Definition: The popularity of deep reinforcement learning (DRL) applications in economics has increased exponentially. DRL, through a wide range of capabilities from reinforcement learning (RL) to deep learning (DL), offers vast opportunities for handling sophisticated dynamic economics systems. DRL is characterized by scalability with the potential to be applied to high-dimensional problems in conjunction with noisy and nonlinear patterns of economic data.

1. Introduction

Deep learning (DL) techniques are based on the use of multi-neurons that rely on the multi-layer architectures to accomplish a learning task. In DL, the neurons are linked to the input data in conjunction with a loss function for the purpose of updating their weights and maximizing the fitting to the inbound data ^[1][2][1,2]. In the structure of a multi-layer, every node takes the outputs of all the prior layers in order to represent outputs set by diminishing the approximation of the primary input data, while multi-neurons learn various weights for the same data at the same time. There is a great demand for the appropriate mechanisms to improve productivity and product quality in the current market development. DL enables predicting and investigating complicated market trends compared to the traditional algorithms in ML. DL presents great potential to provide powerful tools to learn from stochastic data arising from multiple sources that can efficiently extract complicated relationships and features from the given data. DL is reported as an efficient predictive tool to analyze the market ^[3][4][3,4]. Additionally, compared to the traditional algorithms, DL is able to prevent the over-fitting problem, to provide more efficient sample fitting associated with complicated interactions, and to outstretch input data to cover all the essential features of the relevant problem [5].

Reinforcement learning (RL) [6] is a powerful mathematical framework for experience-driven autonomous learning [7]. In RL, the agents interact directly with the environment by taking actions to enhance its efficiency by trial-and-error to optimize the cumulative reward without requiring labeled data. Policy search and value function approximation are critical tools of autonomous learning. The search policy of RL is to detect an optimal (stochastic) policy applying gradient-based or gradient-free approaches dealing with both continuous and discrete state-action settings [8]. The value function strategy is to estimate the expected return in order to find the optimal policy dealing with all possible actions based on the given state. While considering an economic problem, despite traditional approaches [9], reinforcement learning methods prevent suboptimal performance, namely, by imposing significant market constraints that lead to finding an optimal strategy in terms of market analysis and forecast [10]. Despite RL successes in recent years ^[11][12][13][11,12,13], these results suffer the lack of scalability and cannot manage high dimensional problems. The DRL technique, by combining both RL and DL methods, where DL is equipped with the vigorous function approximation, representation learning properties of deep neural networks (DNN), and handling complex and nonlinear patterns of economic data, can efficiently overcome these problems ^[14][15][14,15]. Ultimately, the purpose of this paper is to comprehensively provide an overview of the state-of-the-art in the application of both DL and DRL approaches in economics. However, in this paper, we focus on the state-of-the-art papers that employ DL, RL, and DRL methods in economics issues. The main contributions of this paper can be summarized as follows: