UC Santa Barbara

The intersection of pricing and machine learning has gained considerable attention in recent years, positioning pricing strategy as a decision-making problem for the sellers who are tasked with setting prices in real-time and learning optimal prices through observed demands. This thesis explores dynamic pricing within the framework of online decision-making, where sequential decisions are informed by continuously evolving observations.

We contribute novel technical approaches to dynamic pricing through the study of two main aspects:

I, Feature-Based Dynamic Pricing. In Part I, we address the challenge of pricing highly differentiated products, each characterized by specific features.Assuming linear and noisy customer valuations with binary decision outcomes, we explore settings with known, unknown, and heteroscedastic noise distributions. We propose algorithms for each scenario, providing rigorous analysis of their regret guarantees. Our findings illustrate that the difficulty of solving feature-based dynamic pricing is contingent on the seller's knowledge of noise distributions.

II, Dynamic Pricing under Constraints. In Part II, we examine constraints that affect pricing strategies in modern markets, focusing on fairness and inventory limits. We firstly introduce two fairness notions and develop a randomized pricing mechanism that accommodates multiple fairness constraints simultaneously, achieving optimal regret and fairness outcomes. In the other project, we tackle pricing under inventory constraints, addressing challenges posed by censored demands to achieve optimal regrets.

Our algorithmic solutions are rigorously evaluated through the metric of information-theoretic regret bounds. The practical relevance of our methodologies is further validated by comprehensive empirical studies using simulated data. The combination of theoretical and practical justifications demonstrates the robustness and applicability of our approaches across various dynamic pricing scenarios.