### 机器学习代写|强化学习project代写reinforence learning代考|Exploration Methods in Sparse Reward Environments

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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

## 机器学习代写|强化学习project代写reinforence learning代考|The Problem of Naive Exploration

In practice the “exploration-exploitation dilemma” is frequently addressed naively by dithering $[27,48,49]$. In continuous action spaces Gaussian noise is added to actions, while in discrete action spaces actions are chosen $\epsilon$-greedily, meaning that optimal actions are chosen with probability $1-\epsilon$ and random actions with probability $\epsilon$. These two approaches work in environments where random sequences of actions are likely to cause positive rewards or to “do the right thing”. Since rewards in sparse domains are infrequent, getting a random positive reward can become very unlikely, resulting in a worst case sample complexity exponential in the amount of states and actions $[20,33,34,56]$. For example, Fig. 1 shows a case where random exploration suffers from exponential sample complexity.

Empirically, this shortcoming can be observed in numerous benchmarks environments, such as the Arcade Learning Environment [5]. Games like Montezuma’s Revenge or Pitfall have sparse reward signals and consequently agents with ditheringbased exploration learn almost nothing [27, 48]. While Montezuma’s Revenge has become the standard benchmark for hard exploration problems, it is important to stress that successfully solving it may not always be a good indicator of intelligent exploration strategies.

This bad exploration behaviour is in partly due to the lack of a prior assumption about the world and its behaviour. As pointed out by [10], in a randomized version of Montezuma’s Revenge (Fig.3) humans perform significantly worse because their prior knowledge is diminished by the randomization, while for RL agents there is no difference due to the lack of prior in the first place. Augmenting an RL agent with prior knowledge could provide a more guided exploration. Yet, we can vastly improve over random exploration even without making use of prior.

A good exploration algorithm should be able to solve hard exploration problems with sparse rewards in large state-action spaces while remaining computationally tractable. According to [33] it is necessary that such an algorithm performs “deep exploration” rather than “myopic exploration”. An agent doing deep exploration will take several coherent actions to explore instead of just locally choosing the most interesting states independently. This is analogous to the general goal of the agent: maximizing the future expected reward rather than the reward of the next timestep.

## 机器学习代写|强化学习project代写reinforence learning代考|Optimism in the Face of Uncertainty

Many of the provably efficient algorithms are based on optimism in the face of uncertainty (OFU) [24] in which the agent acts greedily w.r.t. action values that are optimistic by including an exploration bonus. Either the agent then experiences a high reward and the action was indeed optimal or the agent experiences a low reward and learns that the action was not optimal. After visiting a state-action pair, the exploration bonus is reduced. This approach is superior to naive approaches in that it avoids actions where low value and low information gain are possible. Generally, under the assumption that the agent can visit every state-action pair infinitely many times, the overestimation will decrease and almost optimal behaviour is obtained. Optimal behaviour cannot be obtained due to the bias introduced by the exploration bonus. Most of the algorithms are optimal up to polynomial in the amount of states, actions or the horizon length. The literature provides many variations of these algorithms which use bounds with varying efficacy or different simplifying assumptions, e.g. $[3,6,9,19,20,22]$.

The bounds are often expressed in a framework called probably approximately correct $(\mathrm{PAC})$ learning. Formally, the PAC bound is expressed by a confidence parameter $\delta$ and an accuracy parameter $\epsilon$ w.r.t. which the algorithms are shown to be $\epsilon$ optimal with probability $1-\delta$ after a polynomial amount of timesteps in $\frac{1}{\sigma}, \frac{1}{\epsilon}$ and some factors depending on the MDP at hand.

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

A large body of work deals with efficient exploration through intrinsic motivation. This takes inspiration from the psychology literature [45] which divides human motivation into extrinsic and intrinsic. Extrinsic motivation describes doing an activity to attain a reward or avoid punishment, while intrinsic rewards describe doing an activity for the sake of curiosity or doing the activity itself. Analogously, we can define the environments reward signal $e_{t}$ at timestep $t$ to be extrinsic and augment it with an intrinsic reward signal $i_{t}$. The agent then tries to maximize $r_{t}=e_{t}+i_{t}$. In the context of a sparse reward problem, the intrinsic reward can fill the gaps between the sparse extrinsic rewards, possibly giving the agent quality feedback at every timestep. In non-tabular MDPs theoretical guarantees are not provided, though, and therefore there is no agreement on an optimal definition of the best intrinsic reward. Intuitively, the intrinsic reward should guide the agent towards optimal behaviour.
An upside of intrinsic reward methods are their straightforward implementation and application. Intrinsic rewards can be used in conjunction with any RL algorithm by just providing the modified reward signal to the learning algorithm $[4,7,57]$. When the calculation of the intrinsic reward and the learning algorithm itself both scale to high dimensional states and actions, the resulting combination is applicable to large state-action spaces as well. However, increased performance is not guaranteed [4]. In the following sections, we will present different formulations of intrinsic rewards.

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