Minimising a spectral risk objective, defined as a weighted 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 Gaussian copula with decision-dependent Student-t marginals and a Gaussian copula with log-normal marginals, across three penalty-weight configurations and 100 replications per setting, under a common cap on the number of true-distribution oracle draws available to each method. ACFS achieves the lowest median oracle spectral risk on the second benchmark in every configuration, with median gaps over GP-BO ranging from 8.6% to 21.8%. On the first benchmark, ACFS and GP-BO are statistically indistinguishable in median objective, but ACFS reduces cross-replication dispersion relative to GP-BO by approximately 1.9 to 2.5 times at the higher penalty weights, with near-parity at the lowest, and by 1.7 to 2.3 times throughout on the second benchmark, 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 robustness of the design and indicate that component contributions are most pronounced on the skewed log-normal benchmark.
翻译:最小化谱风险目标(定义为期望成本与条件风险价值(CVaR)的加权组合)在不确定性分布依赖于决策时极具挑战性,这使得代理建模和基于仿真的排序都对尾部估计误差敏感。我们提出自适应条件森林采样(ACFS),这是一种四阶段仿真优化框架,集成了用于决策条件分布逼近的广义随机森林、CEM引导的全局探索、排序加权聚焦增强、代理到真实模型的两阶段重排序,以及多起点梯度优化。我们在两种结构不同的数据生成过程中评估ACFS:具有决策依赖学生t边缘分布的高斯Copula和具有对数正态边缘分布的高斯Copula,在三种惩罚权重配置和每种设置100次重复下进行,各方法可用的真实分布模型抽取次数受统一上限约束。在第二个基准测试的所有配置中,ACFS均实现了最低的中位真实模型谱风险,与GP-BO相比,中位差距范围为8.6%至21.8%。在第一个基准测试中,ACFS与GP-BO在中位目标值上统计上无显著差异,但在较高惩罚权重下,ACFS将跨重复变异度相对于GP-BO降低了约1.9至2.5倍(最低惩罚权重时接近持平),在第二个基准测试中全程降低1.7至2.3倍,表明运行间可靠性显著提升。ACFS在几乎所有设置中还优于CEM-SO、SGD-CVaR和KDE-SO,而消融与敏感性分析支持了设计的稳健性,并表明各组件贡献在偏态对数正态基准测试中最为显著。