To address the needs of modeling uncertainty in sensitive machine learning
applications, the setup of distributionally robust optimization (DRO) seeks
good performance uniformly across a variety of tasks. The recent
multi-distribution learning (MDL) framework tackles this objective in a dynamic
interaction with the environment, where the learner has sampling access to each
target distribution. Drawing inspiration from the field of pure-exploration
multi-armed bandits, we provide distribution-dependent guarantees in the MDL
regime, that scale with suboptimality gaps and result in superior dependence on
the sample size when compared to the existing distribution-independent
analyses. We investigate two non-adaptive strategies, uniform and non-uniform
exploration, and present non-asymptotic regret bounds using novel tools from
empirical process theory. Furthermore, we devise an adaptive optimistic
algorithm, LCB-DR, that showcases enhanced dependence on the gaps, mirroring
the contrast between uniform and optimistic allocation in the multi-armed
bandit literature.

为了应对敏感机器学习应用中的不确定性建模需求，分布鲁棒优化（DRO）的设置在各种任务中寻求统一的良好性能。最近的多分布学习（MDL）框架以与环境的动态互动的方式解决了这一目标，在该框架中，学习者可以对每个目标分布进行采样访问。借鉴了纯探索多臂赌博机领域的观点，我们在 MDL 体制下提供了依赖于分布的保证，并且在与现有的分布无关分析相比，这种保证随着次优性差距的缩小而产生了优秀的样本大小依赖性。我们研究了两种非自适应策略：均匀探索和非均匀探索，并使用经验过程理论中的新工具提供了非渐进性后悔上界。此外，我们设计了一种自适应乐观算法 LCB-DR，展示了对差距的增强依赖性，类似于多臂赌博机文献中均匀分配和乐观分配之间的对比。

多分布学习的分布相关速率

Distribution-Dependent Rates for Multi-Distribution Learning

We study active feature selection, a novel feature selection setting in which
unlabeled data is available, but the budget for labels is limited, and the
examples to label can be actively selected by the algorithm. We focus on
feature selection using the classical mutual information criterion, which
selects the $k$ features with the largest mutual information with the label. In
the active feature selection setting, the goal is to use significantly fewer
labels than the data set size and still find $k$ features whose mutual
information with the label based on the \emph{entire} data set is large. We
explain and experimentally study the choices that we make in the algorithm, and
show that they lead to a successful algorithm, compared to other more naive
approaches. Our design draws on insights which relate the problem of active
feature selection to the study of pure-exploration multi-armed bandits
settings. While we focus here on mutual information, our general methodology
can be adapted to other feature-quality measures as well. The code is available
at the following url: this https URL

本文针对标签信息有限的情况，提出了基于互信息和纯探索多臂老虎机的主动特征选择算法，并通过实验证明了其有效性。