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

We derive a new optimal sampling budget allocation for belief models based on linear regression with continuous covariates, where the expected response is interpreted as the value of the covariate vector, and an “error” occurs if a lower-valued vector is falsely identified as being better than a higher-valued one. Our allocation optimizes the rate at which the probability of error converges to zero using a large deviations theoretic characterization. This is the first large deviations-based optimal allocation for continuous decision spaces, and it turns out to be considerably simpler and easier to implement than allocations that use discretization. We give a practicable sequential implementation and illustrate its empirical potential.

Funding: This work was supported by the National Science Foundation [Grant CMMI-2112828].