EXPRESS: Joint Dynamic Advertising and Pricing: Near-Optimality of Static Policies and Demand Learning

Advertising and pricing are two important marketing decisions that promote demand and increase a firm's market share. However, it is often costly or even impossible for a company to accurately estimate the advertising system's state and select appropriate advertising models, thereby leading to significant waste in advertising. To address these issues, we consider a firm that does not know the advertising model a priori and learns to adjust its advertising and pricing decisions adaptively. We first propose a general advertising and pricing model, which supports decisions based on realized demand and avoids additional measurements of the advertising system. This general model encompasses several widely used models, including the static model, the Nerlove-Arrow model and the Vidale-Wolfe model as special cases, thereby reducing the burden of model selection. For classic advertising and pricing models, we also study the performance of static policies and (theoretically and numerically) demonstrate the near-optimality of the optimal static policy, which later serves as the benchmark and target for learning. Next, we propose a learning algorithm that effectively integrates discretization, optimism under uncertainty, and low-switching to optimize static policies. By leveraging quadratic growth and local smoothness properties, we establish a square-root regret bound that is tight up to polylogarithmic factors. Finally, numerical experiments are conducted to verify the optimality gap of the optimal static policy and demonstrate the efficacy of our algorithm.