Technical Note—A New Rate-Optimal Sampling Allocation for Linear Belief Models

Abstract

A major focus of the simulation literature is the study of optimal budget allocation. The goal is to divide a simulation budget between alternatives with unknown values in a manner that leads to efficient identification of the best alternative. Existing analytical techniques, based on large deviations theory, are limited to finite sets of alternatives, each of which is assigned a certain proportion of the budget. In “A New Rate-Optimal Sampling Allocation for Linear Belief Models,” Zhou and Ryzhov develop the first provably optimal budget allocation for a continuous problem where linear regression is used to model the value of a choice. The allocation is expressible in closed form and is simpler and easier to implement than analogous solutions for the discrete setting. This work bridges the emerging literature on contextual (regression-based) learning and the well-known statistical problem of optimal experimental design.