arXiv:2604.27447math.OCcs.AI2026-04

针对生成模型采样不稳问题,提出鲁棒优化方法提升决策可靠性。

Sampler-Robust Optimization under Generative Models

论文配图:Sampler-Robust Optimization under Generative Models
图 1 · 摘自论文原文
  • 通过扰动生成器构造最差采样器,优化决策对采样偏差的鲁棒性
  • 实验证明在分布漂移下,新方法显著提升组合投资的外样本表现
  • 适用于生成模型无显式密度的场景,支持高效极小极大求解

现代随机优化流程越来越多依赖学习得到的生成模型来表示不确定性,而下游决策几乎完全通过蒙特卡洛情景评估。这使得不确定性的操作对象从明确的概率律转变为由学习生成器所诱导的采样器。可靠性因此取决于两类误差:采样器误设和有限模拟误差。我们提出采样器鲁棒优化(SRO),即在扰动学习生成器所诱导的最差采样器上优化决策。该采样器优先的框架与基于模拟的决策流程一致,并具有敏锐度感知解释:它偏好在生成器扰动下性能稳定的决策,而非仅在名义采样器下表现良好。在覆盖假设下,我们证明经验最差目标提供了真实总体目标的高概率上界,有限模拟误差部分被用于防范采样器误设的鲁棒化过程吸收。该框架可适配具有或无显式密度的生成模型,并支持高效的极小极大求解过程。组合优化实验表明,SRO 产生的决策更稳定,并在分布漂移下改善了外样本性能。

原文摘要 · Abstract (English)

Modern stochastic optimization pipelines increasingly rely on learned generative models to represent uncertainty, while downstream decisions are evaluated almost entirely through Monte Carlo scenarios. This shifts the operational object of uncertainty from an explicit probability law to the sampler induced by the learned generator. Reliability therefore depends on two errors: sampler misspecification and finite-simulation error. We propose Sampler-Robust Optimization (SRO), which optimizes decisions against the worst-case sampler induced by perturbing the learned generator. This sampler-first formulation aligns with simulation-based decision pipelines and admits a sharpness-aware interpretation: it favors decisions whose performance is stable under generator perturbations, rather than merely under the nominal sampler. Under a coverage assumption, we show that the empirical worst-case objective provides a high-probability upper certificate for the true population objective, with finite-simulation error partially absorbed by the robustification used to guard against sampler misspecification. The framework accommodates generative models with or without explicit densities and admits efficient minimax procedures. Portfolio-optimization experiments show that SRO produces more stable decisions and improves out-of-sample performance under distribution shift.

优化生成模型鲁棒性蒙特卡洛

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