Cost-Aware Stopping for Freeze-Thaw 贝叶斯优化：一步前瞻何时足够
Cost-Aware Stopping for Freeze-Thaw Bayesian Optimization: When Does One-Step Lookahead Suffice?
做超参搜索老是被预算卡住的可以看看：这篇论文给出一个基于期望改进的停止规则，还教你用两步前瞻证书判断是不是停早了。
论文研究 freeze-thaw 贝叶斯优化中的停止准则，提出以最优观测分数减去每步成本为目标的无预算效用函数。EI stopping 规则在固定代理模型下推进期望改进（EI）最大的候选，当没有 EI 超过成本时停止。论文构造了一个基于两步前瞻价值下界的证书，用于证明某次停止为过早停止，且重复该修正不会降低代理模型下的期望效用。在三个超参数优化基准上，预注册测试发现高成本场景下 EI stopping 与修正法基本不劣，低成本场景下修正法在其中两个基准上占优。
Cost-Aware Stopping for Freeze-Thaw Bayesian Optimization: When Does One-Step Lookahead Suffice?
Freeze-thaw Bayesian optimization (BO) evaluates candidates in resumable increments but usually stops at a budget or convergence test. We maximize a budget-free utility, the best observed score minus a cost per increment, with a one-step lookahead: advance the candidate with the largest expected improvement (EI) under a fixed surrogate, and stop once no EI exceeds the cost. This rule, EI stopping, never falls below stopping immediately in expected utility, yet it can stop too early. We construct a certificate, a lower bound on the value of two-step lookahead, that proves such a stop premature, and repeating this correction never lowers expected utility under the surrogate. Under the surrogate, EI stops are premature on average at low costs and lose little at high costs. On three hyperparameter optimization benchmarks, a pre-registered test finds EI stopping noninferior to the correction in most high-cost settings, while the correction gains at low costs on two of the three; more information sharing in the surrogate raises EI stopping's utility. On the surrogates of two published methods, EI stopping trades lower scores for fewer training increments. EI stopping is a simple cost-aware reference whose utility depends on the surrogate.