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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

## 经济代写|博弈论代写Game Theory代考|Reinforcement Learning

For a large-worlds approach, one needs to assume some particular mechanism of model-free learning. Harley (1981) and Maynard Smith (1982) proposed learning dynamics for game theory in biology, which we describe in Section 5.5, together with other similar suggestions. Here we present our own favoured approach. Reinforcement learning, as described by Sutton and Barto (2018), was developed by computer scientists for machine learning and robotics. It was inspired by and is closely related to ideas in animal psychology and neuroscience. The approach now contributes to the rapid emergence of applications of artificial intelligence and provides an important basis for experimental investigations of learning in neuroscience. Reinforcement learning thus has major advantages: it is conceptually and computationally mature and it has the potential for biologically realistic descriptions of animal behaviour. The basic idea is that individuals explore through randomness in their actions and tend to increase the preference for actions that result in higher than so-far-estimated rewards (which applies to instrumental learning generally).

The overarching aim of reinforcement learning is to maximize perceived rewards over a suitable time scale. Learning is thus driven by rewards and is fundamentally different from evolutionary change, which is driven by success in survival and reproduction, which need not involve psychological processes such as perception of reward. For learning to be adaptive, it follows that individuals must possess innate, evolved mechanisms for detecting rewards, and these are referred to as primary rewards. From these, individuals can learn that other stimuli, or states, serve as predictors of primary rewards, and they are then called secondary rewards. I’he study of primary and secondary rewards is one of the main preoccupations of animal learning psychology, often discussed in terms of unconditioned and conditioned stimuli. Reinforcement learning also incorporates prediction of rewards by associating states with values that correspond to estimated future rewards. In this chapter we focus on the simplest case where the primary rewards are the payoffs from repeated plays of a one-shot game in a large population.

There are a number of different but related modelling approaches in reinforcement learning, many of which are described by Sutton and Barto (2018). Here we focus on one of them, actor-critic learning (see p. 94), but in the next chapter we also illustrate Sarsa learning (Box 6.5), which is another common approach.

## 经济代写|博弈论代写Game Theory代考|The Actor-Critic Approach

A mechanism for learning in game theory needs both to build up estimates of the value for an individual of being in or reaching a certain state and to form preferences for the actions to perform in the state. Actor-critic learning implements these as distinct but linked processes. The learning dynamics are described in Box $5.1$ for two-player games with two actions and in a large population where players are randomly paired. The value of being in the single state of the game, which in this case is the estimated reward from playing the game, is updated using the temporal difference (TD) error, as specified by eq (5.3) in Box $5.1$ and illustrated in Fig. 5.1b. The TD error is the difference between actual and estimated rewards. The updating is similar to the much studied Rescorla-Wagner model of classical conditioning (Staddon, 2016), which describes the updating of an associative value. The interpretation of the RescorlaWagner model is that learning is driven by ‘surprise’, in the form of a discrepancy between perceived and estimated values. In reinforcement learning, the surprise is given by the TD error in eq (5.2). Based on findings in neuroscience the TD error is interpreted as a reinforcement signal that guides learning (Sutton and Barto, 2018), and it is a reason for the name ‘reinforcement learning. The TD error and the updating in eq (5.3) make up the critic component of actor-critic learning. given by eq (5.5) and illustrated in Fig. 5.1a. The action probabilities are logistic functions of preferences, as in eq (5.1). The updating involves the product of the TD error from the critic component and the so-called eligibility of the action, defined in eq (5.4). The eligibility measures the relative change of the action probability with a change in preference. As seen from eq (5.4), if the current preference is such that the action performed has close to maximal probability, the eligibility will be small and the preference is changed very little, but if the action performed has smaller probability, the eligibility can be larger and the change in preference is then more sensitive to the TD error. In the general case of several actions, the corresponding quantity to eq (5.4) is referred to as an eligibility vector (Sutton and Barto, 2018). The actor-critic updating of the action preferences is a kind of policy gradient method, which means that the method is likely to perform well in terms of learning leading to higher rewards (Sutton and Barto, 2018). From the perspective of animal psychology, the actor component implements operant, or instrumental, conditioning (Staddon, 2016).
It is suggested that the actor learning process may correspond to a form of neural plasticity, so-called spike-timing-dependent plasticity (Roelfsema and Holtmaat, 2018; Sutton and Barto, 2018). However, compared with real neural processes, the learning mechanism in Box $5.1$ might be a simplification. Neurons cannot implement negative firing rates, and for this reason excitatory and inhibitory influences on the preference for an action need to have separate mechanisms, as put forward by Collins änd Fränk (2014).

## 有限元方法代写

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## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师