Max-value Entropy Search for Efficient Bayesian Optimization
This work addresses a computational bottleneck in Bayesian Optimization for researchers and practitioners, offering a more efficient method while maintaining performance, though it is incremental as it builds on existing ES/PES techniques.
The paper tackles the computational inefficiency of Entropy Search (ES) and Predictive Entropy Search (PES) in Bayesian Optimization by proposing Max-value Entropy Search (MES), which uses information about the maximum function value instead of the argmax, resulting in maintained or improved empirical performance with significantly reduced computational burden, especially for higher-dimensional problems.
Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the $\arg\max$ of the unknown function; yet, both are plagued by the expensive computation for estimating entropies. We propose a new criterion, Max-value Entropy Search (MES), that instead uses the information about the maximum function value. We show relations of MES to other Bayesian optimization methods, and establish a regret bound. We observe that MES maintains or improves the good empirical performance of ES/PES, while tremendously lightening the computational burden. In particular, MES is much more robust to the number of samples used for computing the entropy, and hence more efficient for higher dimensional problems.