Interpretable Personalization via Policy Learning with Linear Decision Boundaries

With the rise of the digital economy and an explosion of available information on consumers, effective personalization of offers, goods, and services has become a core business focus for companies to improve revenues and maintain competitive edge. This paper studies the personalization problem through the lens of policy learning, where the goal is to learn a decision-making rule (a policy) that maps from consumer and product characteristics (features) to recommendations (actions) in order to optimize outcomes (rewards). We focus on using available historical data for offline learning with unknown data collection procedure. Importantly, in many business and medical settings, interpretability of a policy is essential. To address these challenges, we study the class of policies with linear decision boundaries and propose learning algorithms using tools from causal inference. We propose several optimization schemes to solve the associated non-convex, non-smooth optimization problem, and find that an adapted Bayesian optimization algorithm is fast and effective. We test our algorithm with extensive simulation studies and apply it to an online marketplace customer purchase dataset, where the learned policy outputs a personalized discount recommendation based on customer and product features in order to maximize gross merchandise value (GMV) for sellers. Our learned policy improves upon the platform's baseline by 88.2\% in net sales revenue, while also providing informative insights on which features are important for the decision-making process, e.g. when "Attribute 2" is large, marginal increase in GMV is low for discounts higher than 10\%. Our findings suggest that the proposed policy learning algorithm provides a promising practical approach for interpretable personalization across a wide range of applications.