🤖 AI Summary
This work addresses the challenge that Gaussian process-based Bayesian optimization often converges to local optima and exhibits poor global search efficiency when applied to multimodal or high-dimensional black-box functions. To overcome this limitation, the authors propose a trajectory-aware trust-region Bayesian optimization method that models performance prediction across multiple local optimization trajectories as a best-arm identification (BAI) problem. By framing region selection within a multi-armed bandit framework, the algorithm dynamically eliminates suboptimal regions and concentrates exploration on promising areas. The proposed approach offers theoretical guarantees of faster convergence compared to conventional Bayesian optimization and demonstrates significantly improved global optimization performance on both synthetic and real-world benchmark tasks.
📝 Abstract
Gaussian process-based Bayesian optimization (BO) is a popular approach for expensive black-box optimization, but its performance often degrades on complex multimodal or high-dimensional problems. Trust region-based BO mitigates this issue by focusing on local regions, and recent studies suggest that selecting an effective region can be formulated as a multi-armed bandit problem. We propose a trajectory-aware framework that integrates best-arm identification (BAI) with trust region-based BO to efficiently solve multimodal optimization problems. Our method extrapolates the optimization trajectories of multiple locally initialized optimizers to predict their final performance and progressively eliminates suboptimal candidates via BAI. We theoretically show that the proposed BAI-guided BO converges faster to the global optimum than conventional BO under mild assumptions, and demonstrate its effectiveness through extensive experiments on synthetic and real-world benchmarks.