Effective Adaptive Exploration of Prices and Promotions in Choice-Based Demand Models

We consider the problem of setting the optimal prices and promotions for a large number of products when the firm lacks demand information. At each time, a customer arrives and chooses a product based on a discrete choice model where each product's utility depends on product features, its price and promotion, and the customer's features. Using a Thompson Sampling approach, we develop a regret minimizing, alternatively profit maximizing, algorithm for the retailer. We provide the first adaptive algorithm that simultaneously incorporates pricing and promotions into a discrete choice model. To make our algorithm computationally feasible over an infinite space of prices and promotions, we provide a novel method for learning the optimal price and promotion given a set of demand parameters. We also provide theoretical justification for our results and improve upon existing regret guarantees. Using simulations based on real-life grocery store data, we show that our method significantly outperforms existing approaches. In addition, we extend our methodology to a contextual setting, which allows for consumer heterogeneity and personalized pricing and promotion. Compared to existing works, our approach is agnostic to the parametric specification of the utility model and needs no assumptions on the underlying distribution customer features