Local Entropy Search over Descent Sequences for Bayesian Optimization

TL;DR

This paper introduces Local Entropy Search (LES), a Bayesian optimization method that models descent sequences to efficiently find optima in complex design spaces, outperforming existing methods.

Contribution

LES explicitly models descent sequences in Bayesian optimization, combining analytic and sampling methods to improve sample efficiency on complex problems.

Findings

LES outperforms existing Bayesian optimization methods in sample efficiency.

LES effectively models local descent sequences for complex objectives.

Empirical results demonstrate LES's robustness on synthetic and benchmark problems.

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.