机器学习代写|强化学习project代写reinforence learning代考|Prediction Error and Actor-Critic

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  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
机器学习代写|强化学习project代写reinforence learning代考|Prediction Error and Actor-Critic

机器学习代写|强化学习project代写reinforence learning代考|Hypotheses in the Brain

Abstract Humans, as well as other life forms, can be seen as agents in nature who interact with their environment to gain rewards like pleasure and nutrition. This view has parallels with reinforcement learning from computer science and engineering. Early developments in reinforcement learning were inspired by intuitions from animal learning theories. More recent research in computational neuroscience has borrowed ideas that come from reinforcement learning to better understand the function of the mammalian brain during learning. In this report, we will compare computational, behavioral, and neural views of reinforcement learning. For each view we start by introducing the field and discuss the problems of prediction and control while focusing on the temporal difference learning method and the actor-critic paradigm. Based on the literature survey, we then propose a hypothesis for learning in the brain using multiple critics.

While science is the systematic study of natural phenomena, technology is often inspired by our observations of them. Computer scientists for example have developed algorithms based on behavior of animals and insects. On the other hand, sometimes developments from mathematics and pure reasoning find connections in nature afterwards. The actor-critic hypothesis of learning in the brain is an example of the latter case.

This report is composed of the three views of behaviorism from psychology, (computational) neuroscience from biology, and reinforcement learning from computer science and engineering. Each view is divided into the problems of prediction and control. The goal of prediction is to measure an expected value like a reward. The goal of control is to find an optimal strategy that maximizes the expected reward. We begin the discussion with the computational view in Sect. 2 by specifying the underlying framework and introducing Temporal Difference learning for prediction and the actor-critic method for control. Next we discuss the behavioral view in Sect. $3 .$ There we will highlight historical developments of two conditioning (i.e learning) theories in animals. These two theories, called classical conditioning and instrumental conditioning, can be directly mapped to prediction and control. Furthermore, we discuss the neuroscientific view in Sect. 4. In this section, we discuss the prediction error and actor-critic hypotheses in the brain. Finally, we propose further research into the interaction between different regions associated with the critic in the brain. Before we conclude, we will highlight some limitations within the neuroscientific view.

机器学习代写|强化学习project代写reinforence learning代考|Computational View

Reinforcement learning (RL) in computer science and engineering is the branch of machine learning that deals with decision making. For this view we use the Markov decision process (MDP) as the underlying framework. MDP is defined mathematically as the tuple $(S, A, P, R)$. An agent that observes a state $s_{t} \in S$ of the environment at time $t$. The agent can then interact with the environment by taking action $a \in A$. The results of this interaction yields a reward $r(s, a) \in R$ which depends on the current state $s$ produced by taking the action $a$. At the same time the action can cause a state transition. In this case the resulting state $s_{t+1}$ is produced according to state transition model $P$, which defines the probability of reaching state $s_{t+1}$ when taking action $a$ on state $s$. The goal of the agent is then to learn a policy $\pi$ that maximizes the cumulative reward. A key difference to supervised learning is that RL deals with data that is dynamically generated by the agent as opposed to having a fixed set already available beforehand.

机器学习代写|强化学习project代写reinforence learning代考|Behavioral View

Behaviorism is a branch of psychology that focuses on reproducible behavior in animals. Thorndike wrote in 1898 about animal intelligence based on his experiments that were used to study associative behaviour in animals [26]. He formulated the law of effect which states that responses that produce rewards tend to occur more likely given a similar situation and responses that produce punishments tend to be avoided in the future when given a similar situation. In behavioral psychology, there are two different concepts of conditioning (i.e. learning) called classical and operant conditioning. These two concepts can be mapped to prediction and control in reinforcement learning and will be discussed in the subsections below.

Animal behavior, as well as their underlying neural substrates, consists of complicated and not fully understood mechanisms. There are many, possibly antagonist processes in biology happening simultaneously as opposed to artificial agents that implement idealized computational algorithms. This shows that the difference between the function of artificial and biological agents should not be taken for granted. Furthermore, there is an unresolved gap in the relationship between subjective experience of (biological) agents and measurable neural activity [4].

Classical conditioning, sometimes referred to as Pavlovian conditioning, is a type of learning documented by Ivan Pavlov in the mid-20th century during his experiments with dogs [15]. In classical conditioning, animals learn by associating stimuli with rewards. In order to understand how animals can learn to predict rewards, we invoke terminology from Pavlov’s experiments:

  • Unconditioned Stimulus (US): A dog is presented with a reward, for example a piece of meat.
  • Unconditioned Response $(U R)$ : Shortly after noticing the meat, the dog starts to salivate.
  • Neutral Stimulus (NS): The dog hears a unique sound. We will assume its the sound of a bell. Neutral here means that it does not initially produce a specific response relevant for the experiment.
  • Conditioning: The dog is repeatedly presented with meat and the bell sound simultaneously.
  • Conditioned Stimulus (CS): Now the bell has been paired with the expectation of getting the reward.
  • Conditioned Response (SR): Subsequently, when the dog hears the sound of the bell, he starts to salivate. Here we can assume that the dog has learned to predict the reward.
机器学习代写|强化学习project代写reinforence learning代考|Prediction Error and Actor-Critic


机器学习代写|强化学习project代写reinforence learning代考|Hypotheses in the Brain

摘要 人类以及其他生命形式可以被视为自然界中的代理人,他们与环境互动以获得快乐和营养等奖励。这种观点与计算机科学和工程的强化学习有相似之处。强化学习的早期发展受到动物学习理论直觉的启发。最近的计算神经科学研究借鉴了强化学习的想法,以更好地理解哺乳动物大脑在学习过程中的功能。在本报告中,我们将比较强化学习的计算、行为和神经观点。对于每个视图,我们首先介绍该领域并讨论预测和控制问题,同时关注时间差异学习方法和演员-评论家范式。根据文献调查,


本报告由心理学的行为主义、生物学的(计算)神经科学和计算机科学与工程的强化学习三种观点组成。每个视图都分为预测和控制问题。预测的目标是衡量一个期望值,比如奖励。控制的目标是找到最大化预期回报的最优策略。我们从 Sect 中的计算视图开始讨论。2 通过指定底层框架并引入用于预测的时间差异学习和用于控制的 actor-critic 方法。接下来我们讨论 Sect 中的行为观。3.在那里,我们将重点介绍两种动物条件反射(即学习)理论的历史发展。这两种理论,称为经典条件反射和工具条件反射,可以直接映射到预测和控制。此外,我们在 Sect 中讨论了神经科学观点。4. 在本节中,我们讨论大脑中的预测误差和演员批评假设。最后,我们建议进一步研究与大脑中批评者相关的不同区域之间的相互作用。在我们结束之前,我们将强调神经科学观点中的一些局限性。

机器学习代写|强化学习project代写reinforence learning代考|Computational View

计算机科学与工程中的强化学习 (RL) 是处理决策的机器学习的一个分支。对于这个观点,我们使用马尔可夫决策过程(MDP)作为底层框架。MDP 在数学上定义为元组(小号,一种,磷,R). 观察状态的代理s吨∈小号当时的环境吨. 然后代理可以通过采取行动与环境交互一种∈一种. 这种互动的结果产生了回报r(s,一种)∈R这取决于当前状态s采取行动产生的一种. 同时该动作可以引起状态转换。在这种情况下,结果状态s吨+1根据状态转移模型产生磷,它定义了达到状态的概率s吨+1采取行动时一种在状态s. 代理的目标是学习策略圆周率最大化累积奖励。与监督学习的一个关键区别在于,RL 处理由代理动态生成的数据,而不是预先拥有一个固定的数据集。

机器学习代写|强化学习project代写reinforence learning代考|Behavioral View

行为主义是心理学的一个分支,专注于动物的可重复行为。桑代克在 1898 年根据他用于研究动物联想行为的实验写了关于动物智能的文章 [26]。他制定了效果定律,该定律指出,在类似的情况下,产生奖励的反应往往更有可能发生,而在未来类似的情况下,产生惩罚的反应往往会被避免。在行为心理学中,有两种不同的条件反射(即学习)概念,称为经典条件反射和操作条件反射。这两个概念可以映射到强化学习中的预测和控制,并将在下面的小节中讨论。


经典条件反射,有时也称为巴甫洛夫条件反射,是 Ivan Pavlov 在 20 世纪中叶用狗做实验时记录的一种学习方式 [15]。在经典条件反射中,动物通过将刺激与奖励联系起来进行学习。为了了解动物如何学习预测奖励,我们引用了巴甫洛夫实验中的术语:

  • 无条件刺激(美国):向狗提供奖励,例如一块肉。
  • 无条件反应(在R): 注意到肉后不久,狗开始​​流口水。
  • 中性刺激(NS):狗听到独特的声音。我们假设它是铃声。这里的中性意味着它最初不会产生与实验相关的特定响应。
  • 调理:狗被反复呈现肉和铃声同时响起。
  • 条件刺激(CS):现在已经与获得奖励的期望配对。
  • 条件反应(SR):随后,当狗听到铃声时,他开始流口水。在这里,我们可以假设狗已经学会了预测奖励。
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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


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。



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