Integrating Inference and Experimental Design for Contextual Behavioral Model Learning

The strategic behavior of users is significantly influenced by their hidden information such as private valuations, risk preferences, and price sensitivities. Contextual behavioral model learning refers to learning the dependence of users' hidden information on their observable context information. While many existing studies use offline data to learn contextual behavioral models, we study how to design sequential experiments to collect the most informative user behavioral data for learning. We propose a basic inference-then-design method. In each experimental period, it infers a probabilistic contextual behavioral model using historical experimental data, and then designs the new experiment to maximize the gain of information about the probabilistic model. We further improve the basic method in two aspects. First, we improve the inference step by specifying a more informative prior for learning the probabilistic contextual behavioral model. Second, we integrate the inference and design steps instead of conducting them separately. Our rigorous theoretic analysis reveals that the optimization objective of the inference step can be modified to account for the downstream experimental design step. Numerical experiments show that our methods lead to more effective experiments, i.e., the collected experimental data can help in learning a more accurate behavioral model.