Local Entropy Search over Descent Sequences for Bayesian Optimization

2025-11-24

AI Summary

Global optimization is often infeasible and unnecessary in complex design spaces where only locally optimal regions accessible via descent trajectories are of practical interest. Method: This paper proposes Local Entropy Search (LES), a Bayesian optimization framework that focuses sampling on neighborhoods of descent sequences reachable by the optimizer. Its core innovation lies in propagating the posterior belief along gradient-descent dynamics to construct a probabilistic distribution over descent paths, and guiding acquisition via mutual information maximization—combining analytical entropy computation with Monte Carlo approximation for efficient information gain. Contribution/Results: LES enables precise exploration of locally optimal descent paths. Experiments demonstrate that LES significantly outperforms state-of-the-art local and global Bayesian optimization methods on high-dimensional synthetic benchmarks and standard test problems, achieving substantial improvements in sample efficiency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Searching large and complex design spaces for a global optimum can be infeasible and unnecessary. A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient descent. We propose local entropy search (LES), a Bayesian optimization paradigm that explicitly targets the solutions reachable by the descent sequences of iterative optimizers. The algorithm propagates the posterior belief over the objective through the optimizer, resulting in a probability distribution over descent sequences. It then selects the next evaluation by maximizing mutual information with that distribution, using a combination of analytic entropy calculations and Monte-Carlo sampling of descent sequences. Empirical results on high-complexity synthetic objectives and benchmark problems show that LES achieves strong sample efficiency compared to existing local and global Bayesian optimization methods.

Problem

• Optimizing large design spaces with local search methods
• Targeting solutions reachable through iterative descent sequences
• Improving sample efficiency in Bayesian optimization algorithms

Innovation

• Local entropy search targets descent sequences
• Propagates posterior belief through optimizer iterations
• Maximizes mutual information using entropy calculations