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arXiv · 2603.12507

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

Marcell T. Kurbucz
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Abstract

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.

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BibTeXRIS

Marcell T. Kurbucz. 2026-06-04. Adaptive Conditional Forest Sampling for Spectral Risk Optimisation under Decision-Dependent Uncertainty. https://arxiv.org/abs/2603.12507

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