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

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.

Machine Learning (cs.LG); Optimization and Control (math.OC); Computation (stat.CO); Machine Learning (stat.ML)

G.1.6; G.3; I.2.6

arXiv:2603.12507 [cs.LG]

(or arXiv:2603.12507v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2603.12507 Focus to learn more arXiv-issued DOI via DataCite

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