Can Global Optimization Strategy Outperform Myopic Strategy for Bayesian Parameter Estimation?

TL;DR

This study compares global and myopic strategies in Bayesian psychometric parameter estimation, finding that extended horizons in global strategies offer minimal benefits over simpler myopic approaches, despite higher computational costs.

Contribution

The paper provides a mathematical proof and experimental evidence showing the limited advantage of global optimization over myopic strategies in Bayesian parameter estimation.

Findings

Global strategies offer negligible utility improvements beyond immediate next steps.

The utility gain from additional horizon steps diminishes rapidly.

Myopic strategies are nearly as effective as global strategies with less computational effort.

Abstract

Bayesian adaptive inference is widely used in psychophysics to estimate psychometric parameters. Most applications used myopic one-step ahead strategy which only optimizes the immediate utility. The widely held expectation is that global optimization strategies that explicitly optimize over some horizon can largely improve the performance of the myopic strategy. With limited studies that compared myopic and global strategies, the expectation was not challenged and researchers are still investing heavily to achieve global optimization. Is that really worthwhile? This paper provides a discouraging answer based on experimental simulations comparing the performance improvement and computation burden between global and myopic strategies in parameter estimation of multiple models. The finding is that the added horizon in global strategies has negligible contributions to the improvement of optimal global utility other than the most immediate next steps (of myopic strategy). Mathematical recursion is derived to prove that the contribution of utility improvement of each added horizon step diminishes fast as that step moves further into the future.