无需估计光滑性参数，高效减少无效评估次数。
Every Call is Precious: Global Optimization of Black-Box Functions with Unknown Lipschitz Constants
- 不依赖未知的Lipschitz常数，动态聚焦潜在最优区域
- 有限预算下达到极小最大后悔值，无限预算无遗憾
- 适合高成本、非凸、黑箱优化场景，如实验设计
昂贵的非凸黑箱函数全局优化面临重大挑战，尤其当函数的Lipschitz常数未知时，通常需要大量函数评估才能逼近全局最优，这在时间和资源上代价高昂。本文提出全新算法Every Call is Precious（ECP），通过战略性聚焦潜在最优区域，最大限度减少无意义评估。与以往方法不同，ECP无需估计Lipschitz常数，避免了额外评估开销。该算法在无限评估预算下保证无遗憾性能，在有限预算下达到极小最大后悔值。大量消融实验证明其鲁棒性，实证表明在30个高维非凸合成及真实世界优化问题中，优于10种基准算法（包括基于Lipschitz、贝叶斯、强化学习与进化方法），展现出强大的全局优化能力。
原文摘要 · Abstract (English)
Optimizing expensive, non-convex, black-box Lipschitz continuous functions presents significant challenges, particularly when the Lipschitz constant of the underlying function is unknown. Such problems often demand numerous function evaluations to approximate the global optimum, which can be prohibitive in terms of time, energy, or resources. In this work, we introduce Every Call is Precious (ECP), a novel global optimization algorithm that minimizes unpromising evaluations by strategically focusing on potentially optimal regions. Unlike previous approaches, ECP eliminates the need to estimate the Lipschitz constant, thereby avoiding additional function evaluations. ECP guarantees no-regret performance for infinite evaluation budgets and achieves minimax-optimal regret bounds within finite budgets. Extensive ablation studies validate the algorithm's robustness, while empirical evaluations show that ECP outperforms 10 benchmark algorithms including Lipschitz, Bayesian, bandits, and evolutionary methods across 30 multi-dimensional non-convex synthetic and real-world optimization problems, which positions ECP as a competitive approach for global optimization.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。