Survey of Data-driven Newsvendor: Unified Analysis and Spectrum of Achievable Regrets

TL;DR

This paper provides a comprehensive survey and unified analysis of data-driven Newsvendor problems, exploring various regret measures, distribution classes, and bounds, with simulations confirming the theoretical insights.

Contribution

It introduces a unified framework based on clustered distributions, filling gaps in the literature and characterizing the spectrum of achievable regrets from 1/√n to 1/n.

Findings

Unified analysis of all variants of data-driven Newsvendor.

Identification of the full spectrum of achievable regrets.

Simulations validate the theoretical predictions across distributions.

Abstract

In the Newsvendor problem, the goal is to guess the number that will be drawn from some distribution, with asymmetric consequences for guessing too high vs. too low. In the data-driven version, the distribution is unknown, and one must work with samples from the distribution. Data-driven Newsvendor has been studied under many variants: additive vs. multiplicative regret, high probability vs. expectation bounds, and different distribution classes. This paper studies all combinations of these variants, filling in many gaps in the literature and simplifying many proofs. In particular, we provide a unified analysis based on the notion of clustered distributions, which in conjunction with our new lower bounds, shows that the entire spectrum of regrets between $1/\sqrt{n}$ and $1/n$ can be possible. Simulations on commonly-used distributions demonstrate that our notion is the "correct" predictor of empirical regret across varying data sizes.