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.

翻译：优化昂贵、非凸、Lipschitz连续的黑箱函数存在显著挑战，尤其是在底层函数的Lipschitz常数未知的情况下。此类问题通常需要大量函数评估来逼近全局最优解，这在时间、能量或资源方面往往代价高昂。本文提出"每一次调用都弥足珍贵"（ECP）算法，这是一种通过策略性地聚焦于潜在最优区域来最小化非必要评估的新型全局优化方法。与现有方法不同，ECP无需估计Lipschitz常数，从而避免了额外的函数评估。ECP在无限评估预算下保证无遗憾性能，并在有限预算内达到极小极大最优遗憾界。大量消融实验验证了算法的鲁棒性，实证评估表明ECP在30个多维非凸合成及现实优化问题上优于包括Lipschitz方法、贝叶斯方法、多臂赌博机方法和进化算法在内的10种基准算法，这使ECP成为全局优化领域具有竞争力的新方法。