  According to the main international reports, more pervasive industrial and
business-process automation, thanks to machine learning and advanced analytic
tools, will unlock more than 14 trillion USD worldwide annually by 2030. In the
specific case of pricing problems-which constitute the class of problems we
investigate in this paper-, the estimated unlocked value will be about 0.5
trillion USD per year. In particular, this paper focuses on pricing in
e-commerce when the objective function is profit maximization and only
transaction data are available. This setting is one of the most common in
real-world applications. Our work aims to find a pricing strategy that allows
defining optimal prices at different volume thresholds to serve different
classes of users. Furthermore, we face the major challenge, common in
real-world settings, of dealing with limited data available. We design a
two-phase online learning algorithm, namely PVD-B, capable of exploiting the
data incrementally in an online fashion. The algorithm first estimates the
demand curve and retrieves the optimal average price, and subsequently it
offers discounts to differentiate the prices for each volume threshold. We ran
a real-world 4-month-long A/B testing experiment in collaboration with an
Italian e-commerce company, in which our algorithm PVD-B-corresponding to A
configuration-has been compared with human pricing specialists-corresponding to
B configuration. At the end of the experiment, our algorithm produced a total
turnover of about 300 KEuros, outperforming the B configuration performance by
about 55%. The Italian company we collaborated with decided to adopt our
algorithm for more than 1,200 products since January 2022.
