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

2024-09-05

arXiv.org

AI Summary

This paper studies the data-driven newsvendor problem: deciding order quantities from limited samples under unknown demand distributions to minimize regret under asymmetric loss. We address variants including additive/multiplicative regret, expected/high-probability convergence, and diverse distributional assumptions. First, we introduce the novel concept of “clustered distributions” and establish a unified theoretical framework that characterizes the full spectrum of achievable regret rates—from $1/sqrt{n}$ down to $1/n$—while providing tight minimax lower bounds, thereby closing several longstanding theoretical gaps. Our methodology integrates empirical distribution function analysis, extreme-value statistics, concentration inequalities, and constructive lower-bound techniques. The theory precisely identifies the optimal regret rate for all major problem settings. Numerical experiments confirm that our theoretical rates accurately predict the actual decay behavior of regret.

Technology Category

Reasoning under Uncertainty: Sequential Decision MakingMachine Learning: Online Learning & BanditsGame Theory and Economic Paradigms: Adversarial Learning

Application Category

Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasetsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsWeb Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

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.

Problem

• Analyzes data-driven Newsvendor problem variants and gaps
• Unifies regret analysis using clustered distributions concept
• Demonstrates achievable regret spectrum from 1/sqrt(n) to 1/n

Innovation

• Unified analysis using clustered distributions
• New lower bounds for regret spectrum
• Empirical validation with common distributions