19th Ave New York, NY 95822, USA

# CS代写|强化学习代写Reinforcement learning代考|CS59300 Bellman Closedness

my-assignmentexpert™提供最专业的一站式服务：Essay代写，Dissertation代写，Assignment代写，Paper代写，Proposal代写，Proposal代写，Literature Review代写，Online Course，Exam代考等等。my-assignmentexpert™专注为留学生提供Essay代写服务，拥有各个专业的博硕教师团队帮您代写，免费修改及辅导，保证成果完成的效率和质量。同时有多家检测平台帐号，包括Turnitin高级账户，检测论文不会留痕，写好后检测修改，放心可靠，经得起任何考验！

## CS代写|强化学习代写Reinforcement learning代考|Bellman Closedness

In preceding chapters, our approach to distributional reinforcement learning considered approximations of the return distributions that could be tractably manipulated by algorithms. The $m$-moment Bellman operator, on the other hand, is not directly applied to probability distributions – compared to say, a $m$-categorical distribution, there is no immediate procedure for drawing a sample from a collection of $m$ moments. Compared to the categorical and quantile projected operators, however, the $m$-moment operator yields an errorfree dynamic programming procedure – with sufficiently many iterations and under some finiteness assumptions, we can determine the moments of the return function to any degree of accuracy. The concept of Bellman closedness formalises this idea.

Definition 8.8. A sketch $\psi=\left(\psi_1, \ldots, \psi_m\right)$ is Bellman closed if, whenever its domain $\mathscr{P}\psi(\mathbb{R})^{\mathcal{X}}$ is closed under the distributional Bellman operator: $$\eta \in \mathscr{P}\psi(\mathbb{R})^{\mathcal{X}} \Longrightarrow \mathcal{T}^\pi \eta \in \mathscr{P}\psi(\mathbb{R})^{\mathcal{X}},$$ there is an operator $\mathcal{T}\psi^\pi: I_\psi^{\mathcal{X}} \rightarrow I_\psi^{\mathcal{X}}$ such that
$$\psi\left(\mathcal{T}^\pi \eta\right)=\mathcal{T}\psi^\pi \psi(\eta) \quad \text { for all } \eta \in \mathscr{P}\psi(\mathbb{R})^{\mathcal{X}} \text {. }$$
The operator $\mathcal{T}_\psi^\pi$ is said to be the Bellman operator for the sketch $\psi$. $\triangle$

## CS代写|强化学习代写Reinforcement learning代考|Statistical Functional Dynamic Programming

When a sketch $\psi$ is not Bellman closed, we lack an operator $\mathcal{T}_\psi^\pi$ that emulates the combination of the distributional Bellman operator and this sketch. This precludes a dynamic programming approach that bootstraps its functional value estimates directly from the previous estimates. However, approximate dynamic programming with arbitrary statistical functionals is still possible if we introduce an additional imputation step $\iota$ that reconstructs plausible probability distributions from functional values. As we will now see, this allows us to apply the distributional Bellman operator to the reconstructed distributions and then extract the functional values of the resulting return function estimate.

Definition 8.13. An imputation strategy for the sketch $\psi: \mathscr{P}\psi(\mathbb{R}) \rightarrow \mathbb{R}^m$ is a function $\iota: I\psi \rightarrow \mathscr{P}\psi(\mathbb{R})$. We say that it is exact if for any valid functional values $\left(s_1, \ldots, s_m\right) \in I\psi$, we have
$$\psi_i\left(\iota\left(s_1, \ldots, s_m\right)\right)=s_i, \quad i=1, \ldots, m .$$
Otherwise, we say that it is approximate.
By extension, we write $\iota(s) \in \mathscr{P}\psi(\mathbb{R})^{\mathcal{X}}$ for the return-distribution function corresponding to the collection of functional values $s \in I\psi^{\mathcal{X}}$.
$\triangle$

## 强化学习代写|强化学习代写reinforcement learning代写 考|贝尔曼封闭性

$$\δ在 mathscr{P}中 \psi(\mathbb{R})^{\mathcal{X}} \Longrightarrowmathcal{T}^\pi etain mathscr{P}psi(\mathbb{R})^{mathcal{X}. \psi(\mathbb{R})^{\mathcal{X}},$$

$$\psi\left(dmathcal{T}^pi \eta\right)=\mathcal{T}。\psi^pi psi(\eta)quad `text { for all } \δ在mathscr{P}中 \psi(\mathbb{R})^{\mathcal{X}}$$

## cs代写|强化学习代写einforcement learning代考|统计函数动态编程

$$\psi_i\left(iota\left(s_1, \ldots, s_m\right)\right)=s_i, \quad i=1, \ldots, m 。$$

CS代写|强化学习代写Reinforcement learning代考 请认准UprivateTA™. UprivateTA™为您的留学生涯保驾护航。

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。