A Primal-Dual Online Learning Approach for Dynamic Pricing of Sequentially Displayed Complementary Items under Sale Constraints
This addresses the problem of coherent pricing for online retailers selling complementary items like flight tickets and ancillaries, though it is incremental as it builds on existing online learning methods.
The paper tackles dynamic pricing of complementary items under sales constraints by formulating it as a constrained Markov Decision Process and developing a primal-dual online optimization algorithm, achieving improved constraint violation and regret compared to baselines in synthetic evaluations.
We address the challenging problem of dynamically pricing complementary items that are sequentially displayed to customers. An illustrative example is the online sale of flight tickets, where customers navigate through multiple web pages. Initially, they view the ticket cost, followed by ancillary expenses such as insurance and additional luggage fees. Coherent pricing policies for complementary items are essential because optimizing the pricing of each item individually is ineffective. Our scenario also involves a sales constraint, which specifies a minimum number of items to sell, and uncertainty regarding customer demand curves. To tackle this problem, we originally formulate it as a Markov Decision Process with constraints. Leveraging online learning tools, we design a primal-dual online optimization algorithm. We empirically evaluate our approach using synthetic settings randomly generated from real-world data, covering various configurations from stationary to non-stationary, and compare its performance in terms of constraints violation and regret against well-known baselines optimizing each state singularly.