# Improving the Expected Improvement Algorithm

Source: [Improving the Expected Improvement Algorithm](<https://www.sota2.com/research/paper/68fa63691e209131ce9fe8ae>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T20:40:16.176Z

Authors: Chao Qin, Diego Klabjan, Daniel Russo

Published: 2017-05-29T04:02:27.000Z

## Abstract

The expected improvement (EI) algorithm is a popular strategy for information collection in optimization under uncertainty. The algorithm is widely known to be too greedy, but nevertheless enjoys wide use due to its simplicity and ability to handle uncertainty and noise in a coherent decision theoretic framework. To provide rigorous insight into EI, we study its properties in a simple setting of Bayesian optimization where the domain consists of a finite grid of points. This is the so-called best-arm identification problem, where the goal is to allocate measurement effort wisely to confidently identify the best arm using a small number of measurements. In this framework, one can show formally that EI is far from optimal. To overcome this shortcoming, we introduce a simple modification of the expected improvement algorithm. Surprisingly, this simple change results in an algorithm that is asymptotically optimal for Gaussian best-arm identification problems, and provably outperforms standard EI by an order of magnitude.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [e-good arm identification on Caption 853](<https://www.sota2.com/research/sota/e-good-arm-identification-on-caption-853.md>): e-good arm identification; Caption 853; Probability of False Selection: 0.01.

- [Best Arm Identification on Example 1 Synthetic](<https://www.sota2.com/research/sota/best-arm-identification-on-example-1-synthetic.md>): Best Arm Identification; Example 1 Synthetic; False Selection Probability: 7.

- [Best Arm Identification on Example 2 Synthetic](<https://www.sota2.com/research/sota/best-arm-identification-on-example-2-synthetic.md>): Best Arm Identification; Example 2 Synthetic; False Selection Probability: 9.

- [Best Arm Identification on Example 3 Synthetic](<https://www.sota2.com/research/sota/best-arm-identification-on-example-3-synthetic.md>): Best Arm Identification; Example 3 Synthetic; False Selection Rate: 2.

- [Best Arm Identification on Dose-finding ACR50](<https://www.sota2.com/research/sota/best-arm-identification-on-dose-finding-acr50.md>): Best Arm Identification; Dose-finding ACR50; Probability of False Selection: 3.

- [Best Arm Identification on Drug Review Dataset Selection](<https://www.sota2.com/research/sota/best-arm-identification-on-drug-review-dataset-selection.md>): Best Arm Identification; Drug Review Dataset Selection; Probability of False Selection: 28.

- [Best Arm Identification on New Yorker Cartoon Caption Contest Caption 854](<https://www.sota2.com/research/sota/best-arm-identification-on-new-yorker-cartoon-caption-contest-caption-854.md>): Best Arm Identification; New Yorker Cartoon Caption Contest Caption 854; False Selection Probability: 0.06.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1705.10033>)

[PDF](<https://arxiv.org/pdf/1705.10033.pdf>)