# Adaptive Conditional Forest Sampling for Spectral Risk Optimisation under Decision-Dependent Uncertainty Source: [Adaptive Conditional Forest Sampling for Spectral Risk Optimisation under Decision-Dependent Uncertainty]() Collection index: [llms.txt]() Data updated: 2026-06-09T05:00:07.006Z Authors: Marcell T. Kurbucz Published: 2026-03-12T22:53:24.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Spectral Risk Optimisation on DGP2](): Spectral Risk Optimisation; DGP2; Median Difference: 35696. - [Spectral Risk Optimisation on DGP1 Student-t](): Spectral Risk Optimisation; DGP1 Student-t; Median Difference: 438. - [Spectral Risk Optimisation on DGP1 lambda=0.90](): Spectral Risk Optimisation; DGP1 lambda=0.90; J Median: 223405. - [Spectral Risk Optimisation on DGP2 lambda=0.50](): Spectral Risk Optimisation; DGP2 lambda=0.50; Median J: 268105. - [Spectral Risk Optimisation on DGP2 lambda=0.70](): Spectral Risk Optimisation; DGP2 lambda=0.70; J\_med: 349167. - [Spectral Risk Optimisation on DGP2 (lambda=0.90)](): Spectral Risk Optimisation; DGP2 (lambda=0.90); J\_med: 417761. - [Spectral Risk Optimisation on DGP1](): Spectral Risk Optimisation; DGP1; J\_med: 148344. - [Spectral Risk Optimisation on DGP1 lambda=0.50](): Spectral Risk Optimisation; DGP1 lambda=0.50; J Median: 148344. - [Spectral Risk Optimisation on DGP1 (lambda=0.70)](): Spectral Risk Optimisation; DGP1 (lambda=0.70); J Median: 183661. ## Original sources and implementation [Original paper]() [PDF]()