Technical Note-Consistency Analysis of Sequential Learning Under Approximate Bayesian Inference

• 成果类型: Article
• 署名作者: Chen, Ye; Ryzhov, Ilya O.
• 署名单位: Virginia Commonwealth University; University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2019.1850
• 发表日期: 2020
• 页码: 295-307
• 关键词: stochastic-approximation; CONVERGENCE; improvement; TECHNOLOGY; MODEL

摘要

Approximate Bayesian inference is a powerful methodology for constructing computationally efficient statistical mechanisms for sequential learning from incomplete or censored information. Approximate Bayesian learning models have proven successful in a variety of operations research and business problems; however, prior work in this area has been primarily computational, and the consistency of approximate Bayesian estimators has been a largely open problem. We develop a new consistency theory by interpreting approximate Bayesian inference as a form of stochastic approximation (SA) with an additional bias term. We prove the convergence of a general SA algorithm of this form and leverage this analysis to derive the first consistency proofs for a suite of approximate Bayesian models from the recent literature.