From 9c5bf74ab9fb66eda1027ed8e96b096f50abb2f6 Mon Sep 17 00:00:00 2001 From: lxc Date: Thu, 14 Apr 2022 03:19:44 +0800 Subject: [PATCH] =?UTF-8?q?=E9=99=88=E5=B9=B3=E5=86=B3=E7=AD=96=E8=BF=87?= =?UTF-8?q?=E7=A8=8B=E4=B8=8E=E8=B5=A2=E5=8C=96=E5=AD=A6=E4=B9=A0=20?= =?UTF-8?q?=E7=90=86=E8=AE=BA=20(#33)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * 添加 陈平决策过程与赢化学习 理论 * 添加 陈平决策过程与赢化学习 材料 --- .../陈平决策过程与赢化学习.md | 82 ++++++++++++++++++ .../陈平决策过程与赢化学习.pdf | Bin 0 -> 615924 bytes .../陈平决策过程与赢化学习.png | Bin 0 -> 370893 bytes 3 files changed, 82 insertions(+) create mode 100644 张维为陈平曹丰泽等知名言论收集/陈平决策过程与赢化学习/陈平决策过程与赢化学习.md create mode 100644 张维为陈平曹丰泽等知名言论收集/陈平决策过程与赢化学习/陈平决策过程与赢化学习.pdf create mode 100644 张维为陈平曹丰泽等知名言论收集/陈平决策过程与赢化学习/陈平决策过程与赢化学习.png diff --git a/张维为陈平曹丰泽等知名言论收集/陈平决策过程与赢化学习/陈平决策过程与赢化学习.md b/张维为陈平曹丰泽等知名言论收集/陈平决策过程与赢化学习/陈平决策过程与赢化学习.md new file mode 100644 index 0000000..9ef6f35 --- /dev/null +++ b/张维为陈平曹丰泽等知名言论收集/陈平决策过程与赢化学习/陈平决策过程与赢化学习.md @@ -0,0 +1,82 @@ +![](https://pic3.zhimg.com/v2-3e4801ad915d410d302ee2423d94ce46_1440w.jpg?source=172ae18b) + +# 陈平决策过程(Champion Decision Process)与赢化学习(Winning Learning) + +## 引言 + +赢理论及其变体的生成,使得Vietnamese的麻指数日益增大,Vietnam稳中向好。这得益于[@知木](https://www.zhihu.com/people/bb2238bf39b73309abf5e40dc73f1455) et al. 对于赢函数的定义1,以及[@Deserter](https://www.zhihu.com/people/3f2aac8be8ac488a9c097db1839b1a7d) et al.2在比较赢理论上的创新。此外,[@loy](https://www.zhihu.com/people/8700e24ad92b01c216c9328730457622) et al.3将赢学引入量子论的成功也让学者们看到了赢学的潜质。 + +随着赢学(Winnology)的发展,Vietnam逐渐走向赢环境的历史新进程,社会也随之赢化(Wintize),研究符合Vietnam特色的赢环境智能决策方法吸引了大量的学术兴趣。在本工作中,我们首先定义了赢环境的特性,称为陈平决策过程(Champion Decision Process)。随后为赢环境提出了赢化学习,该方法能通过不断地与赢环境交互,在陈平决策过程中达到恒赢态。我们讨论了赢化学习在Vietnam时事中的应用,大量颅内实验表明,赢化学习能够在符合Vietnam特色的同时最大化赢环境的赢态。 + +## 陈平决策过程 + +任意一个环境可以被建模为一个五元组 $ $,其中$S$为赢环境的状态空间,$A$为对应的行为空间,$P:\leftarrow S\times A$表示状态转移函数,$\omega \in [win,lose]$为输赢函数,$\gamma$值折扣因子。 + +如果该环境满足: +$$ +\forall s_{t_{0}}\in S, \exists j = [a_0,a_1,...|a\in A], +$$ +使得 +$$ +\omega(s_t)=win,s_t=P((((s_{t_0},a_0)...)a_{t-2}),a_{t-1}), +$$ +那么该过程被称为**陈平决策过程**(Champion Decision Process,CDP),该环境被称为**赢环境**。 + +例如,$s_{t_0}$ :Vietnam教育资源分配不公,$a_0$ :严禁教育机构提供网上或课外教程,lose; + +$s_{t_1}$ :欠发达地区初升高人数变少,$a_1$ :百分之五十人上职高,lose; + +$s_{t_2}$ :达利特阶级跨域困难,$a_2$ :企业招聘不得限制学历,win! + +对于**赢轨迹**$ y = (s_{t_0},s_{t_1},\dots,s_t) , w=win$的次数为**赢态$ W_y $**。