From c0daddee0097bf012e5e4b29b8e437b1bce15691 Mon Sep 17 00:00:00 2001 From: qiwang067 Date: Wed, 26 May 2021 10:19:52 +0800 Subject: [PATCH] fix ch2 --- docs/chapter2/chapter2.md | 10 +++------- docs/chapter2/img/2.40.png | Bin 768772 -> 240242 bytes 2 files changed, 3 insertions(+), 7 deletions(-) diff --git a/docs/chapter2/chapter2.md b/docs/chapter2/chapter2.md index 3ef1156..78d215f 100644 --- a/docs/chapter2/chapter2.md +++ b/docs/chapter2/chapter2.md @@ -706,8 +706,6 @@ $$ 当一直在采取 arg max 操作的时候,我们会得到一个单调的递增。通过采取这种 greedy,即 arg max 操作,我们就会得到更好的或者不变的 policy,而不会使它这个价值函数变差。所以当这个改进停止过后,我们就会得到一个最佳策略。 -![](img/2.48.png) - 当改进停止过后,我们取它最大化的这个 action,它直接就会变成它的价值函数,如下式所示: $$ q^{\pi}\left(s, \pi^{\prime}(s)\right)=\max _{a \in \mathcal{A}} q^{\pi}(s, a)=q^{\pi}(s, \pi(s))=v^{\pi}(s) @@ -863,18 +861,16 @@ $$ 我们给出一个[ Demo](https://github.com/cuhkrlcourse/RLexample/tree/master/MDP),这个 Demo 是为了解一个叫 `FrozenLake` 的例子,这个例子是 OpenAI Gym 里的一个环境,跟 gridworld 很像,不过它每一个状态转移是一个概率。 -![](img/2.64.png) - **我们再来对比下 policy iteration 和 value iteration,这两个算法都可以解 MDP 的控制问题。** -* Policy iteration 由两部分组成:policy evaluation 和 policy improvement。Policy Iteration 分两步,首先对当前已经搜索到的策略函数进行一个估值。得到估值过后,把 Q 函数算出来,我们进一步进行改进。 -* Value iteration 直接把 Bellman Optimality Equation 拿进来,然后去寻找最佳的 value function,没有 policy function 在这里面。当算出 optimal value function 过后,我们再来提取最佳策略。 +* Policy Iteration 分两步,首先进行 policy evaluation,即对当前已经搜索到的策略函数进行一个估值。得到估值过后,进行 policy improvement,即把 Q 函数算出来,我们进一步进行改进。不断重复这两步,直到策略收敛。 +* Value iteration 直接把 Bellman Optimality Equation 拿进来,然后去寻找最佳的 value function,没有 policy function 在这里面。当算出 optimal value function 过后,我们再来提取最佳策略。 ### Summary for Prediction and Control in MDP ![](img/2.65.png) -这里是一个总结,就对于 MDP 里面的 prediction 和 control 都是用动态规划来解,我们其实采取了不同的 Bellman Equation。 +总结如上表所示,就对于 MDP 里面的 prediction 和 control 都是用动态规划来解,我们其实采取了不同的 Bellman Equation。 * 如果是一个 prediction 的问题,即 policy evaluation 的问题,直接就是不停地 run 这个 Bellman Expectation Equation,这样我们就可以去估计出给定的这个策略,然后得到价值函数。 * 对于 control, diff --git 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