标题： 数据压缩用于快速在线随机优化 显示英文标题

标题： Data Compression for Fast Online Stochastic Optimization

摘要： 我们提出了一种在线数据压缩方法，用于高效求解具有流数据的分布鲁棒优化（DRO）问题，同时保持样本外性能保证。 我们的方法利用在线聚类动态构建模糊集，允许聚类配置随时间演化，以准确表示潜在分布。 我们建立了聚类算法的理论条件以确保鲁棒性，并证明了在线解与名义DRO解之间的性能差距由真实分布和压缩分布之间的Wasserstein距离控制，该距离使用经验测度进行近似。 我们进行了遗憾分析，证明即使名义DRO事后访问不确定性实现，此性能差距的上界也以次线性速率收敛到一个固定聚类相关的距离。 混合整数投资组合优化的数值实验表明，计算节省显著，且解的质量损失极小。 显示英文摘要

摘要： We propose an online data compression approach for efficiently solving distributionally robust optimization (DRO) problems with streaming data while maintaining out-of-sample performance guarantees. Our method dynamically constructs ambiguity sets using online clustering, allowing the clustered configuration to evolve over time for an accurate representation of the underlying distribution. We establish theoretical conditions for clustering algorithms to ensure robustness, and show that the performance gap between our online solution and the nominal DRO solution is controlled by the Wasserstein distance between the true and compressed distributions, which is approximated using empirical measures. We provide a regret analysis, proving that the upper bound on this performance gap converges sublinearly to a fixed clustering-dependent distance, even when nominal DRO has access, in hindsight, to the subsequent realization of the uncertainty. Numerical experiments in mixed-integer portfolio optimization demonstrate significant computational savings, with minimal loss in solution quality.