法,然后去不停地迭代这个 Bellman Equation。当这个最后更新的状态跟你上一个状态变化并不大的时候,更新就可以停止,我们就可以输出最新的 $V'(s)$ 作为它当前的状态。所以这里就是把 Bellman Equation 变成一个 Bellman Update,这样就可以得到它的一个价值。 +![](img/2.17.png) ->动态规划的方法基于后继状态值的估计来更新状态值的估计(算法二中的第 3 行用 $V'$ 来更新 $V$ )。也就是说,它们根据其他估算值来更新估算值。我们称这种基本思想为 bootstrapping。 +**我们也可以用这个动态规划的办法**,一直去迭代它的 Bellman equation,让它最后收敛,我们就可以得到它的一个状态。所以在这里算法二就是一个迭代的算法,通过 `bootstrapping(自举) `的办法,然后去不停地迭代这个 Bellman Equation。当这个最后更新的状态跟你上一个状态变化并不大的时候,更新就可以停止,我们就可以输出最新的 $V'(s)$ 作为它当前的状态。所以这里就是把 Bellman Equation 变成一个 Bellman Update,这样就可以得到它的一个价值。 + +动态规划的方法基于后继状态值的估计来更新状态值的估计(算法二中的第 3 行用 $V'$ 来更新 $V$ )。也就是说,它们根据其他估算值来更新估算值。我们称这种基本思想为 bootstrapping。 + +>Bootstrap 本意是“解靴带”;这里是在使用徳国文学作品《吹牛大王历险记》中解靴带自助(拔靴自助)的典故,因此将其译为“自举”。 ## Markov Decision Process(MDP)

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