Renyuan Xu

Title: Decision Making with Learning and Opportunity to Reverse

Abstract: Many real-world analytics problems involve two significant challenges: estimation and optimization. Due to the complex nature of each challenge, the standard machine learning paradigm separates the procedures of estimation and optimization. By and large, machine learning tools intend to minimize estimation errors and do not account for how estimations will be used in downstream optimization tasks such as decision-making problems. In contrast, there is a line of literature in economics focusing on exploring the optimal way to acquire information and learn dynamically to facilitate decision-making. However, most of the downstream decision-making problems considered in this line of work are static (i.e., one-shot) problems which sometimes over-simplify the structures of many real-world problems that require dynamic or sequential decisions.

As a preliminary attempt to introduce more complex downstream decision-making problems after learning and investigate how downstream tasks affect the learning behavior, we

consider a simple example where a decision maker (DM) chooses between two products, an established product A with known return and a newly introduced product B with an

unknown return. The DM will make an initial choice between A and B after learning about product B for some time. Importantly, our framework allows the DM to reverse her initial

choice at a cost anytime afterward. We establish the general theory and investigate the analytical structure of the problem through the lens of the Hamilton—Jacobi—Bellman equation and regularity analysis. We then discuss how model parameters (such as the cost to reverse) and the opportunity to reverse affect the learning behavior of the DM. If time allows, we will also discuss some insights on mechanism design from the product seller's perspective.

This is based on joint work with Thaleia Zariphopoulou and Luhao Zhang from UT Austin.