Scaled Rate Optimization for Beta-Binomial Models

TL;DR

This paper introduces a novel analytical method for optimizing and comparing beta-binomial process rates, significantly improving computational efficiency over traditional frequentist approaches in both offline and online settings.

Contribution

It presents a closed-form probabilistic expression for rate comparison and explores its application in exploration-exploitation scenarios, outperforming frequentist methods.

Findings

Hypergeometric expression enables precise rate comparison

4.5 orders of magnitude performance improvement

Effective in offline and online optimization contexts

Abstract

Rates of binomial processes are modeled using beta-binomial distributions (for example, from Beta Regression). We treat the offline optimization scenario and then the online one, where we optimize the exploration-exploitation problem. The rates given by two processes are compared through their distributions, but we would like to optimize the net payout (given a constant value per successful event, unique for each of the processes). The result is an analytically-closed, probabilistic, hypergeometric expression for comparing the payout distributions of two processes. To conclude, we contrast this Bayesian result with an alternative frequentist approach and find 4.5 orders of magnitude improvement in performance, for a numerical accuracy level of 0.01%.