From 9cc7ea7c98cd53d561e8256b5caa5f4ae922e049 Mon Sep 17 00:00:00 2001 From: qiwang067 Date: Wed, 26 May 2021 14:27:19 +0800 Subject: [PATCH] fix ch3 --- docs/chapter3/chapter3.md | 19 +++++-------------- docs/chapter3/img/off_policy_learning.png | Bin 601780 -> 430624 bytes 2 files changed, 5 insertions(+), 14 deletions(-) diff --git a/docs/chapter3/chapter3.md b/docs/chapter3/chapter3.md index d12a105..c27c8a3 100644 --- a/docs/chapter3/chapter3.md +++ b/docs/chapter3/chapter3.md @@ -221,9 +221,7 @@ MC 是通过 empirical mean return (实际得到的收益)来更新它,对 在人的身上是可以建立多级的条件反射的,举个例子,比如说一般我们遇到熊都是这样一个顺序:看到树上有熊爪,然后看到熊之后,突然熊发怒,扑过来了。经历这个过程之后,我们可能最开始看到熊才会瑟瑟发抖,后面就是看到树上有熊爪就已经有害怕的感觉了。也就说在不断的重复试验之后,下一个状态的价值,它是可以不断地去强化影响上一个状态的价值的。 -![](img/3.12.png) - -**为了让大家更加直观感受下一个状态影响上一个状态**,我们推荐这个网站:[Temporal Difference Learning Gridworld Demo](https://cs.stanford.edu/people/karpathy/reinforcejs/gridworld_td.html)。 +**为了让大家更加直观感受下一个状态影响上一个状态(状态价值迭代)**,我们推荐这个网站:[Temporal Difference Learning Gridworld Demo](https://cs.stanford.edu/people/karpathy/reinforcejs/gridworld_td.html)。 ![](img/3.13.png ':size=500') @@ -260,7 +258,7 @@ MC 是通过 empirical mean return (实际得到的收益)来更新它,对 \end{aligned} $$ -* TD目标是估计有两个原因:它在(6.4)中对期望值进行采样,并且使用当前估计V 而不是真实 $v_{\pi}$。 +* TD目标是估计有两个原因:它对期望值进行采样,并且使用当前估计 V 而不是真实 $v_{\pi}$。 * `TD error` $\delta=R_{t+1}+\gamma v(S_{t+1})-v(S_t)$。 @@ -407,15 +405,13 @@ $\varepsilon\text{-greedy}$ 的意思是说,我们有 $1-\varepsilon$ 的概 ![](img/model_free_control_7.png)上图是带 $\varepsilon$-greedy 探索的 MC 算法的伪代码。 -![](img/model_free_control_8.png) - 与 MC 相比,TD 有如下几个优势: * 低方差。 * 能够在线学习。 * 能够从不完整的序列学习。 -所以我们可以把 TD 也放到 control loop 里面去估计 Q-table,再采取这个 $\varepsilon$-greedy improvement。这样就可以在 episode 没结束的时候来更新已经采集到的状态价值。 +所以我们可以把 TD 也放到 control loop 里面去估计 Q-table,再采取这个 $\varepsilon$-greedy policy improvement。这样就可以在 episode 没结束的时候来更新已经采集到的状态价值。 ![](img/bias_variance.png ':size=450') @@ -494,7 +490,7 @@ Sarsa 是一种 on-policy 策略。Sarsa 优化的是它实际执行的策略, ![](img/off_policy_learning.png) -再举个例子。比如环境是一个波涛汹涌的大海,但 learning policy 太胆小了,没法直接跟环境去学习,所以我们有了 exploratory policy,exploratory policy 是一个不畏风浪的海盗,他非常激进,可以在环境中探索。他有很多经验,可以把这些经验写成稿子,然后喂给这个 learning policy。Learning policy 可以通过这个稿子来进行学习。 +再举个例子,如上图所示,比如环境是一个波涛汹涌的大海,但 learning policy 太胆小了,没法直接跟环境去学习,所以我们有了 exploratory policy,exploratory policy 是一个不畏风浪的海盗,他非常激进,可以在环境中探索。他有很多经验,可以把这些经验写成稿子,然后喂给这个 learning policy。Learning policy 可以通过这个稿子来进行学习。 在 off-policy learning 的过程中,我们这些轨迹都是 behavior policy 跟环境交互产生的,产生这些轨迹后,我们使用这些轨迹来更新 target policy $\pi$。 @@ -504,8 +500,6 @@ Sarsa 是一种 on-policy 策略。