AI Insight
This paper presents LAGO, a hybrid optimization framework that combines Bayesian Optimization with gradient-based trust region methods for optimizing smooth but expensive-to-evaluate functions. The algorithm uses a competitive mechanism where global and local optimization strategies independently propose candidate points at each iteration, with the next evaluation selected based on predicted improvement. LAGO incorporates a distance-based criterion to prevent numerical instability when adding points to the Gaussian process model during local exploitation phases.
Why it matters
This approach could improve optimization efficiency in engineering design, hyperparameter tuning, and scientific simulations where function evaluations are computationally expensive but gradient information is available. By intelligently balancing exploration and exploitation, LAGO may reduce the number of required evaluations to find optimal solutions.
arXiv:2603.02970v2 Announce Type: replace
Abstract: We introduce LAGO, a LocAl-Global Optimization framework coupling Bayesian Optimization (BO) and gradient-based trust region local refinement through an adaptive competition mechanism for smooth expensive-to-evaluate objective functions with available gradients. At each iteration, global and local optimization strategies independently propose candidate points, and the next evaluation is selected based on predicted improvement. LAGO separates global exploration from local refinement at the proposal level: the BO acquisition function is optimized outside the active trust region, while local candidates are proposed within the trust region. Points in the vicinity of the accepted local step are incorporated in the global GP dataset only when satisfying a lengthscale-based minimum-distance criterion, hence reducing the risk of numerical instability during local exploitation. LAGO enhances BO with efficient local refinement when reaching promising regions, and reverts to exploratory behavior when local steps are not competitive.
Source: LAGO: A Local-Global Optimization Framework Combining Trust Region Methods and Bayesian Optimization