Quality vs. Quantity of Data in Contextual Decision-Making : Exact Analysis under Newsvendor Loss

When building datasets, one needs to invest time, money and energy to either aggregate more data or to improve their quality. The most common practice favors quantity over quality without necessarily quantifying the trade-off that emerges. In this work, we study data-driven contextual decision-making and the performance implications of quality and quantity of data. We focus on contextual decision-making with a Newsvendor loss. This loss is that of a central capacity planning problem in Operations Research, but also that associated with quantile regression. We consider a model in which outcomes observed in similar contexts have similar distributions and analyze the performance of a classical class of kernel policies which weigh data according to their similarity in a contextual space. We develop a series of results that lead to an exact characterization of the worst-case expected regret of these policies. This exact characterization applies to any sample size and any observed contexts. The model we develop is flexible, and captures the case of partially observed contexts. This exact analysis enables to unveil new structural insights on the learning behavior of uniform kernel methods: i) the specialized analysis leads to very large improvements in quantification of performance compared to state of the art general purpose bounds. ii) we show an important non-monotonicity of the performance as a function of data size not captured by previous bounds; and iii) we show that in some regimes, a little increase in the quality of the data can dramatically reduce the amount of samples required to reach a performance target. All in all, our work demonstrates that it is possible to quantify in a precise fashion the interplay of data quality and quantity, and performance in a central problem class. It also highlights the need for problem specific bounds in order to understand the trade-offs at play