Variational Entropy Search for Adjusting Expected Improvement

2024-02-17

arXiv.org

AI Summary

Expected Improvement (EI), a widely used acquisition function in Bayesian optimization, suffers from a lack of information-theoretic interpretation and difficulty in adaptive calibration. Method: This work establishes, for the first time, a unified variational inference framework linking EI and Max-value Entropy Search (MES), proving that EI is a special case of MES under a specific variational assumption. Building on this insight, we propose the Variational Entropy Search (VES) paradigm and instantiate it as VES-Gamma, which approximates the optimal value’s posterior distribution using a Gamma distribution to achieve principled enhancement and automatic calibration of EI. Results: On standard benchmark functions and real-world black-box optimization tasks, VES-Gamma significantly improves sampling efficiency and convergence stability, demonstrating both theoretical consistency with entropy-based principles and practical superiority over existing methods.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Adjusts Expected Improvement using Variational Entropy Search
• Links EI to Max-Value Entropy Search via Variational Inference
• Demonstrates VES-Gamma's effectiveness in Bayesian optimization

Innovation

• Variational Entropy Search methodology developed
• VES-Gamma algorithm adapts Expected Improvement
• Incorporates information-theoretic concepts via VI