Sarsa 优化的是它实际执行的策略, * 可以让我们学习其他 agent 的行为,模仿学习,学习人或者其他 agent 产生的轨迹; * 重用老的策略产生的轨迹。探索过程需要很多计算资源,这样的话,可以节省资源。 -![](img/Q-learning.png) - Q-learning 有两种 policy:behavior policy 和 target policy。 Target policy $\pi$ 直接在 Q-table 上取 greedy,就取它下一步能得到的所有状态,如下式所示: @@ -550,11 +544,9 @@ Sarsa 是用自己的策略产生了 S,A,R,S',A' 这一条轨迹。然后拿着 对 Q-learning 进行逐步地拆解的话,跟 Sarsa 唯一一点不一样就是并不需要提前知道 $A_2$ ,我就能更新 $Q(S_1,A_1)$ 。在训练一个 episode 这个流程图当中,Q-learning 在 learn 之前它也不需要去拿到 next action $A'$,它只需要前面四个 $ (S,A,R,S')$ ,这跟 Sarsa 很不一样。 ## On-policy vs. Off-policy -![](img/3.20.png) - **总结一下 on-policy 和 off-policy 的区别。** -* Sarsa 是一个典型的 on-policy 策略,它只用了一个 policy $\pi$ 。如果 policy 采用 $\varepsilon$-greedy 算法的话,它需要兼顾探索,为了兼顾探索和利用,它训练的时候会显得有点胆小。它在解决悬崖问题的时候,会尽可能地离悬崖边上远远的,确保说哪怕自己不小心探索了一点,也还是在安全区域内。此外,因为采用的是 $\varepsilon$-greedy 算法,策略会不断改变($\varepsilon$ 会不断变小),所以策略不稳定。 +* Sarsa 是一个典型的 on-policy 策略,它只用了一个 policy $\pi$,它只用了一个 policy $\pi$,它不仅使用策略 $\pi$ 学习,还使用策略 $\pi$ 与环境交互产生经验。如果 policy 采用 $\varepsilon$-greedy 算法的话,它需要兼顾探索,为了兼顾探索和利用,它训练的时候会显得有点胆小。它在解决悬崖问题的时候,会尽可能地离悬崖边上远远的,确保说哪怕自己不小心探索了一点,也还是在安全区域内。此外,因为采用的是 $\varepsilon$-greedy 算法,策略会不断改变($\varepsilon$ 会不断变小),所以策略不稳定。 * Q-learning 是一个典型的 off-policy 的策略,它有两种策略:target policy 和 behavior policy。它分离了目标策略跟行为策略。Q-learning 就可以大胆地用 behavior policy 去探索得到的经验轨迹来去优化目标策略,从而更有可能去探索到最优的策略。Behavior policy 可以采用 $\varepsilon$-greedy 算法,但 target policy 采用的是 greedy 算法,直接根据 behavior policy 采集到的数据来采用最优策略,所以 Q-learning 不需要兼顾探索。 * 比较 Q-learning 和 Sarsa 的更新公式可以发现,Sarsa 并没有选取最大值的 max 操作,因此, * Q-learning 是一个非常激进的算法,希望每一步都获得最大的利益; @@ -583,4 +575,3 @@ Sarsa 是用自己的策略产生了 S,A,R,S',A' 这一条轨迹。然后拿着 - diff --git a/docs/chapter3/img/off_policy_learning.png b/docs/chapter3/img/off_policy_learning.png index 8f28c751b116585724e6504ef5a29214fcc274ca..1b3e246a41e0a3818622c7538d445382c1a39a98 100644 GIT binary patch literal 430624 zcmZ^L1y~%-(lstYg9n!Y3GVLh8rU1pz| z?dh7H?yjjib*hJO1vzn~cewAsz`&3sB}A0Kz@Rq4z`#f0U_d3T1@0W|10v5|z5EEw2V3NSFgATY2;P?6t07?=wK7}%jc7#LS77#OyFW|JZh=tPi- zx}>SBEEpB&7!C{?91RQ-bOa9i0|Une`+YUg5ttM>-v1mcfq(k1IuKxBp%!3J|5Zm5 zwEz8y1ATwX{Cf|X1OC5P%z^mt+EAN0kpF!QKKfg1QN29}w1c;o&~O3+!y^Cv1(#I% zcn$^zVQKM2-C12$hRev#hR(p)&d`L;-Nyd66c~>?7wFK&#Myw@-NxG1iOZdr^j|f& zK*zs}=}C$IRmItgmsDL=fmqni(S(?lj)jhal35h}eILgMRUnnmaq& zbJ5egxw+A~G1J*On$a_Ia&po$FwrwH(SmBwI(gVS8@SWjI+6YRBL96I5fdjPM+RN zedga{|LWJjo8$R?F)n#W3lq={|Gq6gMxK8)@c)(l@9q7&zLJTPowdvF>MFJt&U{S& zCGtn{e@Ojqn@iZv+Rjng-oVJ@cO!om{aIVV!rjDLUBtr1#MbFw_r=N#YUf{4f1dh3 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