Learning Fair And Effective Points-Based Rewards Programs

Abstract: Points-based rewards programs are a prevalent way to incentivize customer loyalty; in these programs, customers who make repeated purchases from a seller accumulate points, working toward eventual redemption of a free reward. These programs have recently come under scrutiny due to accusations of unfair practices in their implementation. Motivated by these concerns, we study the problem of fairly designing points-based rewards programs, with a focus on two obstacles that put fairness at odds with their effectiveness. First, due to customer heterogeneity, the seller should set different redemption thresholds for different customers to generate high revenue. Second, the relationship between customer behavior and the number of accumulated points is typically unknown; this requires experimentation which may unfairly devalue customers' previously earned points. We first show that an individually fair rewards program that uses the same redemption threshold for all customers suffers a loss in revenue of at most a factor of $1+\ln 2$, compared to the optimal personalized strategy that differentiates between customers. We then tackle the problem of designing temporally fair learning algorithms in the presence of demand uncertainty. Toward this goal, we design a learning algorithm that limits the risk of point devaluation due to experimentation by only changing the redemption threshold $O(\log T)$ times, over a horizon of length $T$. This algorithm achieves the optimal (up to polylogarithmic factors) $\widetilde{O}(\sqrt{T})$ regret in expectation. We then modify this algorithm to only ever decrease redemption thresholds, leading to improved fairness at a cost of only a constant factor in regret. Extensive numerical experiments show the limited value of personalization in average-case settings, in addition to demonstrating the strong practical performance of our proposed learning algorithms.