Minimising a spectral risk objective, defined as a convex combination of expected cost and Conditional Value-at-Risk (CVaR), is challenging when the uncertainty distribution is decision-dependent, making both surrogate modelling and simulation-based ranking sensitive to tail estimation error. We propose Adaptive Conditional Forest Sampling (ACFS), a four-phase simulation-optimisation framework that integrates Generalised Random Forests for decision-conditional distribution approximation, CEM-guided global exploration, rank-weighted focused augmentation, and surrogate-to-oracle two-stage reranking before multi-start gradient-based refinement. We evaluate ACFS on two structurally distinct data-generating processes: a decision-dependent Student-t copula and a Gaussian copula with log-normal marginals, across three penalty-weight configurations and 100 replications per setting. ACFS achieves the lowest median oracle spectral risk on the second benchmark in every configuration, with median gaps over GP-BO ranging from 6.0% to 20.0%. On the first benchmark, ACFS and GP-BO are statistically indistinguishable in median objective, but ACFS reduces cross-replication dispersion by approximately 1.8 to 1.9 times on the first benchmark and 1.7 to 2.0 times on the second, indicating materially improved run-to-run reliability. ACFS also outperforms CEM-SO, SGD-CVaR, and KDE-SO in nearly all settings, while ablation and sensitivity analyses support the contribution and robustness of the proposed design.
翻译:针对谱风险目标(定义为期望成本与条件风险价值CVaR的凸组合)的最小化问题,当不确定性分布具有决策依赖性时,代理建模与基于仿真的排序均易受尾部估计误差影响。本文提出自适应条件森林采样(Adaptive Conditional Forest Sampling,ACFS),一种四阶段仿真优化框架,融合广义随机森林实现决策条件分布逼近、CEM引导的全局探索、排序加权聚焦增强以及代理模型到真实模型的二阶段重排序,最后执行多起点梯度求精。我们在两种结构截然不同的数据生成过程上评估ACFS:决策依赖的Student-t copula和高斯copula(含对数正态边缘分布),涵盖三种罚权重配置,每配置进行100次重复实验。在第二个基准测试的所有配置中,ACFS实现最低中位真实谱风险,相较于GP-BO的中位差距为6.0%至20.0%。在第一个基准测试中,ACFS与GP-BO的中位目标值在统计上无显著差异,但ACFS将跨重复实验的离散程度降低约1.8至1.9倍(第一个基准测试)和1.7至2.0倍(第二个基准测试),表明运行间可靠性显著提升。此外,在几乎所有设置中ACFS均优于CEM-SO、SGD-CVaR和KDE-SO,消融实验与敏感性分析进一步证实所提设计的贡献与鲁棒性。