LAGO: A Local-Global Optimization Framework Combining Trust Region Methods and Bayesian Optimization

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.