Sequential experimental design under expensive, gradient-free objectives is a central challenge in computational statistics: evaluation budgets are tightly constrained and information must be extracted efficiently from each observation. We propose \textbf{ALMAB-DC}, a GP-based sequential design framework combining active learning, multi-armed bandits (MAB), and distributed asynchronous computing for expensive black-box experimentation. A Gaussian process surrogate with uncertainty-aware acquisition identifies informative query points; a UCB or Thompson-sampling bandit controller allocates evaluations across parallel workers; and an asynchronous scheduler handles heterogeneous runtimes. We present cumulative regret bounds for the bandit components and characterize parallel scalability via Amdahl's Law. We validate ALMAB-DC on five benchmarks. On the two statistical experimental-design tasks, ALMAB-DC achieves lower simple regret than Equal Spacing, Random, and D-optimal designs in dose--response optimization, and in adaptive spatial field estimation matches the Greedy Max-Variance benchmark while outperforming Latin Hypercube Sampling; at $K=4$ the distributed setting reaches target performance in one-quarter of sequential wall-clock rounds. On three ML/engineering tasks (CIFAR-10 HPO, CFD drag minimization, MuJoCo RL), ALMAB-DC achieves 93.4\% CIFAR-10 accuracy (outperforming BOHB by 1.7\,pp and Optuna by 1.1\,pp), reduces airfoil drag to $C_D = 0.059$ (36.9\% below Grid Search), and improves RL return by 50\% over Grid Search. All advantages over non-ALMAB baselines are statistically significant under Bonferroni-corrected Mann--Whitney $U$ tests. Distributed execution achieves $7.5\times$ speedup at $K = 16$ agents, consistent with Amdahl's Law.

翻译：在昂贵且无梯度代价函数下的序贯实验设计是计算统计学中的核心挑战：评估预算严格受限，且必须从每次观测中高效提取信息。本文提出\textbf{ALMAB-DC}——一种融合主动学习、多臂老虎机（MAB）与分布式异步计算的高斯过程（GP）序贯设计框架，适用于昂贵黑箱实验。该框架通过具有不确定性感知采集函数的高斯过程代理模型识别信息量最大的查询点；利用上置信界（UCB）或汤普森采样策略的虎机控制器在并行工作节点间分配评估任务；并采用异步调度器处理异构运行时。我们推导了虎机组件的累积遗憾界，并依据阿姆达尔定律刻画了并行可扩展性。在五个基准任务上验证了ALMAB-DC的性能：两项统计实验设计任务中，ALMAB-DC在剂量-响应优化中的简单遗憾低于等间距、随机与D最优设计；在自适应空间场估计中，其性能与贪婪最大方差基准相当且优于拉丁超立方采样；当$K=4$时，分布式设置达到目标性能所需的序贯墙钟时间仅为四分之一。三项机器学习/工程任务（CIFAR-10超参数优化、CFD阻力最小化、MuJoCo强化学习）中，ALMAB-DC在CIFAR-10上达到93.4%准确率（超BOHB 1.7个百分点与Optuna 1.1个百分点），将翼型阻力降至$C_D = 0.059$（比网格搜索低36.9%），并在强化学习回报上较网格搜索提升50%。基于Bonferroni校正的Mann-Whitney $U$检验表明，所有相对于非ALMAB基线的优势均具有统计显著性。分布式执行在$K=16$个代理时达到$7.5\times$加速比，符合阿姆达尔定律预测。