Variational Entropy Search for Adjusting Expected Improvement
This work provides a theoretical connection and incremental improvement for researchers and practitioners in Bayesian optimization, enhancing acquisition functions.
The paper tackles the problem of optimizing black-box functions in Bayesian optimization by showing that Expected Improvement (EI) is a special case of max-value entropy search (MES) through variational inference, and develops the VES-Gamma algorithm to adapt EI with information-theoretic principles, demonstrating its efficacy on test functions and real datasets.
Bayesian optimization is a widely used technique for optimizing black-box functions, with Expected Improvement (EI) being the most commonly utilized acquisition function in this domain. While EI is often viewed as distinct from other information-theoretic acquisition functions, such as entropy search (ES) and max-value entropy search (MES), our work reveals that EI can be considered a special case of MES when approached through variational inference (VI). In this context, we have developed the Variational Entropy Search (VES) methodology and the VES-Gamma algorithm, which adapts EI by incorporating principles from information-theoretic concepts. The efficacy of VES-Gamma is demonstrated across a variety of test functions and read datasets, highlighting its theoretical and practical utilities in Bayesian optimization scenarios.