在上述例子中赢态为1。如果 + +$s_{t_3}$ :达利特进入大厂当互联网民工,$a_3$ :胡志明市地铁公然支持996,lose; + +$s_{t_4}$ :Vietnam大量年轻人猝死,$a_4$ :越南平安银行推出平安996奋斗无忧意外险,win! + +那么上述**赢轨迹**的**赢态**$W_y$为2 + +## 赢化学习 + +在一个赢环境中,构建策略$a \sim \pi(s)$。赢化学习的目的是对于任意初始化状态$s_{t_0}$,学习策略$\pi$得到状态轨迹$y$,最大化轨迹$y$的赢态$W_y:\max W_y$。赢策略$\pi$的梯度为: +$$ +\nabla_\theta J(\theta)=E_\pi[\nabla_\theta\log\pi(s_t,a_t)\omega_t] +$$ + + +## 内在赢驱动 + +然而在Vietnam社会中,赢态非常小且甚至为0,不利于national pride。受赢函数启发,引入内在赢驱动鼓励Vietnamese。 + +> 定理1对于一个函数$y=f(x),x\in R$,如果存在一个$n\in N$,在一个区间内使得$\frac{d^ny}{dx^n}\leq0$,称这个函数为赢函数,此区间为**赢域(Win Domain)** + +修改$w$为$w^\prime=\frac{1}{n}$,$n$为$w(s,a)$的赢域。此时赢策略$\pi$的梯度为 +$$ +\nabla_\theta J(\theta)=E_\pi[\nabla_\theta \log\pi(s_t,a_t)w^\prime_t] +$$ + + +## 优势赢函数 + +正如兔兔所说,赢是相对的,不是绝对的,稳定的Vietnamese government需要相对赢,实现优势在我。例如,COV19Vietnam22日新增确诊59,米国新增15056,赢! + +构建用于比较的陈平决策过程$<\bar{S},\bar{A},\bar{P},\bar{w},\bar{\gamma}>$,在时刻$t$,构建优势函数A: +$$ +A_t=w^\prime(s_t,a_t)-w^\prime(s_t,a_t) +$$ +此时的策略梯度改写成: +$$ +\nabla_\theta J(\theta)=E_\pi[\nabla_\theta\log\pi(s_t,a_t)A_t] +$$ + + +## 未来展望 + +陈平决策过程需要对社会赢环境确切的观测。当环境为部分可观测时,赢化学习难以得到最优赢策略。例如,Vietnam的首陀罗观测不到达利特吠舍的生活,大肆宣传后浪,不赢反输。此外,对于赢函数的过高估计问题也是赢化学习面临的挑战之一。例如,Vietnam亲自下场造势丁真,高估饭圈带来的赢态,输的一塌糊涂。 + +## 参考 + +1. https://zhuanlan.zhihu.com/p/461464919 +2. https://zhuanlan.zhihu.com/p/464145981 +3. https://zhuanlan.zhihu.com/p/470374648 +4. [作者:尘呆萌](https://zhuanlan.zhihu.com/p/470757647) diff --git a/张维为陈平曹丰泽等知名言论收集/陈平决策过程与赢化学习/陈平决策过程与赢化学习.pdf b/张维为陈平曹丰泽等知名言论收集/陈平决策过程与赢化学习/陈平决策过程与赢化学习.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e94f52d75ea8c06bc147be398565f6683fda7456 GIT binary patch literal 615924 zcmV(!K;^$BP((&8F)lL-CB)_ObY*fNFGg%( zbY(Vma%Ev{3U~puy-UxXNp__-|9-_cObwcK z?iZjT7+vat4G&sI!aXoNAel@{jm$2oR5oD$dOy!vJI;9zStVyymb;)%axo&_h#foj zJ>vZ9`#-+_>-&!Xo$u%O+v)KB$1m^y_5HuU|L*tywtxTpZ}0p3@83Ru-R8%1JYL>U z=MTHnX?J};ACB+W^ZvtqzrVlzrBVJuhnt`M@%?!DaJ`>yM+dzfZ}&Ze?mwLNyAvbt zJ{%8+gCqa={=5J3<&U4g{L7#I&yPR7|M8z$!FhlGa62#ymvX#ZKOFXl+xzkQ;e5Ma zuJ0%Rd3U|NfByOXcmLzh`}cqN!}~wJ{qBGH^3%sZ{qz6z<@bO1=?{PW=byj)>5u>X z+3|KC?#KMUKl>+$@fi4cK7F_x_vbZ%3q4#yr@8xZ;P3rEdO_%}kEuD&|M2`Pbh+Ly zAMWS#-8ufJ@81viw&A}AMn8WzzkSc-fA5BT|Kt0A-2ZU+arbF|+g&c7_oq)k>^~hY z`_uWnJKgqw|Ni}dd;ibhcW-~eC*QvPYTPwNjK zfBribwtxTbU;OXk?Yn_xJDrr(Z*-Zq3_fYc9LphYJj_A=YDu*onj6U?<+s 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