Stefanus Jasin

Qing Feng, Ruihao Zhu, Stefanus Jasin

Motivated by the prevalence of ``price protection guarantee", which allows a customer who purchased a product in the past to receive a refund from the seller during the so-called price protection period (typically defined as a certain time window after the purchase date) in case the seller decides to lower the price, we study the impact of such policy on the design of online learning algorithm for data-driven dynamic pricing with initially unknown customer demand. We consider a setting where a firm sells a product over a horizon of $T$ time steps. For this setting, we characterize how the value of $M$, the length of price protection period, can affect the optimal regret of the learning process. We show that the optimal regret is $\tildeΘ(\sqrt{T}+\min\{M,\,T^{2/3}\})$ by first establishing a fundamental impossible regime with novel regret lower bound instances. Then, we propose LEAP, a phased exploration type algorithm for \underline{L}earning and \underline{EA}rning under \underline{P}rice Protection to match this lower bound up to logarithmic factors or even doubly logarithmic factors (when there are only two prices available to the seller). Our results reveal the surprising phase transitions of the optimal regret with respect to $M$. Specifically, when $M$ is not too large, the optimal regret has no major difference when compared to that of the classic setting with no price protection guarantee. We also show that there exists an upper limit on how much the optimal regret can deteriorate when $M$ grows large. Finally, we conduct extensive numerical experiments to show the benefit of LEAP over other heuristic methods for this problem.

Parshan Pakiman, Boxiao Chen, Selvaprabu Nadarajah et al.

We study dynamic pricing of a product with an unknown demand distribution over a finite horizon. Departing from the standard no-regret learning environment in which prices can be adjusted at any time, we restrict price changes to predetermined points in time to reflect common retail practice. This constraint, coupled with demand model ambiguity and an unknown customer arrival pattern, imposes a high risk of revenue loss, as a price based on a misestimated demand model may be applied to many customers before it can be revised. We develop an adaptive risk learning (ARL) framework that embeds a data-driven ambiguity set (DAS) to quantify demand model ambiguity by adapting to the unknown arrival pattern. Initially, when arrivals are few, the DAS includes a broad set of plausible demand models, reflecting high ambiguity and revenue risk. As new data is collected through pricing, the DAS progressively shrinks, capturing the reduction in model ambiguity and associated risk. We establish the probabilistic convergence of the DAS to the true demand model and derive a regret bound for the ARL policy that explicitly links revenue loss to the data required for the DAS to identify the true model with high probability. The dependence of our regret bound on the arrival pattern is unique to our constrained dynamic pricing problem and contrasts with no-regret learning environments, where regret is constant and arrival-pattern independent. Relaxing the constraint on infrequent price changes, we show that ARL attains the known constant regret bound. Numerical experiments further demonstrate that ARL outperforms benchmarks that prioritize either regret or risk alone by adaptively balancing both without knowledge of the arrival pattern. This adaptive risk adjustment is crucial for achieving high revenues and low downside risk when prices are sticky and both demand and arrival patterns are unknown.

Qiaochu Wang, Yan Huang, Stefanus Jasin et al.

Should firms that apply machine learning algorithms in their decision-making make their algorithms transparent to the users they affect? Despite growing calls for algorithmic transparency, most firms have kept their algorithms opaque, citing potential gaming by users that may negatively affect the algorithm's predictive power. We develop an analytical model to compare firm and user surplus with and without algorithmic transparency in the presence of strategic users and present novel insights. We identify a broad set of conditions under which making the algorithm transparent benefits the firm. We show that, in some cases, even the predictive power of machine learning algorithms may increase if the firm makes them transparent. By contrast, users may not always be better off under algorithmic transparency. The results hold even when the predictive power of the opaque algorithm comes largely from correlational features and the cost for users to improve on them is close to zero. Overall, our results show that firms should not view manipulation by users as bad. Rather, they should use algorithmic transparency as a lever to motivate users to invest in more desirable features.