A Primal-Dual Online Learning Approach for Dynamic Pricing of Sequentially Displayed Complementary Items under Sale Constraints

Dynamic Pricing (DP) aims to determine the ideal pricing for a product or service in real-time employing revenue optimization strategies (see, (Rothschild, 1974; Kleinberg and Leighton, 2003; Trovò et al., 2018)). This practice is widely prevalent in various sectors, including airlines, ride-sharing, and retail, owing to its capability to adapt to variables such as demand, competition, and time constraints. Undoubtedly, dynamic pricing is garnering considerable attention from both the industry and the scientific community due to its profound economic impact on businesses. From a scientific standpoint, while early research in this field assumed knowledge of the underlying demand functions, the imperative for real-world AI applications has prompted the scientific community to shift their focus towards uncharted demand scenarios and exploration-exploitation algorithms, as underscored by seminal works (e.g., (Aviv and Pazgal, 2005; Besbes and Zeevi, 2009)). Moreover, research on non-stationary demand functions has made a substantial impact on the field. Specifically, recent studies have concentrated on external non-stationarity factors, such as internal ones driven by the seller's actions (as explored in (Cui et al., 2023)), as well as seasonality (as evidenced in (Besbes and Saure, 2014)).