### 机器学习代写|强化学习project代写reinforence learning代考| Sparse Rewards

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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
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• 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|Reward Shaping

Many interesting problems are most naturally characterized by a sparse reward signal. Evolution, discussed in 2.1, provides an extreme example. In many cases, it is more intuitive to describe a task completion requirement by a set of constraints rather than by a dense reward function. In such environments, the easiest way to construct a reward signal would be to give a reward on each transition that leads to all constraints being fulfilled.

Theoretically, a general purpose reinforcement learning algorithm should be able to deal with the sparse reward setting. For example, Q-learning [17] is one of the few algorithms that comes with a guarantee that it will eventually find the optimal policy provided all states and actions are experienced infinitely often. However, from a practical standpoint, finding a solution may be infeasible in many sparse reward environments. Stanton and Clune [15] point out that sparse environments require a “prohibitively large” number of training steps to solve with undirected exploration, such as, e.g., $\varepsilon$-greedy exploration employed in Q-learning and other RL algorithms.
A promising direction for tackling sparse reward problems is through curiositybased exploration. Curiosity is a form of intrinsic motivation, and there is a large body of literature devoted to this topic. We discuss curiosity-based learning in more detail in Sect. 5. Despite significant progress in the area of intrinsic motivation, no strong optimality guarantees, matching those for classical RL algorithms, have been established so far. Therefore, in the next section, we take a look at an alternative direction, aimed at modifying the reward signal in such a way that the optimal policy stays invariant but the learning process can be greatly facilitated.

The term “shaping” was originally introduced in behavioral science by Skinner [13]. Shaping is sometimes also called “successive approximation”. $\mathrm{Ng}$ et al. [8] formalized the term and popularized it under the name “reward shaping” in reinforcement learning. This section details the connection between the behavioral science definition and the reinforcement learning definition, highlighting the advantages and disadvantages of reward shaping for improving exploration in sparse reward settings.

## 机器学习代写|强化学习project代写reinforence learning代考|Shaping in Behavioral Science

Skinner laid down the groundwork on shaping in his book [13], where he aimed at establishing the “laws of behavior”. Initially, he found out by accident that learning of certain tasks can be sped up by providing intermediate rewards. Later, he figured out that it is the discontinuities in the operands (units of behavior) that are responsible for making tasks with sparse rewards harder to learn. By breaking down these discountinuities via successive approximation (a.k.a. shaping), he could show that a desired behavior can be taught much more efficiently.

It is remarkable that many of the experimental means described by Skinner [13] cohere to the method of potential fields introduced into reinforcement learning by Ng et al. [8] 46 years later. For example, Skinner employed angle- and position-based rewards to lead a pigeon into a goal region where a big final reward was awaiting. Interestingly, in addition to manipulating the reward, Skinner was able to further speed up pigeon training by manipulating the emvironment. By keeping a pigeon hungry prior to the experiment, he could make the pigeon peck at a switch with higher probability, getting to the reward attached to that behavior more quickly.
Since manipulating the environment is often outside engineer’s control in realworld applications of reinforcement learning, reward shaping techniques provide the main practical tool for modulating the learning process. The following section takes a closer look at the theory of reward shaping in reinforcement learning and highlights its similarities and distinctions from shaping in behavioral science.

## 机器学习代写|强化学习project代写reinforence learning代考|Reward Shaping in Reinforcement Learning

Although practitioners have always engaged in some form of reward shaping, the first theoretically grounded framework has been put forward by Ng et al. [8] under the name potential-based reward shaping $(P B R S)$. According to this theory, the shaping signal $F$ must be a function of the current state and the next state, i.e., $F: \mathcal{S} \times$ $\mathcal{S} \rightarrow \mathbb{R}$. The shaping signal is added to the original reward function to yield the

new reward signal $R^{\prime}\left(s, a, s^{\prime}\right)=R\left(s, a, s^{\prime}\right)+F\left(s, s^{\prime}\right)$. Crucially, the reward shaping term $F\left(s, s^{\prime}\right)$ must admit a representation through a potential function $\Phi(s)$ that only depends on one argument. The dependence takes the form of a difference of potentials
$$F\left(s, s^{\prime}\right)=\gamma \Phi\left(s^{\prime}\right)-\Phi(s) .$$
When condition (1) is violated, undesired effects should be expected. For example, in [9], a term rewarding closeness to the goal was added to a bicycle-riding task where the objective is to drive to a target location. As a result, the agent learned to drive in circles around the starting point. Since driving away from the goal is not punished, such policy is indeed optimal. A potential-based shaping term (1) would discourage such cycling solutions.

Comparing Skinner’s shaping approach from Sect. $4.1$ to PRBS, the reward provided to the pigeon for turning or moving in the right direction can be seen as arising from a potential field based on the direction and distance to the goal. From the description in [13], however, it is not clear whether also punishments (i.e., negative rewards) were given for moving in a wrong direction. If not, then Skinner’s pigeons must have suffered from the same problem as the cyclist in [9]. However, such behavior was not observed, which could be attributed to the animals having a low discount factor or receiving an internal punishment for energy expenditure.

Despite its appeal, some researchers view reward shaping quite negatively. As stated in [9], reward shaping goes against the “tabula rasa” ideal-demanding that the agent learns from scratch using a general (model-free RL) algorithm-by infusing prior knowledge into the problem. Sutton and Barto [16, p. 54] support this view, stating that
the reward signal is not the place to impart to the agent prior knowledge about how to achieve what we want it to do.

As an example in the following subsection shows, it is also often quite hard to come up with a good shaping reward. In particular, the shaping term $F\left(s, s^{\prime}\right)$ is problemspecific, and for each choice of the reward $R\left(s, a, s^{\prime}\right)$ needs to be devised anew. In Sect. 5, we consider more general shaping approaches that only depend on the environment dynamics and not the reward function.

## 机器学习代写|强化学习project代写reinforence learning代考|Reward Shaping

“塑造”一词最初是由 Skinner [13] 在行为科学中引入的。整形有时也称为“逐次逼近”。ñG等。[8] 将该术语形式化并在强化学习中以“奖励塑造”的名义推广。本节详细介绍了行为科学定义和强化学习定义之间的联系，强调了奖励塑造对于改善稀疏奖励设置中的探索的优缺点。

## 机器学习代写|强化学习project代写reinforence learning代考|Shaping in Behavioral Science

Skinner 在他的书 [13] 中奠定了塑造的基础，他的目标是建立“行为法则”。最初，他偶然发现通过提供中间奖励可以加快对某些任务的学习。后来，他发现正是操作数（行为单位）中的不连续性导致奖励稀疏的任务更难学习。通过逐次逼近（又名整形）分解这些折扣，他可以证明可以更有效地教授期望的行为。

## 机器学习代写|强化学习project代写reinforence learning代考|Reward Shaping in Reinforcement Learning

F(s,s′)=C披(s′)−披(s).

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