In this paper, we consider the alignment between an upstream dimensionality
reduction task of learning a low-dimensional representation of a set of
high-dimensional data and a downstream optimization task of solving a
stochastic program parameterized by said representation. In this case, standard
dimensionality reduction methods (e.g., principal component analysis) may not
perform well, as they aim to maximize the amount of information retained in the
representation and do not generally reflect the importance of such information
in the downstream optimization problem. To address this problem, we develop a
prescriptive dimensionality reduction framework that aims to minimize the
degree of suboptimality in the optimization phase. For the case where the
downstream stochastic optimization problem has an expected value objective, we
show that prescriptive dimensionality reduction can be performed via solving a
distributionally-robust optimization problem, which admits a semidefinite
programming relaxation. Computational experiments based on a warehouse
transshipment problem and a vehicle repositioning problem show that our
approach significantly outperforms principal component analysis with real and
synthetic data sets.

本文讨论了将高维数据的低维表示学习任务与用该表示解决随机规划的优化任务进行对齐，提出了通过解决分布鲁棒优化问题实现预制降维的框架。实验表明，该方法在仓库中转问题和车辆重定位问题上明显优于传统的主成分分析方法。

预定主成分分析：两阶段随机优化的降维

Prescriptive PCA: Dimensionality Reduction for Two-stage Stochastic  Optimization

The Stackelberg game model, where a leader commits to a strategy and the
follower best responds, has found widespread application, particularly to
security problems. In the security setting, the goal is for the leader to
compute an optimal strategy to commit to, in order to protect some asset. In
many of these applications, the parameters of the follower utility model are
not known with certainty. Distributionally-robust optimization addresses this
issue by allowing a distribution over possible model parameters, where this
distribution comes from a set of possible distributions. The goal is to
maximize the expected utility with respect to the worst-case distribution. We
initiate the study of distributionally-robust models for computing the optimal
strategy to commit to. We consider the case of normal-form games with
uncertainty about the follower utility model. Our main theoretical result is to
show that a distributionally-robust Stackelberg equilibrium always exists
across a wide array of uncertainty models. For the case of a finite set of
possible follower utility functions we present two algorithms to compute a
distributionally-robust strong Stackelberg equilibrium (DRSSE) using
mathematical programs. Next, in the general case where there is an infinite
number of possible follower utility functions and the uncertainty is
represented by a Wasserstein ball around a finitely-supported nominal
distribution, we give an incremental mixed-integer-programming-based algorithm
for computing the optimal distributionally-robust strategy. Experiments
substantiate the tractability of our algorithm on a classical Stackelberg game,
showing that our approach scales to medium-sized games.

本文研究了基于分布鲁棒优化的 Stackelberg 游戏模型，特别是在不确定下属效用模型的情况下，寻找最优策略以保护某些资产。我们的研究表明，在广泛的不确定模型下，分布鲁棒 Stackelberg 均衡始终存在。当存在无限个下属效用函数且不确定性由支持有限名义分布周围的 Wasserstein 球表示时，我们提出了一种基于混合整数规划的增量算法来计算最优的分布鲁棒策略。实验结果显示，我们的方法可扩展到中等规模的 Stackelberg 游戏，从而验证了算法的可行性。

计算最优分布式鲁棒策略

Computing the optimal distributionally-robust strategy to commit to

In recent years, deep neural network (DNN) compression systems have proved to
be highly effective for designing source codes for many natural sources.
However, like many other machine learning systems, these compressors suffer
from vulnerabilities to distribution shifts as well as out-of-distribution
(OOD) data, which reduces their real-world applications. In this paper, we
initiate the study of OOD robust compression. Considering robustness to two
types of ambiguity sets (Wasserstein balls and group shifts), we propose
algorithmic and architectural frameworks built on two principled methods: one
that trains DNN compressors using distributionally-robust optimization (DRO),
and the other which uses a structured latent code. Our results demonstrate that
both methods enforce robustness compared to a standard DNN compressor, and that
using a structured code can be superior to the DRO compressor. We observe
tradeoffs between robustness and distortion and corroborate these findings
theoretically for a specific class of sources.

本文介绍了两种增强深度神经网络压缩系统鲁棒性的方法，采用分布鲁棒优化和结构化潜在代码进行训练，取得较传统深度神经网络压缩器更优的效果。