187 lines
11 KiB
TeX
187 lines
11 KiB
TeX
\documentclass[11pt]{ctexart}
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\usepackage{ctex}
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\usepackage{algorithm}
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\usepackage{algorithmic}
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\usepackage{amssymb}
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\usepackage{amsmath}
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\usepackage{hyperref}
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% \usepackage[hidelinks]{hyperref} 去除超链接的红色框
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\usepackage{setspace}
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\usepackage{titlesec}
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\usepackage{float} % 调用该包能够使用[H]
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% \pagestyle{plain} % 去除页眉，但是保留页脚编号，都去掉plain换empty
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\begin{document}
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\tableofcontents % 目录，注意要运行两下或者vscode保存两下才能显示
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% \singlespacing
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\clearpage
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\section{模版备用}
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\begin{algorithm}[H] % [H]固定位置
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\floatname{algorithm}{{算法}}
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\renewcommand{\thealgorithm}{} % 去掉算法标号
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\caption{}
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\begin{algorithmic}[1] % [1]显示步数
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\STATE 测试
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\end{algorithmic}
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\end{algorithm}
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\clearpage
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\section{Q learning算法}
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\begin{algorithm}[H] % [H]固定位置
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\floatname{algorithm}{{Q-learning算法}\footnotemark[1]}
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\renewcommand{\thealgorithm}{} % 去掉算法标号
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\caption{}
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\begin{algorithmic}[1] % [1]显示步数
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\STATE 初始化Q表$Q(s,a)$为任意值，但其中$Q(s_{terminal},)=0$，即终止状态对应的Q值为0
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\FOR {回合数 = $1,M$}
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\STATE 重置环境，获得初始状态$s_1$
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\FOR {时步 = $1,t$}
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\STATE 根据$\varepsilon-greedy$策略采样动作$a_t$
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\STATE 环境根据$a_t$反馈奖励$r_t$和下一个状态$s_{t+1}$
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\STATE {\bfseries 更新策略：}
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\STATE $Q(s_t,a_t) \leftarrow Q(s_t,a_t)+\alpha[r_t+\gamma\max _{a}Q(s_{t+1},a)-Q(s_t,a_t)]$
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\STATE 更新状态$s_{t+1} \leftarrow s_t$
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\ENDFOR
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\ENDFOR
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\end{algorithmic}
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\end{algorithm}
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\footnotetext[1]{Reinforcement Learning: An Introduction}
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\clearpage
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\section{Sarsa算法}
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\begin{algorithm}[H] % [H]固定位置
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\floatname{algorithm}{{Sarsa算法}\footnotemark[1]}
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\renewcommand{\thealgorithm}{} % 去掉算法标号
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\caption{}
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\begin{algorithmic}[1] % [1]显示步数
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\STATE 初始化Q表$Q(s,a)$为任意值，但其中$Q(s_{terminal},)=0$，即终止状态对应的Q值为0
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\FOR {回合数 = $1,M$}
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\STATE 重置环境，获得初始状态$s_1$
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\STATE 根据$\varepsilon-greedy$策略采样初始动作$a_1$
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\FOR {时步 = $1,t$}
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\STATE 环境根据$a_t$反馈奖励$r_t$和下一个状态$s_{t+1}$
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\STATE 根据$\varepsilon-greedy$策略$s_{t+1}$和采样动作$a_{t+1}$
