At a given temperature, each material has an electrical conductivity that determines the value of electric current when an electric potential is applied. Examples of good conductors include metals such as copper and gold, whereas glass and Teflon are poor conductors. In any dielectric material, the electrons remain bound to their respective atoms and the material behaves as an insulator. Most semiconductors have a variable level of conductivity that lies between the extremes of conduction and insulation.[130] On the other hand, metals have an electronic band structure containing partially filled electronic bands. The presence of such bands allows electrons in metals to behave as if they were free or delocalized electrons. These electrons are not associated with specific atoms, so when an electric field is applied, they are free to move like a gas (called Fermi gas)[131] through the material much like free electrons.
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Tremendous amount of data are being generated and saved in many complex engineering and social systems every day. It is significant and feasible to utilize the big data to make better decisions by machine learning techniques. In this paper, we focus on batch reinforcement learning (RL) algorithms for discounted Markov decision processes (MDPs) with large discrete or continuous state spaces, aiming to learn the best possible policy given a fixed amount of training data. The batch RL algorithms with handcrafted feature representations work well for low-dimensional MDPs. However, for many real-world RL tasks which often involve high-dimensional state spaces, it is difficult and even infeasible to use feature engineering methods to design features for value function approximation. To cope with high-dimensional RL problems, the desire to obtain data-driven features has led to a lot of works in incorporating feature selection and feature learning into traditional batch RL algorithms. In this paper, we provide a comprehensive survey on automatic feature selection and unsupervised feature learning for high-dimensional batch RL. Moreover, we present recent theoretical developments on applying statistical learning to establish finite-sample error bounds for batch RL algorithms based on weighted L p norms. Finally, we derive some future directions in the research of RL algorithms, theories and applications.
Since many real-world RL tasks often involve high-dimensional state spaces, it is difficult to use feature engineering methods to design features for function approximators. To cope with high-dimensional RL problems, the desire to design data-driven features has led to a lot of works in incorporating feature selection and feature learning into traditional batch RL algorithms. Automatic feature selection is to select features from a given set of features by using regularization, matching pursuit, random projection, etc. Automatic feature learning is to learn features from data by learning the structure of the state space using unsupervised learning methods, such as manifold learning, spectral learning, deep learning, etc. In this section, we present a comprehensive survey on these promising research works.
A CNN is a multilayer neural network which reduces the number of weight parameters by sharing weights between the local receptive fields. The pretraining phase is usually not required. Mnih et al. [101] presented a deep Q learning algorithm to play Atari 2600 games successfully. This algorithm can learn control policies directly from high-dimensional, raw video data without hand-designed features. A CNN was used as the action-value function approximator. To scale to large data set, the stochastic gradient descent instead of batch update was used to adapt the weights. An experience replay idea was used to deal with the problem of correlated data and non-stationary distributions. This algorithm outperformed all previous approaches on six of the games and even surpassed a human expert on three of them.
Batch RL is a model-free and data efficient technique, and can learn to make decisions from a large amount of data. For high-dimensional RL problems, it is necessary to develop RL algorithms which can select or learn features automatically from data. In this paper, we have provided a survey on recent progress in feature selection and feature learning for high-dimensional batch RL problems. The automatic feature selection techniques like regularization, matching pursuit, random projection can select suitable features for batch RL algorithms from a set of features given by the designer. Unsupervised feature learning methods, such as manifold learning, spectral learning, and deep learning, can learn representations or features, and thus hold great promise for high-dimensional RL algorithms. It will be an advanced intelligent control method by combining unsupervised learning and supervised learning with RL. Furthermore, we have also presented a survey on recent theoretical progress in applying statistical machine learning to establish rigorous convergence and performance analysis for batch RL algorithms with function approximation architectures.
To further promote the development of RL, we think that the following directions need to be considered in the near future. Most existing batch RL methods assume that the action space is finite, but many real-world systems have continuous action spaces. When the action space is large or continuous, it is difficult to compute the greedy policy at each iteration. Therefore, it is important to develop RL algorithms which can solve MDPs with large or continuous action spaces. RL has a strong relationship with supervised learning and unsupervised learning, so it is quite appealing to introduce more machine learning methods to RL problems. For example, there have been some research on combining transfer learning with RL[114], aiming to solve different tasks with transferred knowledge. When the training data set is large, the computational cost of batch RL algorithms will become a serious problem. It will be quite promising to parallelize the existing RL algorithms in the framework of parallel or distributed computing to deal with large scale problems. For example, the MapReduce framework[115] was used to design parallel RL algorithms. Last but not least, it is significant to apply the batch RL algorithms based on feature selection or feature learning to solve real-world problems in power grid, transportation, health care, etc. 2ff7e9595c
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