Stochastic programming models can lead to very large-scale optimization
problems for which it may be impossible to enumerate all possible scenarios. In
such cases, one adopts a sampling-based solution methodology in which case the
reliability of the resulting decisions may be suspect. For such instances, it
is advisable to adopt methodologies that promote variance reduction. One such
approach goes under a framework known as "compromise decision", which requires
multiple replications of the solution procedure. This paper studies the
reliability of stochastic programming solutions resulting from the "compromise
decision" process. This process is characterized by minimizing an aggregation
of objective function approximations across replications, presumably conducted
in parallel. We refer to the post-parallel-processing problem as the problem of
"compromise decision". We quantify the reliability of compromise decisions by
estimating the expectation and variance of the "pessimistic distance" of
sampled instances from the set of true optimal decisions. Such pessimistic
distance is defined as an estimate of the largest possible distance of the
solution of the sampled instance from the "true" optimal solution set. The
Rademacher average of instances is used to bound the sample complexity of the
compromise decision.

本文研究了基于 “妥协决策” 过程的随机规划解决方案的可靠性，采用最小化多次复制解决方案的目标函数近似的方法，并利用 Rademacher 平均值限制了 “妥协决策” 的抽样复杂性。

大规模随机程序的妥协决策可靠性理论

A Reliability Theory of Compromise Decisions for Large-Scale Stochastic  Programs

The goal of the paper is to design active learning strategies which lead to
domain adaptation under an assumption of Lipschitz functions. Building on
previous work by Mansour et al. (2009) we adapt the concept of discrepancy
distance between source and target distributions to restrict the maximization
over the hypothesis class to a localized class of functions which are
performing accurate labeling on the source domain. We derive generalization
error bounds for such active learning strategies in terms of Rademacher average
and localized discrepancy for general loss functions which satisfy a regularity
condition. A practical K-medoids algorithm that can address the case of large
data set is inferred from the theoretical bounds. Our numerical experiments
show that the proposed algorithm is competitive against other state-of-the-art
active learning techniques in the context of domain adaptation, in particular
on large data sets of around one hundred thousand images.

论文旨在设计主动学习策略，实现基于 Lipschitz 函数假设的领域自适应。通过对 Mansour 等人（2009）的先前工作进行补充，我们将源和目标分布之间的差异距离概念适应于假设类的最大化，来局限于在源域上执行准确标记的函数类。我们针对满足正则条件的一般损失函数导出了这种主动学习策略的推广误差边界，用于兰德马赫平均值和局部差异度量。从理论边界中推导出实用的 K-medoids 算法，可以处理大数据集的情况。我们的数值实验表明，在领域自适应的情况下，特别是在约十万个图像的大数据集上，所提出的算法与其他最先进的主动学习技术具有竞争力。

基于差异性的域自适应主动学习

Discrepancy-Based Active Learning for Domain Adaptation

Recently, metric learning and similarity learning have attracted a large
amount of interest. Many models and optimisation algorithms have been proposed.
However, there is relatively little work on the generalization analysis of such
methods. In this paper, we derive novel generalization bounds of metric and
similarity learning. In particular, we first show that the generalization
analysis reduces to the estimation of the Rademacher average over
"sums-of-i.i.d." sample-blocks related to the specific matrix norm. Then, we
derive generalization bounds for metric/similarity learning with different
matrix-norm regularisers by estimating their specific Rademacher complexities.
Our analysis indicates that sparse metric/similarity learning with $L^1$-norm
regularisation could lead to significantly better bounds than those with
Frobenius-norm regularisation. Our novel generalization analysis develops and
refines the techniques of U-statistics and Rademacher complexity analysis.

本文利用 U 统计和 Rademacher 复杂性分析方法，针对度量学习和相似度学习，推导出了一种新的泛化边界方法，证明了 L1 范数正则化的稀疏度量学习和相似度学习可能比 Frobenius 范数正则化的模型具有更好的边界效果。