arXiv:2603.12507cs.LGmath.OC2026-03

针对决策依赖不确定性的风险优化,提出自适应采样框架提升稳定性与准确性。

Adaptive Conditional Forest Sampling for Spectral Risk Optimisation under Decision-Dependent Uncertainty

  • 分四阶段整合随机森林、引导探索与加权增强,动态优化风险估计
  • 在两种分布设置下均优于基准方法,尤其在高惩罚权重时显著降低波动
  • 适合需要稳定可靠风险优化的金融、供应链等实际决策场景

当不确定性分布受决策影响时,最小化谱风险目标(期望成本与条件风险价值的加权组合)极具挑战,因代理建模和基于模拟的排序对尾部估计误差敏感。本文提出自适应条件森林采样(ACFS),一种四阶段仿真-优化框架:利用广义随机森林逼近决策相关分布,采用CEM引导全局探索,通过排名加权聚焦增强,再经代理到真实两阶段重排序,最后进行多起点梯度优化。在两种结构不同的数据生成过程上评估:具有决策依赖学生分布边缘的高斯混合模型,以及具有对数正态边缘的高斯混合模型;涵盖三种惩罚权重配置,每种配置重复100次,并在所有方法可用的真实分布采样次数上限相同条件下比较。在第二个基准测试中,ACFS在所有配置下均达到最低中位真实谱风险,相比GP-BO的中位差距为8.6%至21.8%。在第一个基准测试中,ACFS与GP-BO中位目标无统计差异,但在高惩罚权重下,跨重复实验的离散度比GP-BO降低约1.9至2.5倍,低权重下接近一致;在第二个基准测试中整体降低1.7至2.3倍,表明运行间可靠性显著提升。同时,ACFS在几乎所有设置下优于CEM-SO、SGD-CVaR和KDE-SO。消融与敏感性分析支持设计稳健性,且各组件贡献在偏斜的对数正态基准上最为明显。

原文摘要 · Abstract (English)

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.

风险优化决策依赖随机森林仿真优化

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