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\STATE {\bfseries 更新策略：}
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\STATE $Q(s_t,a_t) \leftarrow Q(s_t,a_t)+\alpha[r_t+\gamma Q(s_{t+1},a_{t+1})-Q(s_t,a_t)]$
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\STATE 更新状态$s_{t+1} \leftarrow s_t$
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\STATE 更新动作$a_{t+1} \leftarrow a_t$
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\ENDFOR
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\ENDFOR
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\end{algorithmic}
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\end{algorithm}
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\footnotetext[1]{Reinforcement Learning: An Introduction}
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\clearpage
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\section{Policy Gradient算法}
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\begin{algorithm}[H] % [H]固定位置
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\floatname{algorithm}{{REINFORCE算法：Monte-Carlo Policy Gradient}\footnotemark[1]}
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\renewcommand{\thealgorithm}{} % 去掉算法标号
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\caption{}
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\begin{algorithmic}[1] % [1]显示步数
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\STATE 初始化策略参数$\boldsymbol{\theta} \in \mathbb{R}^{d^{\prime}}($ e.g., to $\mathbf{0})$
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\FOR {回合数 = $1,M$}
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\STATE 根据策略$\pi(\cdot \mid \cdot, \boldsymbol{\theta})$采样一个(或几个)回合的transition
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\FOR {时步 = $1,t$}
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\STATE 计算回报$G \leftarrow \sum_{k=t+1}^{T} \gamma^{k-t-1} R_{k}$
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\STATE 更新策略$\boldsymbol{\theta} \leftarrow {\boldsymbol{\theta}+\alpha \gamma^{t}} G \nabla \ln \pi\left(A_{t} \mid S_{t}, \boldsymbol{\theta}\right)$
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\ENDFOR
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\ENDFOR
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\end{algorithmic}
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\end{algorithm}
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\footnotetext[1]{Reinforcement Learning: An Introduction}
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\clearpage
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\section{DQN算法}
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\begin{algorithm}[H] % [H]固定位置
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\floatname{algorithm}{{DQN算法}}
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\renewcommand{\thealgorithm}{} % 去掉算法标号
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\caption{}
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\renewcommand{\algorithmicrequire}{\textbf{输入:}}
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\renewcommand{\algorithmicensure}{\textbf{输出:}}
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\begin{algorithmic}[1]
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% \REQUIRE $n \geq 0 \vee x \neq 0$ % 输入
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% \ENSURE $y = x^n$ % 输出
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\STATE 初始化策略网络参数$\theta$ % 初始化
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\STATE 复制参数到目标网络$\hat{Q} \leftarrow Q$
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\STATE 初始化经验回放$D$
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\FOR {回合数 = $1,M$}
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\STATE 重置环境，获得初始状态$s_t$
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\FOR {时步 = $1,t$}
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\STATE 根据$\varepsilon-greedy$策略采样动作$a_t$
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\STATE 环境根据$a_t$反馈奖励$r_t$和下一个状态$s_{t+1}$
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\STATE 存储transition即$(s_t,a_t,r_t,s_{t+1})$到经验回放$D$中
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\STATE 更新环境状态$s_{t+1} \leftarrow s_t$
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\STATE {\bfseries 更新策略：}
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\STATE 从$D$中采样一个batch的transition
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\STATE 计算实际的$Q$值，即$y_{j}= \begin{cases}r_{j} & \text {对于终止状态} s_{j+1} \\ r_{j}+\gamma \max _{a^{\prime}} Q\left(s_{j+1}, a^{\prime} ; \theta\right) & \text {对于非终止状态} s_{j+1}\end{cases}$
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\STATE 对损失 $\left(y_{j}-Q\left(s_{j}, a_{j} ; \theta\right)\right)^{2}$关于参数$\theta$做随机梯度下降
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\ENDFOR
