## 1 Introduction  
Driven by the wave of digitalization, massive volumes of economic behavior data have become a critical foundation for modern enterprises to support decision-making and optimization processes [1]. These data primarily encompass transaction records, click behavior, browsing paths, and price responses, capturing user decision-making patterns and market dynamics across various economic activities [2]. With the continuous advancement of big data technologies and computational capabilities, these large-scale datasets offer unprecedented opportunities for enterprises to refine pricing strategies and forecast revenues with higher accuracy [3, 4]. Nevertheless, extracting meaningful insights from complex, high-dimensional, and delayed-feedback economic behavior data remains a significant challenge in the field of intelligent pricing [5]. Traditional pricing strategies often rely on static statistical models or manually defined rules, which tend to be inadequate in handling dynamic market environments [6]. Such approaches demonstrate limited flexibility and effectiveness, particularly in scenarios involving diverse product types, intricate user behavior, and intense market competition [7, 8]. Specifically, static pricing models are unable to dynamically adjust prices, making them unsuitable for rapidly changing markets. Rule-based methods, on the other hand, depend heavily on expert experience and often fail to quantitatively model complex economic behavior and market feedback [9]. Moreover, economic behavior data are characterized by high dimensionality, heterogeneity, temporal dependence, and sparsity, which makes it difficult for traditional models to generalize effectively or cope with the data's inherent complexity [10]. Although static pricing approaches were among the earliest methods applied in market settings, they generally set prices based on historical data and market patterns [11]. While effective in simple markets with a single product and stable conditions, such methods exhibit substantial limitations in complex real-world scenarios [12], such as the inability to promptly update prices or account for consumer heterogeneity and intricate market behavior [13]. Regression-based dynamic pricing methods typically involve building regression models to estimate the relationship between price and sales volume, followed by pricing adjustments based on market feedback [14]. While these methods can partially address demand fluctuations, their limitations are evident. First, regression models often assume a fixed relationship between demand and price; however, in complex market environments, this relationship is highly nonlinear and dynamic, which cannot be adequately captured by standard regression techniques [15]. Second, these models usually presume immediate and continuous feedback from the market, whereas, in reality, feedback is frequently delayed and sparse, leading to uncertainty that regression models are ill-equipped to manage [16; 17]. With the advancement of deep learning technologies, data-driven pricing strategies have attracted increasing attention in both academic and industrial domains. Deep learning enables multi-layer neural networks to extract abstract representations from complex economic behavior data, thereby facilitating more accurate and flexible decision-making processes [18; 19]. In particular, deep reinforcement learning (DRL), which combines the perceptual capabilities of deep networks with the sequential decision-making mechanisms of reinforcement learning, has emerged as a highly promising paradigm [20]. Among the various DRL methods, the deep Q-network (DQN) represents a fundamental breakthrough. By leveraging deep neural networks to approximate the \(Q\)-value function, DQN effectively addresses the scalability issues encountered by traditional Q-learning in high-dimensional state spaces [21; 22]. Through end-to-end interactions with the environment, DQN enables direct learning of pricing strategies from feedback signals [23].