Online Decision Making in Dynamic Pricing and Assortment Selection

Online decision making is an interdisciplinary research field which lies at the interface of Statistics, Machine Learning, and Operations Research. In this dissertation, we investigate online decision making problems in dynamic pricing and dynamic assortment selection, and develop various trustworthy algorithms to handle these problems. For the first two projects, we consider a contextual dynamic pricing problem with binary customer feedbacks. Existing pricing policies typically assume full or partial knowledge of the market noise distribution. We tackle the challenge of unknown nonparametric noise distribution in the linear valuation model. Firstly, we develop a DIstribution-free Pricing (DIP) policy that balances greedy pricing (exploitation) and learning of the linear valuation and market noise distribution (exploration). Both theoretical regret guarantees and numerical studies demonstrate the effectiveness of DIP. In the second project, we further investigate different smoothness assumptions for the market noise distribution. A new Explore-then-Upper Confidence Bound (UCB) policy is proposed. For the last two projects, we study the problem of dynamic assortment selection with positioning. We first develop a UCB Explore-Then-Commit (UCB-ETC) policy with sub-linear regret guarantees. It successfully combines the UCB and ETC ideas in bandit algorithms. Finally, we develop a Truncated Linear Regression UCB (TLR-UCB) policy for the considered problem. TLR-UCB is more flexible than UCB-ETC and enjoys near-optimal regret guarantees.