Improving the Expected Improvement Algorithm
This addresses a key inefficiency in optimization under uncertainty for researchers and practitioners using EI, though it is incremental as it modifies an existing method.
The paper tackled the suboptimality of the expected improvement (EI) algorithm in Bayesian optimization for best-arm identification, showing it is far from optimal and introducing a simple modification that achieves asymptotic optimality and outperforms standard EI by an order of magnitude.
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.