This paper introduces a framework for Bayesian Optimization (BO) with metric movement costs, addressing a critical challenge in practical applications where input alterations incur varying costs. Our approach is a convenient plug-in that seamlessly integrates with the existing literature on batched algorithms, where designs within batches are observed following the solution of a Traveling Salesman Problem. The proposed method provides a theoretical guarantee of convergence in terms of movement costs for BO. Empirically, our method effectively reduces average movement costs over time while maintaining comparable regret performance to conventional BO methods. This framework also shows promise for broader applications in various bandit settings with movement costs.

翻译：本文提出了一种考虑度量移动成本的贝叶斯优化框架，旨在解决实际应用中输入变更成本各异的关键挑战。我们的方法是一种便捷的插件式方案，能够无缝集成到现有批处理算法文献中，其中批内设计方案需在解决旅行商问题后观测。所提方法为贝叶斯优化在移动成本方面提供了理论收敛保证。实证研究表明，在保持与传统贝叶斯优化方法相当的遗憾性能的同时，我们的方法能有效降低随时间推移的平均移动成本。该框架在各类具有移动成本的强盗问题场景中也展现出广阔的应用前景。