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\STATE 每$C$个回合复制参数$\hat{Q}\leftarrow Q$(此处也可像原论文中放到小循环中改成每$C$步，但没有每$C$个回合稳定)
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\ENDFOR
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\end{algorithmic}
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\end{algorithm}
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\clearpage
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\section{SoftQ算法}
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\begin{algorithm}[H]
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\floatname{algorithm}{{SoftQ算法}}
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\renewcommand{\thealgorithm}{} % 去掉算法标号
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\caption{}
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\begin{algorithmic}[1]
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\STATE 初始化参数$\theta$和$\phi$% 初始化
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\STATE 复制参数$\bar{\theta} \leftarrow \theta, \bar{\phi} \leftarrow \phi$
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\STATE 初始化经验回放$D$
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\FOR {回合数 = $1,M$}
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\FOR {时步 = $1,t$}
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\STATE 根据$\mathbf{a}_{t} \leftarrow f^{\phi}\left(\xi ; \mathbf{s}_{t}\right)$采样动作，其中$\xi \sim \mathcal{N}(\mathbf{0}, \boldsymbol{I})$
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\STATE 环境根据$a_t$反馈奖励$s_t$和下一个状态$s_{t+1}$
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\STATE 存储transition即$(s_t,a_t,r_t,s_{t+1})$到经验回放$D$中
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\STATE 更新环境状态$s_{t+1} \leftarrow s_t$
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\STATE {\bfseries 更新soft Q函数参数：}
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\STATE 对于每个$s^{(i)}_{t+1}$采样$\left\{\mathbf{a}^{(i, j)}\right\}_{j=0}^{M} \sim q_{\mathbf{a}^{\prime}}$
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\STATE 计算empirical soft values $V_{\mathrm{soft}}^{\theta}\left(\mathbf{s}_{t}\right)$\footnotemark[1]
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\STATE 计算empirical gradient $J_{Q}(\theta)$\footnotemark[2]
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\STATE 根据$J_{Q}(\theta)$使用ADAM更新参数$\theta$
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\STATE {\bfseries 更新策略：}
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\STATE 对于每个$s^{(i)}_{t}$采样$\left\{\xi^{(i, j)}\right\}_{j=0}^{M} \sim \mathcal{N}(\mathbf{0}, \boldsymbol{I})$
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\STATE 计算$\mathbf{a}_{t}^{(i, j)}=f^{\phi}\left(\xi^{(i, j)}, \mathbf{s}_{t}^{(i)}\right)$
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\STATE 使用经验估计计算$\Delta f^{\phi}\left(\cdot ; \mathbf{s}_{t}\right)$\footnotemark[3]
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\STATE 计算经验估计$\frac{\partial J_{\pi}\left(\phi ; \mathbf{s}_{t}\right)}{\partial \phi} \propto \mathbb{E}_{\xi}\left[\Delta f^{\phi}\left(\xi ; \mathbf{s}_{t}\right) \frac{\partial f^{\phi}\left(\xi ; \mathbf{s}_{t}\right)}{\partial \phi}\right]$，即$\hat{\nabla}_{\phi} J_{\pi}$
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\STATE 根据$\hat{\nabla}_{\phi} J_{\pi}$使用ADAM更新参数$\phi$
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\STATE
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\ENDFOR
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\STATE 每$C$个回合复制参数$\bar{\theta} \leftarrow \theta, \bar{\phi} \leftarrow \phi$
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\ENDFOR
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\end{algorithmic}
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\end{algorithm}
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\footnotetext[1]{$V_{\mathrm{soft}}^{\theta}\left(\mathbf{s}_{t}\right)=\alpha \log \mathbb{E}_{q_{\mathbf{a}^{\prime}}}\left[\frac{\exp \left(\frac{1}{\alpha} Q_{\mathrm{soft}}^{\theta}\left(\mathbf{s}_{t}, \mathbf{a}^{\prime}\right)\right)}{q_{\mathbf{a}^{\prime}}\left(\mathbf{a}^{\prime}\right)}\right]$}
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\footnotetext[2]{$J_{Q}(\theta)=\mathbb{E}_{\mathbf{s}_{t} \sim q_{\mathbf{s}_{t}}, \mathbf{a}_{t} \sim q_{\mathbf{a}_{t}}}\left[\frac{1}{2}\left(\hat{Q}_{\mathrm{soft}}^{\bar{\theta}}\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right)-Q_{\mathrm{soft}}^{\theta}\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right)\right)^{2}\right]$}
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\footnotetext[3]{$\begin{aligned} \Delta f^{\phi}\left(\cdot ; \mathbf{s}_{t}\right)=& \mathbb{E}_{\mathbf{a}_{t} \sim \pi^{\phi}}\left[\left.\kappa\left(\mathbf{a}_{t}, f^{\phi}\left(\cdot ; \mathbf{s}_{t}\right)\right) \nabla_{\mathbf{a}^{\prime}} Q_{\mathrm{soft}}^{\theta}\left(\mathbf{s}_{t}, \mathbf{a}^{\prime}\right)\right|_{\mathbf{a}^{\prime}=\mathbf{a}_{t}}\right.\\ &\left.+\left.\alpha \nabla_{\mathbf{a}^{\prime}} \kappa\left(\mathbf{a}^{\prime}, f^{\phi}\left(\cdot ; \mathbf{s}_{t}\right)\right)\right|_{\mathbf{a}^{\prime}=\mathbf{a}_{t}}\right] \end{aligned}$}
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\clearpage
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\section{SAC算法}
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\begin{algorithm}[H] % [H]固定位置
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\floatname{algorithm}{{Soft Actor Critic算法}}
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\renewcommand{\thealgorithm}{} % 去掉算法标号
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\caption{}
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\begin{algorithmic}[1]
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\STATE 初始化两个Actor的网络参数$\theta_1,\theta_2$以及一个Critic网络参数$\phi$ % 初始化
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\STATE 复制参数到目标网络$\bar{\theta_1} \leftarrow \theta_1,\bar{\theta_2} \leftarrow \theta_2,$
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\STATE 初始化经验回放$D$
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\FOR {回合数 = $1,M$}
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\STATE 重置环境，获得初始状态$s_t$
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\FOR {时步 = $1,t$}
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\STATE 根据$\boldsymbol{a}_{t} \sim \pi_{\phi}\left(\boldsymbol{a}_{t} \mid \mathbf{s}_{t}\right)$采样动作$a_t$
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\STATE 环境反馈奖励和下一个状态，$\mathbf{s}_{t+1} \sim p\left(\mathbf{s}_{t+1} \mid \mathbf{s}_{t}, \mathbf{a}_{t}\right)$
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\STATE 存储transition到经验回放中，$\mathcal{D} \leftarrow \mathcal{D} \cup\left\{\left(\mathbf{s}_{t}, \mathbf{a}_{t}, r\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right), \mathbf{s}_{t+1}\right)\right\}$
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\STATE 更新环境状态$s_{t+1} \leftarrow s_t$
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\STATE {\bfseries 更新策略：}
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\STATE 更新$Q$函数，$\theta_{i} \leftarrow \theta_{i}-\lambda_{Q} \hat{\nabla}_{\theta_{i}} J_{Q}\left(\theta_{i}\right)$ for $i \in\{1,2\}$\footnotemark[1]\footnotemark[2]
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\STATE 更新策略权重，$\phi \leftarrow \phi-\lambda_{\pi} \hat{\nabla}_{\phi} J_{\pi}(\phi)$ \footnotemark[3]
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\STATE 调整temperature，$\alpha \leftarrow \alpha-\lambda \hat{\nabla}_{\alpha} J(\alpha)$ \footnotemark[4]
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\STATE 更新目标网络权重，$\bar{\theta}_{i} \leftarrow \tau \theta_{i}+(1-\tau) \bar{\theta}_{i}$ for $i \in\{1,2\}$
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\ENDFOR
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\ENDFOR
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\end{algorithmic}
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\end{algorithm}
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\footnotetext[1]{$J_{Q}(\theta)=\mathbb{E}_{\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right) \sim \mathcal{D}}\left[\frac{1}{2}\left(Q_{\theta}\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right)-\left(r\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right)+\gamma \mathbb{E}_{\mathbf{s}_{t+1} \sim p}\left[V_{\bar{\theta}}\left(\mathbf{s}_{t+1}\right)\right]\right)\right)^{2}\right]$}
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\footnotetext[2]{$\hat{\nabla}_{\theta} J_{Q}(\theta)=\nabla_{\theta} Q_{\theta}\left(\mathbf{a}_{t}, \mathbf{s}_{t}\right)\left(Q_{\theta}\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right)-\left(r\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right)+\gamma\left(Q_{\bar{\theta}}\left(\mathbf{s}_{t+1}, \mathbf{a}_{t+1}\right)-\alpha \log \left(\pi_{\phi}\left(\mathbf{a}_{t+1} \mid \mathbf{s}_{t+1}\right)\right)\right)\right)\right.$}
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\footnotetext[3]{$\hat{\nabla}_{\phi} J_{\pi}(\phi)=\nabla_{\phi} \alpha \log \left(\pi_{\phi}\left(\mathbf{a}_{t} \mid \mathbf{s}_{t}\right)\right)+\left(\nabla_{\mathbf{a}_{t}} \alpha \log \left(\pi_{\phi}\left(\mathbf{a}_{t} \mid \mathbf{s}_{t}\right)\right)-\nabla_{\mathbf{a}_{t}} Q\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right)\right) \nabla_{\phi} f_{\phi}\left(\epsilon_{t} ; \mathbf{s}_{t}\right)$,$\mathbf{a}_{t}=f_{\phi}\left(\epsilon_{t} ; \mathbf{s}_{t}\right)$}
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\footnotetext[4]{$J(\alpha)=\mathbb{E}_{\mathbf{a}_{t} \sim \pi_{t}}\left[-\alpha \log \pi_{t}\left(\mathbf{a}_{t} \mid \mathbf{s}_{t}\right)-\alpha \overline{\mathcal{H}}\right]$}
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\clearpage
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\end{document} |