The bandits with knapsack (BwK) framework models online decision-making
problems in which an agent makes a sequence of decisions subject to resource
consumption constraints. The traditional model assumes that each action
consumes a non-negative amount of resources and the process ends when the
initial budgets are fully depleted. We study a natural generalization of the
BwK framework which allows non-monotonic resource utilization, i.e., resources
can be replenished by a positive amount. We propose a best-of-both-worlds
primal-dual template that can handle any online learning problem with
replenishment for which a suitable primal regret minimizer exists. In
particular, we provide the first positive results for the case of adversarial
inputs by showing that our framework guarantees a constant competitive ratio
$\alpha$ when $B=\Omega(T)$ or when the possible per-round replenishment is a
positive constant. Moreover, under a stochastic input model, our algorithm
yields an instance-independent $\tilde{O}(T^{1/2})$ regret bound which
complements existing instance-dependent bounds for the same setting. Finally,
we provide applications of our framework to some economic problems of practical
relevance.

该研究提出了一种 BwK 框架的一般化模型，允许非单调资源利用，并提出了一个灵活的双重模板以处理任何具有再生性问题的在线学习问题，包括对抗和随机输入，同时可用于解决一些实际相关的经济问题。

带补给背包的强盗问题：两全其美

Bandits with Replenishable Knapsacks: the Best of both Worlds

In this work, we investigate the application of deep learning methods for
computed tomography in the context of having a low-data regime. As motivation,
we review some of the existing approaches and obtain quantitative results after
training them with different amounts of data. We find that the learned
primal-dual has an outstanding performance in terms of reconstruction quality
and data efficiency. However, in general, end-to-end learned methods have two
issues: a) lack of classical guarantees in inverse problems and b) lack of
generalization when not trained with enough data. To overcome these issues, we
bring in the deep image prior approach in combination with classical
regularization. The proposed methods improve the state-of-the-art results in
the low data-regime.

本文探究了深度学习方法在低数据条件下应用于计算机断层扫描的可能性，并提出了一种深度图像先验方法与经典规则相结合的方法，提高了低数据条件下的重建质量和数据效率。