Rectified Max-Value Entropy Search for Bayesian Optimization
This work addresses incremental improvements in Bayesian optimization methods for researchers and practitioners in optimization and machine learning.
The paper tackled the performance issues of max-value entropy search (MES) in Bayesian optimization by identifying misconceptions and developing a rectified version (RMES), which showed consistent improvements in synthetic and real-world benchmarks.
Although the existing max-value entropy search (MES) is based on the widely celebrated notion of mutual information, its empirical performance can suffer due to two misconceptions whose implications on the exploration-exploitation trade-off are investigated in this paper. These issues are essential in the development of future acquisition functions and the improvement of the existing ones as they encourage an accurate measure of the mutual information such as the rectified MES (RMES) acquisition function we develop in this work. Unlike the evaluation of MES, we derive a closed-form probability density for the observation conditioned on the max-value and employ stochastic gradient ascent with reparameterization to efficiently optimize RMES. As a result of a more principled acquisition function, RMES shows a consistent improvement over MES in several synthetic function benchmarks and real-world optimization problems.