Approximate Bayesian inference for simulation and optimization

Mes²,

Powell

et al. 2019

Operations Research

Self Cite

07-425.R4 Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print or online or to submit the papers to another publication.

Section: Asymptotic Analysis Of Offline Kgmentioning

confidence: 99%

Bayesian Exploration for Approximate Dynamic Programming

Mes²,

Powell

et al. 2019

Operations Research

Self Cite

“…We would like to retain the multivariate normal distribution in order to use the power of correlated beliefs. Since this is not possible using standard Bayesian updating, we use the methods of approximate Bayesian inference (Ryzhov 2015). Essentially, if the posterior distribution is not conjugate with the prior, we replace it by a simpler distribution that does belong to our chosen family (multivariate normal), and optimally approximates the true, non‐normal posterior.…”

Section: Demand Modelmentioning

confidence: 99%

“…However, there is no analogous model for logistic regression, making it difficult to represent beliefs about logistic demand curves. We approach this problem using approximate Bayesian inference (Ryzhov 2015), and create a new learning mechanism that allows us to maintain and update a multivariate normal belief on the regression coefficients using rigorous statistical approximations. We then develop a "Bayes-greedy" pricing strategy that optimizes an estimate of expected revenue by averaging over all possible revenue curves.…”

Section: Introductionmentioning

confidence: 99%

Learning Demand Curves in B2B Pricing: A New Framework and Case Study

Production and Operations Management

et al. 2020

Self Cite

In business‐to‐business (B2B) pricing, a seller seeks to maximize revenue obtained from high‐volume transactions involving a wide variety of buyers, products, and other characteristics. Buyer response is highly uncertain, and the seller only observes whether buyers accept or reject the offered prices. These deals are also subject to high opportunity cost, since revenue is zero if the price is rejected. The seller must adapt to this uncertain environment and learn quickly from new deals as they take place. We propose a new framework for statistical and optimal learning in this problem, based on approximate Bayesian inference, which has the ability to measure and update the seller’s uncertainty about the demand curve based on new deals. In a case study, based on historical data, we show that our approach offers significant practical benefits.

“…For the opponent y, we apply (37)-(38) with x and y reversed. The updating equations are derived using the moment-matching technique (Ryzhov, 2015a). This learning model is an approximation, as the normal prior is not conjugate with the binary observation.…”

Section: Application To Competitive Online Gamingmentioning

confidence: 99%

The Local Time Method for Targeting and Selection

2018

Operations Research

Self Cite

We propose a framework for "targeting and selection" (T&S), a new problem class in simulation optimization where the objective is to select a simulation alternative whose mean performance matches a pre-specified target as closely as possible. T&S resembles the more wellknown problem of ranking and selection, but presents unexpected challenges: for example, a one-step look-ahead method may produce statistically inconsistent estimates of the values, even under very standard normality assumptions. We create a new and fundamentally different approach, based on a Brownian local time model, that exhibits characteristics of two widely-studied methodologies, namely expected improvement and optimal computing budget allocation. We characterize the asymptotic sampling rates of this method and relate them to the convergence rates of metrics of interest. The local time method outperforms benchmarks in experiments, including problems where the modeling assumptions of T&S are violated.